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Optical Spectroscopy of Single Impurity Molecules in Solids.

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Volume 32
-
Number 4
April 1993
Pages 457-628
International Edition in English
Optical Spectroscopy of Single Impurity Molecules in Solids
By W. E. Moerner" and Thomas Baschk*
Optical spectroscopy of a single impurity molecule provides the first truly local probe of
host-guest interactions in doped solids. In conventional optical high-resolution experiments
with many molecules only ensemble averages of the microscopic parameters can be obtained.
In the single-molecule regime, the exquisite sensitivity of an individual dopant molecule to
both the local environment and to external perturbations has been exploited in recent experiments to reveal a wealth of fascinating novel phenomena such as spectral diffusion in crystals
and polymers, optical modification of a single impurity molecule (spectral hole-burning), local
field measurements at the site of a single impurity molecule, and quantum optics in a solid.
1. Introduction[**'
Significant progress in the optical spectroscopy of single
quantum systems confined in traps or on surfaces has occurred in the last decade. For example, imaging and spectroscopy of single ions confined in electromagnetic traps has
led to novel measurements that test the foundations of quantum physics. In particular, various workers have reported
direct measurement of quantum jumps, Doppler sidebands,
photon antibunching, extremely narrow optical linewidths,
and other fundamental phenomena such as ion crystallization and chaos.['-31 The original work on trapped single
electrons and on the Paul trap led to the Nobel Prize in
physics for Dehmelt, Paul, and Ramsey in 1989.[41
At the other extreme, recent advances in various near-field
spectroscopies such as scanning tunneling microscopy
~
[*I
[**I
Dr. W. E. Moerner
IBM Research Division, Almaden Research Center
San Jose. CA 95120-6099 (USA)
Dr. T. Basche
lnstitut fur Physikalische Chemie der Universitdt
Sophienstrasse 11, D-W-8000 Munchen 2 (FRG)
Important terms and abbreviations are listed in a glossary (Section 10) at
the end of the review.
Angrw. C'lrem. l n t . Ed. Engl. 1993, 32. 451 -416
8
(STM)''. 7bl have provided detailed images of single atoms,
and
of single molecules of benzene and CO on Rh
of liquid crystal molecules on graphite"] to name only a few
examples. The invention of STM earned Binnig and
Rohrer''' the Nobel Prize in physics in 1986, and many
workers around the world are applying this technique to a
large variety of systems. Moreover, the STM work has inspired a broad array of sensitive surface measurements based
on the atomic force microscope.[7b9s1
A requirement of STM
is the need for a strong bond between the molecule of interest
and the underlying surface so that the molecule can remain
in a fixed configuration long enough for the tunneling spectrum to be obtained.
By contrast, the relatively new field of single-center optical
spectroscopy in condensed matter is only now beginning to
provide novel chemical and physical insights. For single molecules in liquids, the emphasis has been on the detection of
single molecules labeled with fluorophores for analytical applications without recording detailed spectra. In the early
work, use of laser-induced fluorescence and a hydrodynamically focused flow to reduce the scattering volume allowed
the detection of single molecules of the protein B-phycoerythrin, whose fluorophore is equivalent to 25 rhodamine 6G
molecules.[9*l o ] Recent enhancements of the method have
VCH Verlugsgesellsrhuft mhH, W-6940 Weinhrim,1993
OS?0-0833/93/0404-0457$ 10.OOf .2SK
451
allowed the detection of single molecules of rhodamine 6G in
a flowing liquid.[”%12] One distinct advantage here is that
the experiments are usually conducted at room temperature;
however, the fluorescent molecule and the solution must be
chosen carefully to maximize photostability. In the first
work to go beyond digital (present/not present) detection of
a molecule, two fluorescent species were distinguished by the
difference in fluorescence lifetime.“ 31
This review concerns single-center spectroscopy when the
center of interest is a molecular or ionic dopant (defect)
hidden deep inside a solid. The detection and spectroscopy of
a single absorber in a solid (in the case of a molecular impurity called single-molecule detection, SMD) provides a natural complement to the earlier hole-burning and coherent
transient spectroscopy of impurities in solids.[’4- ”I Singlecenter spectroscopy in solids provides a useful tool for the
study of local host-guest interactions where the absorbing
center is essentially at rest, confined by the host lattice, and
where the normal averaging over many “equivalent” centers
is removed. Although this paper focuses on molecular impurity centers, the physical concepts apply equally well to ions,
color centers, and other defect absorptions in solids.
As an important first step toward single-molecule detection (SMD), it was necessary to make a very detailed examination of the inhomogeneously broadened optical absorption line of a defect in a solid with large numbers of
absorbers (the usual regime). In this limit, a fundamental
effect called statistical fine structure (SFS) was observed for
the first time.[’8’ 1 9 ] SFS results from (static) fluctuations in
the spectral density of absorbers with optical wavelength,
and therefore scales as the square root of the number of
absorbers in resonance. The observations of SFS and other
steps toward S M D will be described in Section 2. Crucial to
these measurements was the use of a powerful zero-background laser technique called frequency modulation (FM)
spectroscopy, first described by Bjorklund[’O1 in 1980.
With a firm understanding of SFS in inhomogeneous
lines, it became possible to approach the ultimate limit of
single-molecule detection (SMD) and spectroscopy. One
motivation for the development of S M D comes from the fact
that for an inhomogeneously broadened line, the centers
located within a homogeneous width of a given laser frequency are located at that particular spectral position for a
variety of possible reasons. This intrinsic multidimensional
inhomogeneity cannot be removed with spectral hole-burning o r coherent transient techniques. However, with S M D
the absorption spectrum of a unique individual absorber in
its particular environment can become directly accessible, as
long as no other centers absorb at the same frequency. This
is the primary reason for pursuing the spectroscopy of individual centers in condensed matter. The use of powerful
spectroscopic methods (FM spectroscopy) and the properties of the inhomogeneous line itself make S M D feasible; the
first successful S M D experiments[21 241 will be described in
Section 3.
The advent of a superior technique, fluorescence excitation with extremely high collection efficiency,[251allowed
greatly increased signal-to-noise ratio (SNR) for singlemolecule spectra. Examples of precise measurements of the
optical linewidth[261 and other phenomena which then became observable will be presented in Section 4. In studies of
pentacene molecular defects in crystalline para-terphenyl, a
novel physical effect called spectral diffusion was ob~ e r v e d , [ ~ ’which
, ~ ~ ] will be summarized in Section 5. Section 6 describes how extensions of SMD to polymeric
hosts[29,301 allow direct observations of hole-burning and
stochastic kinetics for an individual center. Section 7 presents results of very recent single-molecule spectroscopy in
which spectral shifts due to external electric fields (the Stark
effect) have been measured in both crystalline and amor321 Finally, Section 8 reviews a novel
phous
new experiment on quantum optics in solids, where the fundamental photon antibunching expected for the fluorescence
emission from a single molecule in a solid has been observed.[331With these results, a new regime of optical spectroscopy may be envisioned in which some of the scientific
W. E. Moerner was born in 1953 in Pleasanton, California. After receiving three Bachelor’s
degrees in 1975,from Washington University, St. Louis, he obtained M . S. (1978) and Ph.D.
(1981) degrees in physics from Cornell University, where he worked with A . J. Severs. He joined
the IBM Research Division, Almaden Research Center in 1981, and worked extensively in the
area of spectral hole-burning. He received the Roger I . Wilkinson Outstanding Young Electrical
Engineer Awardfrom the Eta Kappa Nu Honorary Electrical Engineering Society of the U S . in
1984 and an Outstanding Technical Achievement Awardfrom IBM in 1988 and in 1992. He is a
Fellow of the Optical Society of America and the American Physical Society, a Senior Member
ofthe Institute of Electrical and Electronics Engineers, and a member of the American Chemical
Society. His current interests include single-molecule spectroscopy in solids, optical storage, and
polymeric photorefractive materials.
Thomas BaschP, born 1959 in Bingen, Germany, did his undergraduate studies in chemistry at the
University of Munich where he received his Ph.D. in 1990,for his work with C. Brauchle. In 1991
and 1992 he was a postdoctoralfellow with W E. Moerner at the IBM Almaden Research Center
in Sun Jose. His current research interests include optical line-narrowing experiments with
adsorbed molecules and single-molecule spectroscopy in condensed phases.
458
A n p w . Chem. In[. Ed. Engl. 1993,32, 451-476
advances and observations of physical effects made possible
by the ion trap and STM techniques may be applied to condensed matter.
2. First Steps toward Single-Molecule
Spectroscopy
2.1. Background on Inhomogeneously Broadened
Optical Lines
It is well known that absorbing guest centers in solids with
zero-phonon transitions give rise to inhomogeneously
broadened
351 where the overall line profile is caused
by an approximately Gaussian distribution of center frequencies for the individual absorbers that is broader than the
(usually Lorentzian[”]) homogeneous lineshape of the individual absorbers. This situation is shown schematically in
Figure 1 and by simulation in Figure 2, which will be described in Section 2.2. The distribution of center frequencies
is caused by dislocations, point defects, or random internal
electric and strain fields and field gradients in the host material. Inhomogeneous broadening is not only a universal feature of high-resolution laser spectroscopy of defects in
soIids.1’5,371but it also appears in a fundamental way in
other spectroscopies of impurity centers such as N M R , ESR,
and Mossbauer spectroscopy. Inhomogeneous broadening
also occurs in amorphous hosts, where the (generally broad)
center frequency distribution is caused by the large multiplicity of local environments. Although the work reviewed here
is focused mainly on the lowest electronic transition of the
inhomogeneous line IGaussionl
1
line Lorentzionl
n-
line c e n t e r
wings of line
Fig. 1. Top: Schematic representation of an inhomogeneous absorption band at
low temperatures and the principle of single-molecule detection in solids. The
entire band is formed as a superposition of Lorentzian profiles of the individual
absorbers, a distribution of center resonance frequencies is caused by random
strains and imperfections. The lower part of the figure shows how the number
of impurity molecules in resonance in the probed volume can be varied by
changing the laser wavelength. The laser linewidth (13 MHz) is negligible
(after ref. [ 2 3 ] ) .
AnRim Chern. Int. Ed. Engl. 1993. 32, 451-476
absorbing molecule, all of the concepts apply equally well to
inhomogeneously broadened vibronic lines as well as to inhomogeneously broadened purely vibrational zero-phonon
lines.
Inhomogeneous broadening generally dominates at low
temperatures, because the homogeneous zero-phonon lines
become much narrower than the inhomogeneous distribution of center frequencies only when the host phonons are
quenched. For example, for pentacene in p-terphenyl, the
homogeneous width of the lowest electronic transition at
593 nm is 7.8 MHz at 1.5 K,[381while the overall inhomogeneous line is 42 G H z in width in crystals grown by the Bridgman method.[391In the single-molecule spectroscopy to be
described in Section 3, inhomogeneous broadening will be
used to select one single absorber for study by proceeding
out into the wings of the inhomogeneous line as shown on
the right side of Figure 1.[401 Since the center frequencies for
these absorbers are displaced very far from the most common center frequencies near the center of the inhomogeneous line, such absorbers have highly unique and strained
sites. For this reason, various recent SMD experiments have
also considered the situation where the concentration of impurity centers is lowered and single molecules are measured
much closer to the center of the inhomogeneous line.
