17078
J. Phys. Chem. 1995,99, 17078-17081
Measurement of Optical Dephasing of a Single Terrylene Molecule with Nanosecond Time Resolution S. Kummer, S. Mais, and Th. BaschC* Institut jiir Physikalische Chemie, Universitat Miinchen, Sophienstrasse 11, 80333 Munchen, FRG Received: July 17, 1995; In Final Form: October 4, 1995@
We report on the investigation of temperature dependent optical dephasing of single tenylene molecules in a p-terphenyl host crystal using two different techniques. The temperature dependence of the optical linewidth between 2 and 7.2 K can be described by an exponentially activated process with an activation energy AE = 18 f 2 cm-', which is attributed to optical dephasing of the electronic transition by scattering of a pseudolocal mode. By measuring the fluorescence intensity autoconelation function we demonstrate that the dephasing time of a single terrylene molecule can also be extracted from coherent transients (Rabi oscillations) appearing in the correlation function in the nanosecond time regime. These oscillations experience an increased damping at temperatures above 2 K due to pseudolocal mode-induced pure dephasing.
Introduction Optical dephasing of molecular electronic transitions in lowtemperature solids has been studied extensively with time and frequency domain techniques. In the time domain coherent optical transients as optical nutation and photon echoes were employed,' while in the frequency domain spectral hole burning2 or fluorescence line narrowing3 was used. All these linenarrowing techniques allow the determination of energy ( T I ) and phase (7'3 relaxation rates and their temperature dependence by measuring the homogeneous line width in the presence of the ubiquitous inhomogeneous broadening. In disordered solids spectral diffusion may contribute as an additional mechanism to the line ~ i d t h . ~ . ~ The optical excitation line shape of a single molecule in a solid6-* directly gives-in the absence of spectral diffusion-the homogeneous line width of the electronic transition as, once a single molecule has been isolated, no inhomogeneity is left. In this respect single-molecule spectroscopy (SMS) can be regarded as a line-narrowing technique. In this paper we report on temperature-dependent optical measurements with single terrylene molecules doped into a p-terphenyl crystal. This system was introduced recently for the purpose of SMS9 and due to the high single-molecule signal strength allowed the observation of several new effects, e.g., quantum jumps between the singlet and triplet statelo and the dynamical Stark effect (light shift)." The temperature dependence of the excitation line shape has been measured for single molecules in crystalline'2 and amorphous systems.I3 For single pentacene molecules in p-terphenyl the temperature broadening of the optical line width between 1.6 and 10 K was shown to be exponentially activatedI2 in accordance with earlier photon-