2.2. Statistical Fine Structure
Before the single-molecule limit can be approached, however, it is necessary to review the statistical properties of
inhomogeneous lines. To quantify the number of impurity
centers absorbing at a particular frequency or wavelength, it
is useful to define the quantity HH,which is the average
number of centers in the probed volume whose center frequencies are within one homogeneous width of the laser
wavelength. Due to the unavoidable randomness associated
with the imperfections in solid hosts even for a single molecular orientation or “site”, inhomogeneous absorption lines
(at least where E, $ 1 ) are often approximated by smooth,
Gaussian profiles.r34.391 However, since the inhomogeneous
line on a microscopic scale is simply a superposition of discrete homogeneous lines with widths as much as 1000 times
narrower than the overall inhomogeneous profile, the true
shape of the inhomogeneous line cannot be a smooth function. In fact, unavoidable fluctuations in the number of absorbers per unit wavelength interval should give rise to a
“spectral noise” on the overall Gaussian background that
scales as the square root of the mean number of centers in
resonance. In other words, there should be a statistical fine
structure (SFS) present on the absorption profile scaling in
absolute magnitude as
(in the limit of EH$1). Since
SFS arises from the absorption of many overlapping impurity absorptions, the absolute magnitude of the SFS is clearly
larger than a single-molecule absorption signal (where
EHz 1). Therefore, observations of SFS would be expected
to precede true single-molecule o r single-center detection.
This is more than just a pedagogical point: in fact, in any
experiment with sensitivity capable of reaching the singlemolecule limit, SFS should be observed first and used as a
“test signal” to optimize the detection conditions.
Figure 2 shows a computer simulation of an inhomogeneous lineshape for various total numbers of centers N and
459
30 I
A
I
I
I
I
20
A
10
+
0
-4
frequency lock-in amplifier at v,. 2) The background is zero
in the absence of residual amplitude modulation (RAM).
3) The noise on the signal is derived from the laser noise at
v,, which may be at the quantum limit if no excess noise is
introduced by the detector. 4) The signal is largest when the
width of the spectral feature is comparable to or less than v,;
broad spectral features produce no signal. More precisely, in
F M spectroscopy the detected signal (in the cosine phase) is
proportional to [a(v vm) - a(v - v,)]L, where v is the laser
frequency and L is the sample thickness. Thus the F M signal
measures the difference in stL a t the two sideband frequencies. It can easily be shown[’91 that as long as the optical
density is not too large the F M signal resulting from statistical fine structure is described by Equation (a), where c is the
-2
0
2
4
VFig. 2 . Simulated absorption spectra with different total numbers of absorbers
N . A Gaussian random variable was used to select center frequencies. The
homogeneous linewidth is one-tenth of the standard deviation of the inhomogeneous distribution. A = absorption in arbitrary units, v = frequency in units of
u,,~(see text).
hence different values of N,. Here yH is the (assumed
Lorentzian) homogeneous width (full width at half-maximum absorption, FWHM), and din,,is the standard deviation of the normally distributed distribution of center frequencies. For clarity, a small value of the ratio cinh/yH= 10
was chosen for the simulation; in real solids, this ratio usually ranges from 102-105. The main point here is that even
though the center frequencies were chosen by sampling from
a (smooth) normally distributed random variable, the actual
center frequencies never form a smooth uniform covering of
the allowed frequency space. This is merely a statement that
the usual number fluctuations encountered in many areas of
physics and chemistry must occur here as well. As Figure 2
shows, the average absorption ct grows linearly with N,,
while the relative fluctuations in absorption Aa/ct decrease
with (NH)-’12.Therefore, in terms of relative changes in
absorption it appears that low-concentration samples
(N,< 10, for example) might be expected to be optimal for
the observation of SFS. While this is true for most techniques, SFS was in fact first observed in a different regime.
(Acc)L= O ( N ~ ) ” ~=/ Ac(p,L/A)”’
(a)
peak absorption cross section, A is the beam area, and the
volume density per homogeneous linewidth is given by
pH= N H / A L .Therefore, the F M signal increases if the concentration of absorbers or the sample length increases, and
increases for smaller laser spots. Further, centers with higher
cross section lead to larger F M signals.
For the well-studied model system“
pentacene in pterphenyl crystals statistical fine structure can be easily detected by F M spectroscopy at 1.5 K.[’’? A schematic illustration of the location of the pentacene molecules in the
p-terphenyl host crystal is shown in Figure 3. Pentacene can
5 3 4 2 1
2.3. Detection of Statistical Fine Structure with Laser
Frequency Modulation Spectroscopy
The limit NH-+1 is in fact the single-molecule regime itself.
In the early work, it was realized that statistical fine structure
could be measured without completely solving the problem
of single-molecule detection. The zero-background technique of laser frequency modulation (FM) spectroscopy[201
provides a solution, because the variable measured is Aa
itself, which increases with (N,)’”. In other words, statistical
fine structure is easier to detect at large ZHif F M spectroscopy is used. A glance a t Figure 2d verifies that the size
of the absorption variations due to SFS in terms of departures from the average absorption is indeed far larger than
the size of the absorption signal from a single molecule.
Rather than describe the details[41] of F M spectroscopy
here, it is more useful to describe the characteristics of the
method: 1) The laser is phase-modulated at the radio frequency v,, and the transmitted beam is detected with a radio
460
Fig. 3. Schematic representation of the crystal struture ofp-terphenyl showing
one possible location for a pentacene dopant molecule. This depiction of the
pseudomonoclinic crystal structure (projected onto the ab plane) was adapted
from ref. [43]
substitute for any one of the four p-terphenyl molecules in
the low-temperature unit
431 giving rise to four
S, + So optical absorption origins near 593 nm, called O , ,
O,, O,, and 0,. It is convenient to focus on the inhomogeneously broadened origins 0, and 0,, because the homogeneous linewidths are smaller here than for the other origins.
An example of the static nature (and repeatability) of the
SFS spectra measured with F M spectroscopy is shown in
Figure 4, where the bottom panel shows a 5-GHz-wide scan
near the peak of the 0, line. The spectra were acquired by
Angeu Chem. Ini. Ed. Engf. 1993, 32,451-416
pentacene
para-terphen yl
perylene
terry 1ene
More insight into the source of SFS can be derived from
spectra from different sample volumes. The formation of a
specific set of center frequencies for a given sample volume
is a random process which reflects the underlying probability
distribution for center frequencies; thus SFS should be different for different sample volumes. A “SFS landscape” of
the sample can be generated by acquiring multiple SFS spectra as a function of the position of the laser spot, as shown
in Figure 5. This display allows one to search for “mi-
repeatedly scanning the desired frequency range with a Rhodamine 6G single-frequency dye laser (2.8 MHz linewidth).
Contrary to what the reader might think, this is not a recording of some noisy signal. The many peaks and valleys are
actual, repeatabfe fine structure as is demonstrated by the
two expanded traces in the top panel of Figure 4, the lower
r
0.2
1
0.1
Fig. 5. Statistical fine structure (SFS) versus laser spot position d and laser
frequency uL (0 MHz = 592.32 nm) near the inhomogeneous line center for
pentacene in p-terphenyl. A sequence of 100 spectra were obtained; the 20 pm
laser spot was moved by 2 pm after each spectrum, and the results plotted as a
three-dimensional plot of the SFS signal to show the SFS “landscape” (after ref.
~91).
IIVI
-0.1
I
1
r-
?
-2000 -1000
O
F
0
A u k IMHzl
1000
2000
Fig. 4. Frequency modulation spectrum over a wide scan range showing statistical fine structure. The lower panel shows the result of 64 averages of a 5 GHz
region of the inhomogeneous line of pentacene inp-terphenyl ( T = 1.4 K). The
upper panel shows a portion of the same spectrum o n an expanded frequencyscale together with another acquisition of the spectrum taken 20 min later,
offset for clarity. Laser power 3 pW,focal spot diameter 20 pm (after ref. [19]).
I is the intensity of the SFS signal in Volts.
of which is an expansion of the trace in the bottom panel and
the upper of which is a subsequent acquisition of the same
spectral region more than 20min later. The agreement is
quite good, indicating that at 1.4 K there is little or no rearrangement or annealing of the strains and other imperfections in the p-terphenyl crystal which defined the inhomogeneous distribution when the crystal was cooled. Most, if not
all, of the slight differences between the spectra are due to the
quantum and avalanche noise of the detection system. As
expected from Equation (a), the root mean square amplitude
of the SFS spectra should grow as (NH)’I2,and indeed a
‘ . O 5 has been observed
measured dependence of (NH)0.54’
experimentally.[’ ‘1
AngrM. Chem. Int.
Ed. Engl. 1993, 32. 451-416
crosites”, special (more probable) frequencies that would
appear as ridges in this three-dimensional plot. No evidence
for microsites or departures from the statistical source for
SFS have been observed in this system. As a final point, the
value of the underlying homogeneous linewidth can be determined directly by an autocorrelation analysis of the SFS
spectra.“9’ In systems with weak spectral hole-burning and
weak spectral diffusion, this method of obtaining the homogeneous width should work as well as the older, more established techniques of coherent transients or hole-burning, as
long as the signal-to-noise ratio of the SFS spectrum is reasonable.
2.4. Further Steps Toward the Single-Center Limit
Subsequent to the first observations of statistical fine
structure, other researchers utilized both FM spectroscopy
and fluorescence excitation to observe SFS in other classes of
materials at smaller and smaller values of NH.Lange et al.[441
relied upon fluorescence excitation of Sm2+ ions in CaF, at
77 K with a fixed-frequency laser in tightly focused spots.
They saw Poisson fluctuations in the detected fluorescence as
a function of the position of the focal spot, and concluded
that they had reached the level NH= 5. In a particularly
novel approach, developed by the Yen group at the University of G e ~ r g i a , ~ ~laser
’ . ~ fluorescence
~]
excitation was used in
a glass fiber doped with Nd3’ ions. Here the fiber geometry
effectively maintained a small focus and a small sample volume, and background signals from the host were reduced.
The measured SFS led these researchers to conclude that
they had reached SHvalues on the order of a few tens of ions,
46 1
although the spectral features were somewhat broad. In both
of these cases, special detection geometries were required to
reduce interfering background fluorescence from Rayleigh
and Raman scattering.
Equation (a) shows that SFS becomes harder and harder
to detect when cr decreases. The drop in signal can be partially offset by increasing the concentration of centers, but for
constant optical density the signal still suffers as the square
root of the cross section. Nevertheless, F M techniques with
the addition of secondary Stark modulation to remove residual amplitude modulation (RAM) allowed the observation
of SFS for Cr3+ ions in ale~andrite.[~’I
Another approach
when cr is low is maintaining a focused spot over a long
distance in an optical fiber. In this case the SFS signal increases as the square root of the fiber length, as long as the
optical density is less than unity. Using this approach and
F M spectroscopy techniques, Brocklesby et al.[481observed
SFS for Nd3’ ions in a silica fiber. These experiments
demonstrated that SFS can indeed be detected for absorbers
in amorphous hosts and for relatively weakly absorbing centers.
3. Detection of Single Molecules in Solids with
Absorption Techniques
3.1. Detection with FM Double-Modulation Techniques
Compared to the previous single-absorber experiments on
ions in traps, molecules on surfaces, and molecules in hydrodynamic flows, single-molecule detection in solids provides
a different set of experimental challenges. The problem can
be likened to finding a needle in a haystack, because unlike
the ion-trap experiments, for example, the molecule of interest is hidden within a solid containing a large number
( z10’’ of nonabsorbing, potentially interfering
host molecules within the laser focal volume. If laser-induced
fluorescence excitation were used for S M D and the host
molecules had appreciable Raman (or Rayleigh) scattering
cross sections, the signal from the one absorbing molecule
could be swamped by the scattering signal from the host.
The first successful S M D experiment,[2‘I also performed
on the pentacenelp-terphenyl system, avoided the problem
of fluorescence background from the host “haystack” by
using the powerful zero-background properties of F M spectroscopy.[201This method also has the advantage that it is
sensitive only to spectral features with widths on the order of
the modulation frequency v,. Therefore, any impurity molecules in the host matrix with wide absorption lines as a result
of stronger electron-phonon coupling or much shorter excited state lifetimes than that of pentacene d o not contribute to
the observed signal. In this method narrow spectral features
in the sample are used to convert the frequency- (phase-)
modulated light beam into an amplitude-modulated beam.
Since the method directly measures the conversion of frequency into amplitude modulation, any residual amplitude
modulation (RAM) from imperfections in the modulator
can give rise to a spurious background signal. To overcome
this, a secondary modulation of the spectral feature itselfwas
implemented by using oscillating Stark (or separately, ultrasonic) fields.
462
In the case of pentacene, the applied secondary Stark
modulation with oscillating electric fields at frequency f(in
the kHz range) shifts the absorption profile twice each cycle
by the quadratic Stark effect.[49*501 The secondary modulation with demodulation at 2fgenerates the first derivative of
the F M signal. Because the physical effects giving rise to the
R A M are insensitive to the Stark modulating field, this
detection system yields a signal that is free from RAM background. It is clear that other local perturbations of the impurity molecule might also be used for double-modulation detection. Other RAM suppression methods that d o not
require secondary modulation could also be utilized.[5’. 5 2 1
The size of the expected absorption signal from a single
molecule in an F M spectrum is straightforward to estimate.[”] The change in absorbance, (Aa)L, is given by the
probability of absorption of a photon in the incident beam
by the molecule, a / A , where cr is the peak absorption cross
section and A is the area of the laser beam. Clearly, then, one
would prefer tightly focused laser spots and molecules with
strong absorptions. In the first experiments, the focal spot
was N 3 pm in diameter, and the peak (low-temperature)
absorption cross section for pentacene is 9.3 x lo-’’ cm’,
yielding an absorbance change of
This is not an
extremely small signal, but detection must be performed with
a light intensity that does not produce extreme power broadening. To meet this constraint in a tightly focused spot, the
measurements were performed with only 0.1 pW of light at
the detector, which is an extremely small laser power for F M
spectroscopy. Such a low light level required an avalanche
photodiode to avoid detector Johnson (thermal) noise and
resulted in detection approximately 3 dB above the quantum
limit.
In spite of these limitations, the FM/Stark and FM/ultrasound methods can be used to detect the optical absorption
of a single molecule of pentacene in a solid crystal of p-terpheny1.[21*231
Figure 6 shows examples of the spectra for the
FM/Stark case. The first three traces are simulations to illustrate the expected single-molecule lineshape for either Stark
o r ultrasonic double-modulation. Trace a shows a Lorentzian absorption profile of width y , trace b the expected simple
F M signal:[411two copies of the absorption line with opposite sign, spaced by 2v, =I50 MHz (in the limit y << v,,
where v m is the rf modulating frequency). With secondary
modulation that causes frequency shifts less than the
linewidth, the resulting double-modulation lineshape is the
derivative of the simple F M lineshape (trace c). Thus the
signature of a single molecule is a W-shaped feature with a
large negative slope and a large positive slope separated by
2v,.
In a typical experiment, the laser frequency was set near
the center of the inhomogeneous line, and the resulting
strong SFS signal was used to optimize the optical and electronic configuration. Then as the laser wavelength was
moved out into the wings of the line, the SFS amplitude
dropped uniformly. Eventually spectra that appear to be
superpositions of two to five single-molecule spectra were
observed. Finally, sufficiently far out into the wings of the
line, true single-molecule spectra could be recorded. Trace d
in Figure 6 shows a set of eight FM/Stark double-modulation spectra of a strong in-focus molecule far out in the
long-wavelength edge of 0,, along with several unavoidable,
Angew. Chem. Int. Ed. Engl. 1993, 32, 451-416
of such signals in undoped samples, and the appearance of
single-molecule spectra with both the FM/Stark and FM/ultrasound techniques, led to the conclusion that the recorded
spectra were indeed due to single molecules of pentacene.
However, in both cases, the signal-to-noise ratio (SNR) was
only approximately 3 - 5, and further improvements in this
SNR proved difficult since the measurements were already
performed near the quantum limit and power broadening
was already present. Indeed, one cannot underestimate the
difficulty in acquiring spectra like those in Figure 6 , especially since later work to be described in Section 4 showed that
many molecules spectrally diffuse within seconds. The single
molecules observed by FM spectroscopy must have been
class I (see Section 4) stable pentacene molecules with no
spectral diffusion.
I
I IV1
0
3.2. Signal-to-Noise Limits in FM Detection
-0.8
0
200
-
400
600
Av, [MHzl
Fig. 6. Single-molecule spectra obtained with the FM/Stark technique
(quadratic Stark effect) for pentacene in p-terphenyl. a) Simulation of the absorption line. b)Simulation of the FM spectrum with v, =75 MHz.
c) Simulation of FM/Stark double-modulation lineshape. d) SMD spectra at
i.
= 592.423 nm, 512 averags, 8 traces overlaid; the bar corresponds to 2 ,Y =
150 MHz. (0,line center is at 592.326 nm.) e) Average of traces in (d) and the
fit to the in-focus molecule (smooth curve). f) Signal at i.
= 597.514 nm very far
from the line center; same conditions. g) Traces of SFS at the 0, line center,
i.= 592,186 nm. 128 averages each. The vertical scale is correct for traced; the
other traces have the same scale but are offset vertically for clarity (after ref.
[21]). I = intensity of the double-modulation signal.
weak, repeatable features from out-of-focus molecules at the
left and right edges of the laser scan range. These out-offocus features were caused by molecules not located at the
peak of the laser intensity profile. The fiducial bar in Figure 6 marks a spectral range equal to 2v,. Trace e shows the
average of the eight scans in trace d, along with a fit to the
central feature generated by a simple model for the doublemodulation process.[231The fit to the essential features of the
SMD lineshape is reasonable, and the homogeneous width
required by the fitting process is somewhat larger than the
low-power homogeneous width, as expected.
Trace f i n Figure 6 shows the detected signal from a laser
wavelength so far away from the pentacene site origins that
no absorptions are expected to lie in the laser scan range; this
is the background shot and avalanche noise. I n samples of
undoped pure p-terphenyl, only a baseline noise level similar
to the off-line data in trace f was observed, even near the
center of the inhomogeneous line. Trace g shows spectra of
the strong SFS observed near the center of the inhomogeneous line for which a smaller number of averages were used.
This spectrum is composed of a superposition of many W
profiles similar to trace d in Figure 6 with many different
center frequencies, illustrating the qualitative difference between spectra of large numbers of molecules (trace g) and
spectra of one molecule (trace d). By using the related FM/
ultrasound technique and both longitudinal and transverse
(shear) ultrasonic waves,[z’’231 single-molecule detection
was confirmed.
I n summary, the shape of the observed features, the position relative to the pentacene in p-terphenyl origins, the lack
A n g e w C‘hm?. Int. Ed. EngI. 1993.32, 457-476
The characteristics of the signal-to-noise ratio (SNR) for
nonsaturating absorbers in FM spectroscopy have been described in ref. [41]. We will outline here the additional complications of avalanche photodiode detection and saturation
of the optical transition as they affect single-molecule detection.[*’ The analysis in this section is the result of unpublished work by W. P. Ambrose and one of the authors
(W. E. M.). For simplicity, the signal-to-noise ratio for
simple frequency modulation will be presented, with the assumption that the principal effect of the double-modulation
is to remove residual amplitude modulation (RAM) and that
the secondary modulation is strong enough to provide maximal signal.
The signal-to-noise ratio (SNR) of simple frequency modulation (FM) can be expressed in terms of a voltage or current ratio [Eq. (b)], where the (homogeneous) saturation of
the absorption is described by Equation (c). Po is the laser
SNR
= [C
]
G2(AccL)’
&+J
‘I2
power at the detector, cro is the unsaturated peak cross section, I, is the saturation intensity, and I , = p2Po/4AT, is the
laser intensity in the first-order sideband at the sample, fl is
the modulation index, and T, is the total transmittance of all
optical components between the sample and the detector.
The SNR limits of FM spectroscopy derive from the two
noise terms in the denominator of Equation (b), which represent the contributions of the shot noise of the laser beam
(carrier) and the Johnson (thermal) noise of the detector,
respectively. The constant J i s given by 4kT/2eRLRG:F,with
k Boltzmann’s constant, T the absolute temperature, e the
electron charge, R, the load resistance, R the detector responsivity in AW-’, G, the avalanche gain, and F, the
avalanche excess noise factor. As one can see, the effect of
the Johnson noise in reducing SNR is suppressed due to the
[*] Readers not interested in this particular problem may move on to the next
section.
463
gain of the avalanche photodiode. Similarly, the constant C
is given by Rp2/16eBF,, with B the detection bandwidth.
While FM spectroscopy has been shown to be capable of
in a 1 Hz
detecting absorption changes as small as
bandwidth if several mW of power is available at the detector, the severe limitations on the laser power in singlemolecule detection greatly reduce the sensitivity of the technique. When the best possible gains for Si avalanche
detectors of approximately 100 and F, factors near 2.2 are
used, the peak FM SNR is on the order of 1 for a saturation
intensity of 70 mWcm-’, which is the value for pentacene in
p-terphenyl including triplet saturation. This SNR is consistent with the observed SNR in the FM experiments, and can
be improved only by the use of laser beams with reduced
quantum noise. As will be shown below, many pentacene
centers have smaller values of saturation intensity and thus
were probably not observable in the FM experiments.
monitored as a function of the excitation wavelength. The
fluorescence excitation spectrum then represents an image of
the absorption spectrum. An example of the experimental
arrangement used by the IBM group is shown in Figure 7.
(In the original setup by Omit et al. a focusing lens was not
used and the sample was placed at the end of a single-mode
optical fiber.) For optimal collection of the emitted photons,
the sample is placed at the joint focus of a lens focusing the
laser beam and a paraboloid with numerical aperture near
1.O. The sample is mounted on a transparent substrate made
of an alkali metal halide to reduce the possibility of firstorder Raman scattering from the substrate. The emitted radiation passes through a long-pass color filter before detection with photon-counting apparatus.
The attainable signal-to-noise ratio (SNR) for singlemolecule detection in a solid by fluorescence excitation can
be approximated by Equation (d), where S, is the peak fluoS,
4. Improvements in Signal-to-Noise Ratio by
Fluorescence Excitation
4.1. Signal-to-Noise Limits in Fluorescence Excitation
The relatively low signal-to-noise ratio (SNR) availabIe
from FM absorption spectroscopy and the high powers required to attain this SNR placed severe limits on the physical
and chemical information that could be obtained. The
demonstration by Orrit et al. (see Section 4.2) that fluorescence excitation with high collection efficiency can be accomplished with acceptable background scattering levels
provided greatly increased SNR at lower probing intensity,
thus opening the door for additional detailed spectroscopic
studies. In the fluorescence excitation method the frequency
of a single-mode laser is tuned across the molecular absorption line, and the Stokes-shifted fluorescence intensity is
S,
~-
(noise),,,
-
D Qf
cr POT/
Qccr
P,z I A h v
D Qf cr Po z
L
[
Ahv
U
,
+ CbP07+ N d z
rescence signal from one molecule, Qf is the fluorescence
quantum yield, cr ist the peak absorption cross section on
resonance, Po is the laser power, z is the integration time
(counting interval), hv is the photon energy, Nd is the dark
count rate, and C, is the background count rate per Watt of
excitation power. The factor D = qQFp4F$describes the
overall efficiency for the detection of emitted photons, where
‘lo
is the photomultiplier tube quantum efficiency, F, is the
fraction of the total emission solid angle collected by the
paraboloid, 4 is the fraction of emitted fluorescence which
passes through the long-pass filter, and E; is the total transmission of the windows and collection optics along the way
to the photomultiplier. The three terms in the denominator
of Equation (d) represent shot noise contributions from the
emitted fluorescence, background, and dark signals, respecti vel y .
According to Equation (d) there are several important
criteria that have to be fulfilled for optimum SNR, once the
collection efficiency D is maximized. First, the peak absorption cross section cr and the fluorescence quantum yield Gf of
the impurity in the matrix should be as high as possible.
Further, the area of the laser spot at the sample plane should
be as small as possible, which requires tight focusing of the
probing laser beam. The power Pocannot be increased arbitrarily because saturation causes the peak absorption cross
section to drop,[s31cr + a(Z) = cr,/(l
Z/fs),where I is the
laser intensity. For maximum fs for organic molecules, it is
favorable to have the triplet quantum yield low and the
triplet lifetime short (expressions for I, are given in ref. 1541).
To give a concrete example of the application of Equation (d) to a specific material we now consider the parameters appropriate for the model system pentacene in p-terphenyl at 1.5 K. Prior work has established that
QF = 0.78[”] and that cr,, = 9 x 10-l’ cm2.1231
For iswe use
the measured[551value of 2.5 mW c r K 2 ,which is lower than
the value one would calculate using published photophysical
parameters.’”. 5 7 1 The collection optics and GaAs photomultiplier tube yielded a collection efficiency of D = 0.01,
and background and dark count parameters of C, = 7 x lo1’
+
M
C
Fig. 7. Experimental set-up for single-molecule fluorescence excitation spectroscopy in a solid at liquid helium temperatures. The excitation laser beam
enters from the left and is focused by a lens (L) with a 10 mm focal length into
the sample (S), which is mounted on an alkali metal halide plate. The excitation
beam is terminated with a piece of black tape (B). The fluorescence from the
sample is collected by a parabolic mirror (P). which collimates the emission into
a beam propagating to the right in the figure. Fine positioning of the lens (L)
relative to the sample is accomplished with an electromagnetic actuator consisting of a coil ( C ) and magnet (M). Vertical displacement of the sample relative
to the laser focal spot (resolution: 10 fim) is performed with a translation stage
and micrometer screw (not shown) (after ref. [28]).
464
Angeu,. Chem. Ini. Ed. Engl. 1993. 32, 457-476
studies, Orrit et al. were the first to apply fluorescenceexcitation with high-efficiency collection to this system.[''] Figure 9 shows the first spectra generated with apparatus similar to that in Figure 7 except that an optical fiber rather than
a lens was used. The sample itself was a thin sublimed
platelet which helped to reduce the volume available for
scattering. In the upper traces, the single-molecule signals
appear as isolated dots; expansion of the scan range in the
lower trace shows a clear, well-defined single-molecule profile with much improved SNR. These results led most investigators to subsequently use the fluorescence excitation
method.
20
15
SNR 10
5
0
I(
Fig. 8 . Signal-to-noise ratio (SNR) for fluorescence excltation of pentacene in
p-terphenyl versus laser power P and laser beam cross-sectional area A .
counts W - ' s - ' and Nd = 30 cps, respectively. With these
values. a three-dimensional plot of S N R for an integration
time of 1s versus laser power and beam area can be produced
(Fig. 8). It is clear that for a fixed laser spot area, an optimal
power exists which maximizes the tradeoff between the saturating fluorescence signal and the linearly increasing (with P )
background signal. The lens focusing arrangement shown in
Figure 7 produced a spot size of = ( 5 pm)' located at the
midpoint of the area axis. The S N R values predicted by
Equation (d) are in reasonable agreement with the experimentally obtained values. One final fact to recognize from
Figure 8 is that the best-case S N R at smaller and smaller
beam areas levels off. This is due to the effect of saturation
and shot noise; at smaller and smaller areas the power must
be reduced eventually to the point where the SNR is controlled by the shot noise of the detected signal [first term in
the denominator of Eq. (d)].
Of course. in single-molecule studies in solids, a crucial
physical effect not included in Equation (d) must be taken
into account. Persistent spectral hole-burning (PSHB),
which can be observed for certain impurities in crystals and
which is a more or less general phenomenon in amorphous
hosts."41 can cause the single impurity to change its absorption frequency before it emits enough photons to be detected
above the noise level. The amount of hole-burning that can
be tolerated depends upon the total number of molecular
excitations required to achieve adequate SNR. A general
rule of thumb for practical situations with collection efficiency D near 1 % is that approximately lo5 excitations are required to achieve a S N R on the order of 10 with 1 s integration time. This means that the hole-burning quantum
efficiency should be
This indeed may be the most
important factor limiting the number of materials systems
suitable for single-molecule studies.
4.2. Fluorescence Excitation Measurements for
Pentacene in p-Terphenyl
Recognizing from the S M D experiments using F M detection that pentacene in p-terphenyl is nearly ideal for such
Anpi.
C/iw7i. 1171.Ed.
EngI. 1993, 32, 451-416
The entire inhomogeneous line may now be measured over
a wide wavelength range in order to provide specific data
that can be contrasted with the schematic picture in Figure 1.
Figure 10 shows data for a ~ 1 0 - p m - t h i c k ,low-concentration, sublimed sample of pentacene in p-terphenyl at
1.5 K,12'] which was carefully mounted to avoid strain. This
18 GHz spectrum, obtained by scanning a 3 MHz linewidth
dye laser, contains 20000 points; showing all the fine structure usually requires several meters of linear space. Figure 10
top shows the frequency region covering the central part of
the inhomogeneous line for the 0, site at 592.321 nm. The
structures appearing to be noise are not; they are direct
measurements of the statistical fine structure (SFS) as described in Section 2. This structure is static and repeatable
and arises directly from statistical variations in the spectral
density of absorbers with laser frequency. It is immediately
obvious that the inhomogeneous line is Par from Gaussian in
shape and that there are tails extending out many standard
deviations from the center both to the red and to the blue.
More interesting are the spectral features in the wings of
the inhomogeneous line (Fig. 10 bottom). At a detuning of
- 2.7 G H z and elsewhere, clearly resolved, individual singlemolecule peaks can be observed. Similar single-molecule
peaks are present on the blue edge of the inhomogeneous
line. There is a slight variation in the height of the singlemolecule peaks since some molecules are not exactly in the
center of the Gaussian intensity profile of the laser beam.
465
without causing excited state decay, as for example when a
lattice phonon scatters off the impurity molecule. In the pentacenelp-terphenyl system T: goes to infinity for low temperatures ( T < 4 K), because the host phonons and local
modes are essentially quenched. Therefore, the homogeneous width as shown in Figure 11 is given solely by the
16
12
8
l 4
NFl
0
15
7.8
NF, 300
10
+ 0.2
MHz
IS-’]
200
5
100
n
-3
-2
-
-1
Av, IGHz 1
0
Fig. 10. Fluorescence excitation spectrum of pentacene in p-terphenyl ( T =
1.5 K). The value of 0 on the frequency axis corresponds to a wavelength of
592.321 nm, which is near the center of the 0, site inhomogeneous distribution.
N,, = Fluorescence count rate, Av,, = laser detuning. The unit lo3 s - ’ means
lo3 counts per second. Top: An excitation spectrum obtained over 10 min with
2 nW of laser power. Bottom: Two spectra on an expanded scale (the upper
trace is displaced from the lower) in the wing of the 0, site inhomogeneous
distribution. The isolated peaks out in the wing are excitation peaks for single
pentacene defects (after ref. [28]).
The total pentacene concentration for the sample can be
estimated directly by counting the number of molecules
in the spectrum; a value of 1 . 7 1013cm-3
~
or 8 x
molmol- is obtained. At different concentrations and
in samples with differing levels of strain from mounting, the
inhomogeneous linewidth can be varied over a wide range. It
has been observed (as in Fig. 9 and confirmed by the IBM
group) that in some samples epoxied to the end of an optical
fiber the strain can become so great as to spread out the
inhomogeneous line over several hundred GHz in frequency
space.
Upon close examination of an individual single-molecule
peak, the lifetime-limited linewidth of 7.8 f 0.2 MHz can be
observedIZ6l(Fig. 11). This value is in excellent agreement
with previous photon echo measurements on large ensembles of pentacene molecules.‘38*’*I The single-molecule excitation profile is well described by a Lorentzian function, as
would be expected, since all inhomogeneous broadening has
been removed. The laser intensity required for this measurement was 0.5 mWcm-2 (laser power 89 pW), and special
care was required to remove the interfering effect of laser
frequency drift during the measurements.
In general the homogeneous linewidth (full width at halfmaximum, FWHM) of an optical transition in a solid is
given by Equation (e), where TI is the excited state lifetime
’
and T? is the (pure) relaxation time (dephasing time). Pure
dephasing effects alter the phase of the excited transition
466
t
OL
I
-40
’
I
-20
’
’
‘
0
AvL lMHzl
’
‘
20
I
40
I
Fig. 11. Low-power fluorescence excitation spectrum for a single pentacene
molecule in a sublimed crystal of p-terphenyl ( T = 1.5 K). 0 MHz =
592.407 nm, which is in the wing of the 0, site inhomogeneous line. The solid
line is a Lorentzian fit to the data (after ref. [26]).
lifetime contribution TI. It is important to recall that in
hole-burning experiments[161the width of a spetral hole is
given in principle by twice the homogeneous width, because
a spectral hole is a convolution of the population hole (with
width Av,, produced during the burning step) and the homogeneous lineshape (produced during the readout step). In
many real (especially amorphous) systems, the hole width,
however, can be much larger than 2Av, due to spectral diffusion occurring on a broad range of time scale^.['^^ The effect
of spectral diffusion on the single-molecule lineshape in a
polymeric host is described in Section 6. The point here is
that the lineshape in Figure 11 shows neither spectral diffusion nor pure dephasing effects; the width has reached the
smallest value allowed by Equation (e) and thus is the true
homogeneous linewidth.
By slowly translating the laser focal spot across the face of
the crystal and obtaining spectra at each position, one may
observe single-molecule peaks localized in both frequency
and position. It is thus possible to acquire a “spectral landscape” from the fluorescence excitation spectrum of the
sample similar to that obtained for the statistical fine structure at high concentration near the inhomogeneous line center (see Fig. 5). Figure 12 shows a three-dimensional color
plot of spectra taken at a series of overlapping laser spots
0.568 pm apart, in which the displacement was accomplished
by translating the incident laser beam across the sample.[2s’
Within the 300 MHz tuning range shown, isolated singlemolecule excitation peaks occur at laser detunings of 20,
+ 130, and - 120 MHz (relative to the center of the scan) at
different positions in the crystal of 30, 35, and 40 pm. The
shape of an excitation peak along the position axis is a direct
measure of the (Gaussian) intensity profile of the laser beam
in the crystal, as probed with the fluorescence emitted by a
single molecule. In Figure 12, the spatial width (FWHM) of
+
Angew. Chem. Int. Ed. Engl. 1993. 32, 457-476
Fig. 1 2 “Spectral landscape” of the fluorescence excitation of a single pentacene molecule in a crystal of p-terphenyl ( T = 1 . 5 K). The horizontal axis
covers 300 MHz: the center of the axis corresponds to 592.544 nm. The axis
extending into the page was generated by measuring successive,excitation spectra (scan time 2 min). The laser focal spot was displaced laterally by 0.57 pm
between each measurement to cover a total distance of 40 pm. The intensity of
the fluorescence is plotted on the vertical axis.
a single-molecule peak, and hence that of the laser focal spot
is ~5 _+ 0.5 pm. The fluorescence peaks have different sizes
because the molecules do not pass directly through the center
of the laser focus and “experience” different peak laser intensities. The frequency widths of the peaks in Figure 12 are
slightly larger than the lifetime-limited width (Fig. 11) due to
the higher probing intensity used. The other oddly shaped
peaks in the figure result from molecules that are spectrally
diffusing. This effect will be discussed in more detail in the
next section.
Spectra like those shown in Figure 11 are ideal for detailed
measurements. For example, the intensity saturation behavior of both the linewidth and the emission rate for several
single molecules in the wings of the inhomogeneous line was
yielding a (free-space) value for the saturation
intensity of I, = 2.5 mWcm-’. Usually, absolute intensity
measurements are difficult because of the Gaussian shape of
the laser spot and the difficulty in determining the size of the
laser spot in the sample. Here, however, the laser spot diameter may be easily determined simply by using the single molecule as a probe. In the high-intensity limit, the peak fluorescence emission rate saturates at (7.2 0.7) x lo5 photons
per second. As the peak emission rate saturates, the emission
rate in the wings of the line continues to increase with intensity, and the homogeneous linewidth broadens according to
the expected form [Eq. (f)].1601It is remarkable that the value
of I, expected based on previously determined photophysical
parameters for pentacene in p-terphenyl is larger than the
measured value by more than a factor of 20. The exact reason for this discrepancy is unknown, although it is reasonable that some of the photophysical parameters are modified
for the single molecules located in the wings of the inhomogeneous line. It is likely that the intersystem-crossing rate
and/or triplet lifetime are affected rather than the fluoresAngcw. Chem. Int. Ed. Engl. 1993,32,451-4?6
cence lifetime, since the intersystem-crossing process is more
likely to be affected by strain.[561
It is also possible to measure the linewidths (FWHM) of
the signals of single pentacene molecules as a function of
temperature. Such data have been acquired at temperatures
up to 10 K where the linewidth increases by almost a factor
of 100 compared to the value at low temperatures.[28]The
data are in excellent agreement with previous photon echo
experiments“’. 61, 621 in which the temperature dependence
of the echo decay time was found to follow a form described
by dephasing via a single pentacene librational moder6’]with
librational energy AE/k = 38 _+ 1 K = 27 If: 0.7 cm-’. To
date, this same temperature dependence was found for all
single molecules studied, indicating that the local mode is
intrinsic to the defect center and is not influenced by the
specifics of the local environment. This is to be contrasted
with the local electric fields which do show a distribution
(Section 7).
5. Detection of Spectral Diffusion of a Single
Molecule in a Solid
In the course of the fluorescence excitation studies by Ambrose et al. on pentacene inp-terphenyl, an unexpected physical effect was observed : spectral diffusion of individual pentacene impurity molecules in a crystal at 1.5 K.[”I Here,
spectral diffusion means changes in the resonance frequency
of a defect at low concentration due to changes in the nearby
host, rather than the energy transfer effects that can occur
for impurity centers at high c o n ~ e n t r a t i o n . ~Two
~ ’ ~distinct
classes of impurity molecules were identified: class I, which
have center frequencies that are stable in time, and class 11,
which show spontaneous, discontinuous jumps in resonance
frequency of 20-60 MHz on a timescale of 1-420 s. Class I1
molecules were responsible for the distorted single-molecule
peaks in Figure 12 which appeared to change shape between
the individual laser scans. Figure 13 shows the behavior of a
particular class I1 defect more clearly; the laser scan speed
was increased to 1 scan every 2.7 s so that the spectral position of the molecule could be recorded with improved time
resolution. The upper part of the figure shows how the resonance frequency of a spectrally “jumping” class I1 defect
evolved with time, where each trace was digitally smoothed.
A digital waveform recorder located the peak in each scan
and recorded this resonance frequency as a function of time
in the lower part the figure. For this defect, the optical transition energy appears to have a preferred set of values, and
the defect performs spectral jumps between these values that
are discontinuous on the one-second timescale of the measurement. This type of jumping behavior occurred for some
tens of class I1 defects. In one case, one single molecule was
observed that discontinuously jumped between only two allowed frequencies, but spectral jumps between a larger number of allowed frequencies was much more common (see
below).
Before summarizing other types of behavior, we should
present two crucial observations: First, the occurrence of
class I1 defects was quite common in the wings of the inhomogeneous line (increasing to 40 YOof the studied molecules
at a distance of + 0.23 nm from line center), but only class I
467
-200
-100
0
Av, [MHz]
100
behavior like that in Figure 14 were found almost exclusively, which reflects the increased disorder in these samples. In
future work, it should be possible to obtain useful temperature-dependence data even with the lens arrangement
(Fig. 7) by cooling below 1.5 K with 3He or a dilution refrigera tor.
200
200
1
100
YO
[MHz]
0
-100
t
I
i
t k1
.Fig. 13. Spectral jumps in the resonance frequency Y” of a class II single pentiicene defect in p-terphenyl ( T = 1.5 K). In the upper half of the figure are
individual excitation spectra measured successively (scan time 2.7 s). The peak
i n each spectrum is represented a s a function of time I in the lower half of the
figure (after ref. 12x1). A!,, is the laser detuning.
defects were observed in a spectral region from 0.003 to
0.01 nm from line center. The fraction of pentacene molecules showing class 11 behavior increased for wavelengths
further and further from line center, suggesting that disorder
in the crystal is partially responsible for the spectral migration. Second, the jumping rate did not depend upon the laser
power used to measure the fluorescence excitation spectrum.
This is the main reason that the observed changes in resonance frequency were attributed to a spontaneous process
rather than a light-induced spectral hole-burning efThe behavior shown in Figure 13 shows relatively discontinuous resonant frequency changes, but in fact a wide array
of characteristics was observed. Figure 14 provides an example that also illustrates the general effect of increasing
temperature. These measurements of the time dependence of
the resonance frequency of a single molecule were taken on
a sample mounted on the end of a single-mode optical fiber
placed at the focus of the collection paraboloid. This “wandering” defect spectrally diffused rapidly, and was found at
a new frequency in every laser scan. During the 1600-second
measurement at 1.5 K (Fig. 14 top), the spectral wandering
for this defect was confined to a 500 MHz region. At 4.0 K
(Fig. 14 bottom), the wandering range expanded to
700 MHz, and the spectral diffusion rate also appears to be
higher. This could have been due to a larger number of small
jumps between the laser scans, or the spectral jump sizes may
have increased with temperature.
Of course, a detailed study of the temperature dependence
of an appropriately defined average jumping rate would help
to identify the source of the spectral diffusion effect. Such
data have not been obtained to date for technical reasons
relating to the difficulty of following the same single molecule over the entire temperature range. In samples attached
to the end of the optical fiber molecules with wandering
r
1
Fig. 14. Qualitative increase in spectral diffusion rate with temperature. In both
traces the resonance frequencies v g for a spectrally jumping molecule near the
592.582 nm excitation wavelength are shown. This molecule jumps often. appearing at a new frequency in each spectrum (scan time 2.7 s). Raising the
temperature from 1.5 K (top trace) to 4.0 K (bottom trace) appears t o increase
the spectral diffusion rate and jumping range (after ref. 12x1).
As a final illustration of the fascinating spectral diffusion
phenomenon, Figure 15 shows the peak frequency trend of
another pentacene defect over 1.6 h at 1.5 K. For this defect,
which is on the low-frequency side of the inhomogeneous
distribution, the overall trend can be described as “creeping”
by successive jumps towards higher optical frequencies. As
400
*
____--~.__L_-L--
t Is1
-
Fig. 15. Frequency “creep” of a spectrally jumping pentacene defect over an
extended time. The peak frequency tlo of a class 11 defect near 592.544 nm (on
the long-wavelength side of the 0, inhomogeneous distribution) spectrally
jumps no more than 100 MH7 o n short timescales. hut tends towards higher
frequencies over 1 .h h. The inset. an expansion of the trace recorded over 600s.
shows the individual jumps <80 MHz. (after ref. (281).
shown in the inset, there are residence times on the order of
30 s. and the molecule appears at new, higher frequencies at
later times. This “creeping” pentacene defect may be in an
environment that is structurally relaxing at 1.5 K into a n
environment more typical of those found at the center of the
inhomogeneous line.
The resonance frequency of an impurity molecule in an
inhomogeneously broadened line is extremely sensitive to the
strain at the position of the molecule. Thus the spectral
jumps appear to occur because the class I1 pentacene molecules are coupled to an (unidentified at present) ensemble of
two-level systems (TLS) in the host crystal undergoing
phonon-assisted tunneling o r thermally activated barrier
crossing. One possible source for the tunneling transitions
could be discrete librations of the central ring of the nearby
p-terphenyl molecules about the molecular axis. As Figure 3
shows, the p-terphenyl molecules have a particular dihedral
angle between the central and outer phenyl rings, depending
upon the specific position in the
When the monoclinic, room-temperature crystal strucure becomes triclinic
below 170 K, it is not unreasonable to postulate that the
sample may contain several single-crystal domains even
though the phase transition is not destructive to the sample.[h31Thep-terphenyl molecules in a domain wall may have
lowered barriers to such central-ring tunneling motions, and
the pentacene molecules near the domain walls would
“sense” such local motions and show class I1 behavior.
Further experiments are necessary to conclusively identify
the molecular motions responsible for the effect. Of course,
the spectral diffusion surprisingly observed here in a crystalline system is analogous to spectral diffusion processes
that play a crucial role in the physics of glasses and other
amorphous materials.[h41Most importantly, with the singlemolecule detection technique the spectral changes can be
followed in real time for each individual impurity molecule;
n o ensemble averages over “equivalent” centers need be
made.
6. Single-Molecule Spectroscopy in Polymeric
Hosts
6.1. Physical Properties of Glasses and Polymers
at Low Temperatures
The experiments described so far were performed with
single impurity molecules doped into a crystalline matrix.
Amorphous systems such as glasses and polymers have a
number of interesting physical properties at low temperatures that are quite different from those for crystalline
A wealth of information on the low-temperature dynamics of amorphous systems was obtained by doping these materials with optical impurities and probing them
with optical line-narrowing techniques such as fluorescence
l i n e - n a r r ~ w i n g , [ ~persistent
’~
spectral h~le-burning,[’~]
and
photon
To understand the optical properties of these systems, a
brief description of the amorphous state is in order. A glassy
or amorphous material is characterized by a complex, multidimensional potential energy surface. According to the twolevel system (TLS) model, the potential energy surface can be
AngiJ!t,.(’licm. int. Ed. EngI. 1993, 32, 451-476
approximated by a distribution of asymmetric double-well
potentials o r so-called two-level systems. The TLS model
assumes that at low temperatures only the two lowest energy
levels of each double-well are important. Transitions from
one side of the double-well to the other occur by phononassisted tunneling and represent changes in the local structure of the glass. As a result of the broad distribution of
barrier heights and well-asymmetries, structural relaxation
processes can occur on a wide distribution of timescales.
When an impurity molecule is doped in an amorphous solid,
its optical transition can couple to the TLSs (e.g. by dipoledipole coupling), and the lineshape of the optical transition
reflects the dynamicdl processes of the host.‘“’
One important physical effect that occurs often in amorphous hosts is persistent spectral hole-burning (PSHB). In
PSHB experiments, narrow bandwidth laser irradiation is
used to select a reasonantly absorbing subensemble of
molecules out of the inhomogeneously broadened absorption band. The optical excitation induces either photochemical changes in the excited centers or photophysical (nonphotochemical) alterations in the nearby host, and a narrow
spectral hole can develop in the absorption because the altered centers no longer absorb at the laser wavelength. While
photochemical hole-burning can occur in amorphous or
crystalline systems, the nonphotochemical process is an almost general phenomenon in amorphous systems and is
most likely caused by TLS transitions induced by the laser
e~citation.’~’]
By measuring the hole-shape as a function of
temperature and/or thermal cycling,[16] information on the
host dynamics can be obtained.
6.2. Detection of Single Perylene Molecules in
Polyethylene
Aromatic hydrocarbons in non-hydrogen-bonding matrices are systems that show nonphotochemical hole-burning
and have low PSHB quantum efficiencies. Taking this important prerequisite into account, perylene in a polyethylene
matrix was found to be a suitable candidate for singlemolecule d e t e ~ t i 0 n . l Furthermore,
~~~
the photophysical
parameters for this system are favorable: the homogeneous
linewidth of the optical transition is narrow, the absorption
cross section ((r, = 3.5 x 10-l‘ cm2) and the fluorescence
quantum yield (P, = 0.98 are high, and the triplet yield and
lifetime are low.
The maximum of the inhomogeneous line for the lowest
electronic transition of perylene in polyethylene lies at approximately 440 nm. The width of the inhomogeneous distribution is much larger than in a crystalline system, and single
molecules were detected in the red wing of this distribution
between 445 and 450 nm. In Figure 16 a fluorescence excitation “spectral landscape” of a perylene-doped thin film of
polyethylene is shown at 1.5 K. This picture was taken with
the same procedure as Figure 12. The signal sizes of the six
strong single-molecule fluorescence peaks are again different, partly because the molecules “experience” different
peak laser intensities. In an amorphous matrix, however, the
orientations of the impurity transition dipoles are statistically distributed, and with a fixed polarization of the incoming
laser the single molecule fluorescence intensities vary as
469
the TLS model is employed, the experimental findings can be
qualitatively explained by a hierarchy of TLSs surrounding
the impurity. Distant TLSs produce fast shifts that are small
in magnitude; in this case spectral diffusion appears as a
broadening of the linewidth on the one-second timescale of
the measurement. The closer TLSs produce larger shifts that
are more infrequent; in this case spectral diffusion appears as
frequency jumps which can be resolved on the experimental
timescale.
6.4. Spectral Hole-Burning of a Single Molecule
Fig. 16. “Spectral landscape” of the fluorescence excitation of single perylene
defects in a polyethylene film. Each “mountain” represents the fluorescence
from an individual molecule as the probing laser scans the frequency (6.1 GHz,
horizontal axis) and is translated spatially across the face of the sample (23 pm,
axis extending up and right).
cos2H,where H is the angle between the laser polarization and
the transition dipole axis. Hence, in this case there are two
mechanisms that can lead to varying signal intensities. A
close examination of the signal shapes along the frequency
axis reveals that these shapes are slightly distorted. This distortion is due to a real physical effect, namely spectral diffusion, the various manifestations of which will be described in
the next section.
A spectral hole usually refers to a dip in the inhomogeneously broadened absorption spectrum of many molecules
when light irradiation alters the absorption frequencies of a
portion of the resonant absorbers. In the single-molecule
regime, however, only the isolated absorption profile of a
single center is present. When photochemical or photophysical changes occur as a result of optical excitation, the absorption line simply appears to vanish as the resonance frequency of the single center shifts away from the laser
frequency. As the underlying mechanisms are the same in
both cases, we will continue to use the term persistant spectral hole-burning (PSHB) even for the single-molecule case.
An example of spectral hole-burning of a single perylene
molecule in a polyethylene host is presented in Figure 17.
6.3. Spectral Diffusion in a Polymeric Host
In the pentacenelp-terphenyl system the observation of
spectral diffusion of single molecules was quite surprising, as
the phenomenon occurred in an ordered crystalline material.
By contrast, in disordered, amorphous matrices spectral diffusion is a well-known p h e n ~ m e n o n . [ ~ ~In~ “the
* ] TLS picture spectral diffusion occurs due to spontaneous (phonondriven) transitions in the double-well potentials of the host
when the impurity molecules are in their electronic ground
states. In hole-burning experiments spectral diffusion is observable by the time-evolution of the hole shapes (broadening) after the burning process.[691How does spectral diffusion manifest itself in single-molecule experiments in a
polymer?
In the perylene/polyethylene system spectral diffusion appeared in two ways in single-molecule spectra.[701First, discontinuous jumps in frequency space on the scale of several
hundred M H z between or during consecutive laser scans
(scan time 2.86 s) were observed which were similar to the
effects observed with pentacenelp-terphenyl (Section 5). Second, a broadening of the single-molecule Iineshape was observed which varied from molecule to molecule. The observed linewidths ranged from 52 MHz to 142 MHz, and all
these values were larger than the lifetime-limited width of
22.7 MHz. It should be mentioned that part of the observed
line-broadening could be due to pure homogeneous
dephasing by fast, global (non-local) TLS transitions. According to standard theories, this contribution to the width,
however, is generally assumed to be the same for all molecules.
These results give direct evidence that spectral diffusion
may occur over a range of frequencies and timescales. When
470
1200
1
600
n
A
400
-
-1000-500
0
500 1000
AuL [MHzl
Fig. 17. Persistent spectral hole-burning (PSHB) of a single perylene molecule
in a polyethylene film at 1.5 K (see text). 0 MHz = 488.021 nm. The laser power
for burning and scanning is 9 nW, and the scan time is 25 s (after ref. [29]). The
vertical scale is correct for trace a, the other traces have the same scale but are
offset vertically for clarity.
Before the traces shown in the figure were recorded, the
molecule was scanned five times, and no significant changes
were observed. Traces a, b, and c show three additional scans
of the molecule. After trace c the laser was tuned into resonance with the molecule until the fluorescence decreased
suddenly. Trace d was then acquired, which showed that the
resonance frequency had shifted by more than f1.25 GHz
Angew. Chem. inr. Ed. Engi. 1993,32,457-476
ered and a transition of the TLS can take place. The spontaneous return of perylene molecules after a burning event to
exactly the same wavelength was somewhat surprising,
though not absolutely unexpected. It suggests that coupling
to exactly one dominant nearby TLS, rather than a succession of TLS configurations, is involved in the hole-burning
process. In this picture optical excitation induces a (phononassisted) transition in the double-well potential in one direction which is reverted by a spontaneous (phonon-assisted)
transition at some time later when the molecule is in its
electronic ground state.
as a result of the light-induced change; in other words, PSHB
had occurred. A further scan some minutes later (trace e)
showed that the molecule surprisingly returned to the burning frequency. After trace g the molecule was “burnt” again,
and the whole sequence could be repeated several times.
The exact location of the new resonance frequency, however, could not be determined in these experiments. By analogy with previous nonphotochemical hole-burning studies
of large ensembles of molecules,” ’I the shift may be expected
to be as much as IOOcrn-’. Besides the reversible singlemolecule hole-burning illustrated in Figure 17, it was possible to observe other single molecules where the lightinduced change was irreversible on the timescale of the experiment. The irreversible process was more common at high
light power levels.
The possibility of burning one and the same molecule several times was used to determine the power dependence of
single-molecule PSHB and to measure the kinetics of this
process. Figure 18 shows that with increasing power, the
burning time, although stochastically distributed, decreases.
The power dependence of the hole-burning process was confirmed in this way for many single molecules. The experiments unambiguously showed that the single-molecule holeburning is truly a light-driven process in contrast to
excitation-power-independent spectral diffusion.
6.5. Measurement of the Stochastic Phototransformation
Kinetics of a Single Molecule
The single-molecule hole-burning experiments are measurements with a single quantum system, although the molecule and its surrounding matrix cage have to be regarded as
a kind of “supermolecule”. Therefore, it is not surprising
that the burning time for one molecule at a fixed power level
is a stochastic quantity. By measuring a large number of
burning events for one and the same perylene molecule in a
polyethylene host it was shown that the burning times are
exponentially distributed (Fig. 1 9).I7O1 This may be understood by the following simple argument.
I
400 1
350
300
t
250
200
NFI
[IOS”I
150
1800
1600
1400
ts Is1
1200
1000 1
0
200
t IS1
-
..
400
Fig. 18. Illustration of the power dependence of the hole-burning process for a
single perylene molecule in a polyethylene film. a) The laser is tuned to resonance ( i = 448.159 nm) with the single molecule in the first 10 s a t a power level
of 4.5 nW. The abrupt drop of the fluorescence signal at 260 s is the hole-burning event; the return of the fluorescence signal indicates that the molecule has
returned to its original frequency, only to be burnt again, and so on. b) The
laser power level was increased to 27 nW; now the time in resonance, although
stochastic. is clearly shorter (after ref. [29]).
In Section 6.3 two types of TLSs interacting with the impurity were discussed, those producing broadened singlemolecule lineshapes, and those producing resonance frequency jumps. There are, however, also the so-called
external TLSs which are created by doping the host with the
impurity molecules.1711These TLSs are thought to be in the
close vicinity of the impurity and effectively locked because
the barrier to configurational changes is too high. A common model for nonphotochemical hole-burning” 71 assumes
that by optical excitation of the impurity this barrier is lowA n j y w . Chein. I n [ . Ed. EngI. 1993. 32, 457-476
.
600
-
Fig. 19. Histogram of a random sample of 54 burning events measured for a
single perylene molecule in a polyethylene matrix by using a power level of
4.5 nW ( T = 1.5 K, 1 = 448.156 nm). The plotted curve is the result ofan exponential fit to the data (after ref. 1701). N is the number of events per time interval.
Single-molecule hole-burning is an example of a Poisson
random process. The probability distribution for r successes
(hole formation) in a finite time interval 7 is therefore given
by P(r,7) = exp( - Az)/(Azyr!. In the hole-burning experiment, however, the waiting time before the first burning
event (ix. r = 0) was measured, and this waiting time therefore has the probability distribution P(O,r) = exp( - 1-7).
This corresponds to the familiar result that the distribution
of waiting times between Poisson random events is exponential. The smooth curve in Figure 19 is a result of a fit of a
simple exponential to the data. The histogram of the random
sample of burning times is reasonably well approximated by
an exponential distribution function with rate parameter
A = 0.18 s-I. This also means that the single perylene molecule investigated has an average hole-burning quantum eficieny of 2.9 x
per photon absorbed.
47 1
It is interesting to point out a formal analogy between
these experiments and “quantum-jump” measurements with
single trapped ions in a vacuum. In the latter investigations
the bright fluorescence from a strong (allowed) transition
ceases when the single atom “‘jumps” into a dark state which
is weakly coupled to the ground state by a forbidden transition. In this case the number of quantum jumps per unit time
is given by a Poisson distribution and the waiting times between quantum jumps by an exponential distribution as
we.l,172, 731
positions of the various single molecules. The data were used
to determine that the internal fields ranged from - 1.6 x
lo3 kVcm-’ to +0.8 x lo3 kVcm-’, and that the polarizability change Ax ranged from 1.1 x
Fm2 to 2.5 x
Fm2. The unambiguous observation of a quadratic
shift, which was relatively constant from molecule to rnolecule, and a first-order shift, which varied considerably from
molecule to molecule, gives direct evidence for one underlying source of inhomogeneous broadening that has been long
postulated -randomness in the local crystal field.
7. Stark Effect Studies with Single Molecules
7.2. Terrylene in Polyethylene
The fact that spectra of a single molecule in a solid can be
obtained with high signal-to-noise ratios naturally leads to
measurements of such spectra under the influence of external
fields. One can imagine that Zeeman effects, Stark effects.
and stress-induced splittings and shifts can be observed. In
recent work, two groups have completed Stark effect studies
on single molecules, in one case in a crystalline host and in
the other case, a polymeric host.
Numerous Stark effect studies of impurity molecules in
amorphous materials have been performed over the last
decade by using hole-burning technique^."^. ”I Even with
centrosymmetric molecules, only linear Stark effects were
observed, due to the reduction of symmetry caused by local
fields. To address the important question as to whether or
not linear Stark effects persist down to the single-molecule
level, Orrit et al. have recently studied a new system composed of terrylene molecules in low-density polyethylene.1321
The terrylene molecule is similar to perylene, except that
three rather than two naphthalene molecules are condensed
at the peri positions. This modification conveniently shifts
the first electronic transition to longer wavelengths. The thin
films were sandwiched between two transparent conducting
plates for the optical measurements. As with pentacene in
p-terphenyl, only shifts of the single-molecule lines were observed.
Figure 21 shows the observed frequency shifts for a selection of six single molecules. Only linear Stark shifts were
detected, suggesting that the local fields were quite effective
7.1. Pentacene in p-Terphenyl Crystals
The first single-molecule Stark effect studies of the pentacenelp-terphenyl system were performed by Wild et al. using a longitudinal geometry in which the sample was held
between a thin metal plate with a 5 pn pinhole and a Sn0,coated glass plate.[311(In fact, both the linear and quadratic
Stark effects for this single-molecule system were utilized in
the double-modulation scheme reported in Section 3 for the
initial detection of single molecules with F M absorption.) In
the recent work, fluorescence excitation spectra of single
molecules were recorded with various DC external electric
fields applied in order to determine specific values for the
polarizability change and the internal field. In all cases. only
shifts and no splittings of the single molecule spectra were
observed.
Figure 20 shows the energy shifts recorded for four single
molecules, along with best-fits to the data using second-
1.0
-
0.0
--
dU
[GHzl
€ [kV crn-’l
-
Fig. 20 Stark shift of four molecules of pentacene A-D in p-terphenyl as ii
function of electric field The plotted curves are the result of second-order
polynomial fits to the data (after ref. [ i l l ) .
order polynomial^.[^ In general, a quadratic shift was observed with an offset from zero which was different for different molecules. The high symmetry of the pentacene molecule is consistent with a quadratic shift, and the linear
term was attributed to different internal crystal fields at the
472
E IkV cm-‘]
-
Fig. 21. Stark shift o f single terrylene molecules 111 polyethylene as a function of
electric field. The plots are linear to within experimental error; the magnitudes
and signs of the slopcs depend upon the orientation of the field relative to the
molecule and the matrix cage. The largest slope corresponds to a change in
dipole moment of several Debye (after ref. [ 3 2 ] ) .
Angeu. Chrm. hi.Ed. Engl. 1993, 32, 457 -476
in lowering the molecular symmetry. By studying a large
number of single molecules, the distribution of Stark coefficients could be sampled, and positive coefficients were found
to be more common than negative coefficients. It is certainly
clear that these results provide individual measurements of
the local fields, and that such perturbations are averaged in
the conventional measurements at large values of NH.If it
will be possible to measure the splitting coefficients for a
single molecule with several directions of applied field, more
specific information about the local symmetries may be obtained.
8. Measurements of Quantum Effects with Single
Molecules in Solids
In all the experiments described in the preceding sections
the single molecule served as an ultrasensitive probe for measuring truly local host-guest interactions. A single molecule
can also be used to study the fundamental interaction of light
and matter in experiments in which the fully quantummechanical nature of this interaction is revealed. So far investigations of this type with single particles were limited to
single atoms stored in radio-frequency traps by photonrecoil cooling. A variety of fascinating experiments such as
quantum jumps, quantum collapse and revival, photon antibunching, and many others were realized with laser-cooled
ions.“. However, for all molecules, even diatomic species,
the internal degrees of freedom prevent laser-cooling, and
therefore trapping of a single molecule in a vacuum has not
been achieved to date. As illustrated in the earlier part of this
paper, however, single molecules can be easily “trapped”
and observed optically in a solid. When the molecules are
impurities in a solid and the samples are cooled to liquidhelium temperatures, the solid acts as a “trap” for the single
impurity molecules. They are effectively held at rest, and in
many cases, rotation of the impurity molecule is quenched
and recoil effects are usually small (less than the optical
line~idth).‘~’.
761
One interesting aspect of the interaction of light and matter concerns the correlation between photons radiated by a
single atom or molecule. As was shown for Na atoms in a
weak atomic beam177Jor a single trapped Mg’ ion,[781the
correlation between successive photons emitted by a single
atom (ion) decreases near t = 0 (photon antibunching). This
is in marked contrast to the case for coherent light, where the
correlation is independent of the time separation between
photons, and for thermal light, which shows an increase in
correlation (photon bunching) near t = 0.
Photon antibunching in the resonance fluorescence of a
single atom was predicted by Carmichael and Walls.[791This
phenomenon is a true signature of a quantum-mechanical
radiation field which can be nicely rationalized with the following simple picture. In the correlation measurement the
joint probability for the arrival of a photon at time t = 0 and
the arrival of a photon at t > 0 is recorded. After emission of
a photon at i = 0 the quantum system is in its ground state
since it just emitted the photon. The probability of emitting
a second photon at t = 0 is zero because the molecule cannot
emit from the ground state. On the average, a time of half a
Rabi period must elapse for the molecule to have a finite
Angew. Chrm. Inr. Ed. Engl. 1993, 32, 451-476
probability of being in the excited state and hence emitting a
second photon.
Photon antibunching must be observed on a short timescale comparable to the excited singlet-state lifetime. Correlation measurements on the nanosecond timescale, or to be
more specific, measurements of the second-order or intensity
correlation function g(”(2) were performed with single pentacene molecules in a p-terphenyl host.[331The exciting laser
pumped the lowest zero-phonon purely electronic transition
S , + So,and the photon correlation properties of the vibronically shifted fluorescence from the excited singlet state S,
were analyzed. As in the single-atom experiments. the delay
time distribution of consecutive pairs, N ( z ) , which is proportional to g”)(T), was measured in a Start-Stop experiment,
that is, by using a beamsplitter and two photomultipliers
(PMTs) to record the emitted fluorescence. Detection of a
photon from the first PMT starts a delay time counter, and
the detection of a photon by a second PMT stops the counter. The distribution of such delay times is recorded for many
Start-Stop pairs.
Plots of N(z) are shown in Figure 22 for different levels of
Rabi frequency (which is proportional to the square root of
the intensity). The antibunching in the correlation function
is clearly evident at short times t -+ 0. With increasing power
the background due to accidental pair correlations increases,
leading to an increasing deviation of N(2) from zero at the
origin. The solid lines in Figure 22 show the resuIts of numerical fits to the data using the solutions of the optical Bloch
equations for a three-level system. At the highest power level
(Fig. 22 c) the correlation function shows, besides the antibunching, the expected Rabi oscillations which are damped
out during the excited state lifetime.
40
30
N I’d
20
10
12
1
8
NIT)
4
0
-100
0
100
thsl
-
200
Fig. 22. Measured intensity correlation N(T)(in counts per 0.9 ns] for a single
pentacene molecule ( A % 593.4 nm). The antibunching is clearly seen for f -t 0.
Rabi frequencies SZ: a) 11.2 MHz; b) 26.2 MHz; c) 68.9 MHr. The solid lines
are fits to the data with $2= I -10 MHz (a), 25.5 MHz (b), and 71.3 MHz (c)
(after ref. [33]).
473
Since pentacene in p-terphenyl is effectively a three-level
system when lowest triplet state is included, photon bunching should be observed for much longer times, comparable to
the 40 ps triplet lifetime. This is a consequence of the fact
that on average, the pentacene molecule emits roughly
200 photons due to singlet-singlet excitation before intersystem crossing into the “dark” triplet state occurs (the triplet
yield is 0.0047[57]).This purely classical effect was observed
clearly by Orrit et al.[251and used to prove that the spectra
in the early experiments arose from single molecules.
These first results on quantum optics in a solid demonstrate that single-molecule spectroscopy in solids can be used
to investigate truly quantum-mechanical effects for multiatom molecules with zero-phonon optical transitions. Here
the experimental data were not affected by transit time or
secular motion effects as are the beam or ion-trapping methods. However, background signals and intersystem crossing
into the triplet state did limit the single-molecule antibunching signal and must be controlled in each specific case. As
long as the lowest electronic transition of the molecule is
pumped, the presence of vibrational levels in the ground
state and the detection of nonresonant fluorescence does not
prevent the observation of photon antibunching.
9. Summary and Outlook
By utilizing the near-quantum-limited performance and
low background of laser frequency modulated (FM) spectroscopy, the intrinsic fine structure on inhomogeneous lines
in solids, statistical fine structure (SFS), was detected for the
first time. With a detailed understanding of SFS and improvements to FM spectroscopy to remove residual amplitude modulation (RAM), it thus became possible to measure
the optical absorption spectrum of a single molecule of pentacene in p-terphenyl. Dramatic improvements in the signalto-noise ratio resulting from the use of fluorescence excitation with high-efficiency collection led to the observation of
lifetime-limited widths, to saturation and dephasing studies,
and to the surprising observation of spectral diffusion for a
single impurity molecule in a crystal. Extensions of these
investigations to systems with polymeric hosts allowed study
of the spectral diffusion process widely postulated in amorphous materials, as well as to the observation of spectral
hole-burning and stochastic kinetics for a single molecule.
Stark effect studies in both crystals and polymers have yielded important new information about local symmetries and
local fields. Fially, single-molecule techniques in recent work
have led to the first quantum optics in a solid-the detection
of photon antibunching for a single molecule.
The success of single-molecule detection and spectroscopy
in solids opens up a new frontier of single-absorber experiments in which the measured properties of the absorbing
center are not averaged over many “equivalent” absorbers.
Here the absorbing entity is exquisitely sensitive to the symmetry and perturbations introduced by the local environment such as the local vibrational modes and the true local
fields. While as a general technique the method presented
here is not applicable to all molecular impurities, it can be
applied to the large number of absorbing ions and molecules
in solids that have zero-phonon transitions, reasonable ab474
sorption strength, and efficient fluorescence. The detectability of the resulting single-center signal, which ultimately depends upon the specific sample and weak or absent spectral
hole-burning, must be evaluated in each case.
A number of fascinating future experiments based on the
single-molecule detection techniques presented here may be
contemplated. The temperature dependence of the spectral
diffusion process in crystals may help to identify the source
of the effect. It would be particularly interesting to measure
the temperature dependence of the linewidth in a polymeric
host to attempt to resolve the current controversy about
dephasing processes in these systems. Nonlinear spectroscopy to measure the dynamic Stark effect for a single
isolated molecule may also be performed. With the proper
choice of lifetimes, one would expect quantum jumps and
other processes observed for single ions in vacuum electromagnetic traps to become directly observable. The door is
also open to true photochemical experiments on single absorbers, measurements of the dispersed fluorescence from a
single molecule, and the possibility of optical storage with
single m o I e c u I e ~ . [ ~ ~ ~
In one novel experiment now possible the emission from a
single molecule could be used as a light source of subnanometer-dimensions for near-field optical microscopy.
Another possibility would be to perform cavity quantum
electrodynamics studies with a single molecule in a solid. It
is to be expected that single-molecule spectra will be obtained at higher and higher temperatures to extend the applicability of these studies to a wider range of materials. In all
cases, improvements in the signal-to-noise ratio would be
expected to open up a new class of applications. Because this
field is only in its infancy, the possibilities are only limited at
present by the imagination and the persistence of the experimenter and the continuing interest of the theoretician in the
properties of single-quantum systems in solids.
10. Glossary
Coherent transient spectroscopy and photon echoes: In the
present context we will limit our short explanation to the
case of optical coherent spectroscopy where only two levels,
the ground and excited electronic state of an atom or molecule, are involved. Coherent excitation of such a system with
sufficiently high intensity lasers creates a coherent superposition of the ground and excited state wave functions. The
coherent superposition, which is characterized by a welldefined phase relation between the two levels, leads to interference effects whose time evolution can be monitored with
special spectroscopic techniques. The coherent state is described by the off-diagonal elements of the two-level density
matrix in the optical Bloch equation formalism. The coherence is a transient phenomenon which is destroyed rapidly
by population and phase relaxation processes. One example
of coherent transient spectroscopy is the photon echo where
the decaying coherence initially created by a first intense
light pulse can be reestablished by a properly timed second
light pulse. The photon echo can be formally described by
the time evolution of a pseudo-spin vector in a fashion equivalent to the spin echo in magnetic resonance spectroscopy.
Angew. Chem. h i . Ed. Engl. 1993,32,457-416
The time decay of the photon echo amplitude also gives
information about the underlying homogeneous width
when inhomogeneous broadening is present. See for example, L. Allen, J. H. Eberly, Optical Resonance and TwoLevel Atoms, Dover, New York, 1987.
Electron-phonon coupling and zero-phonon transition :
When an impurity molecule in a solid matrix is electronically
excited, the host vibrations (phonons) can couple to the electronic excitation (electron-phonon coupling) in the same
way as is well known for the intramolecular vibrations of the
impurity. Linear electron-phonon coupling, where the coupling strength is given by the displacement of the excited
state potential surface with respect to the ground state potential surface, gives rise to phonon sidebands of the purely
electronic transition line in absorption and emission. The
purely electronic transition with no net creation or destruction of phonons is called the zero-phonon transition and can
be viewed as the optical analogue of the recoil-free
Mossbauer line. Quadratic electron-phonon coupling leads
to a broadening of the zero-phonon line by phonon scattering. See for example, A. M. Stoneham, Rev. Mod. Phys.
1969, 41, 82; R. H. Silsbee, in Optical Properties of Solids,
(Eds.: S . Nudelman, S. S. Mitra), Plenum, New York, 1969,
p. 607; K. K. Rebane, Impurity Spectra of Solids, Plenum,
New York, 1970, p. 99.
Frequency modulation (FM) spectroscopy: In FM spectroscopy the laser is frequency-modulated at a high frequency, narrow spectral features in the sample convert the frequency modulation into amplitude modulation, and the
amplitude modulation of the light beam is detected with a
high-speed detector and a lock-in amplifier. See G. C.
Bjorklund, M. D. Levenson, W. Lenth, C. Ortiz, Appl. Phys.
B 1983, 32, 145.
FWHM: Full width at half-maximum; a convention for
measuring the width of spectral lines or of laser beam profiles.
Photon antibunching: A purely quantum-mechanical correlation property of a light beam which states that the probability of detecting two photons separated by a small time
interval At approaches zero as At 0. See for example,
R. Loudon, The Quantum Theory of Light, Clarendon,
Oxford, 1983, pp. 226-229.
Rabi period: In the time evolution of a two-level atomic
system pumped by light, the Rabi period is the time required
for the superposition of the two states to go from pure
ground state, through the excited state, and back to the pure
ground state again. See L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms, Dover, New York, 1987.
Residual amplitude modulation (RAM): Unwanted amplitude modulation of the laser beam in FM spectroscopy
which represents a spurious background signal that can limit
sensitivity. See for example, E. A. Whittaker, M. Gehrtz,
G. C. Bjorklund, J. Opt. SOC.Am. B 1985, 2, 1320.
Statistical fine structure (SFS): This effect refers to the
intrinsic variations in absorption coefficient versus wavelength which occur for inhomogeneously broadened transitions due to number fluctuations in the spectral density of
absorbers. See T. P. Carter, M. Manavi, W. E. Moerner, J.
Chem. Phys. 1988, 89, 1768.
SMD: Single-molecule detection.
SNR: Signal-to-noise ratio.
--f
Angew. Chem. Int. Ed. Engl. 1993. 32,457-476
Spectral hole-burning: In spectral hole-burning experiments, narrow-bandwidth laser irradiation is used to select
the resonantly absorbing subensemble of molecules out of an
inhomogeneously broadened absorption profile. The optical
excitation induces either photochemical changes in the excited centers or photophysical (nonphotochemical) alterations
in the nearby host, and a narrow dip (spectral hole) can
develop in the absorption spectrum because the altered centers no longer absorb at the laser wavelength. The width of
the spectral hole can provide information about the underlying homogeneous linewidth when spectral diffusion effects
are absent. Peristent spectral hole-burning (PSHB) refers
to the situation in which the spectral hole lasts longer than
any excited state lifetime. See for example, J. Friedrich,
D. Haarer, Angew. Chem. 1984, 96, 96; Angew. Chem. Int.
Ed. Engl. 1984, 23, 113; R. Jankowiak, G. J. Small, Science
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We are grateful to the Research Division of International
Business Machines Corporation and to the U . S. Office of
Naval Research for support of this research. We also acknowledge our colleagues, Drs. PV P . Ambrose, T P . Carter, and L.
Kador for their work which laid the,foundationsfor singlemolecule spectroscopy in solids.
Received: August 13, 1992 [ A 898 IE)
German version: Angew. Chem. 1993, 105, 537
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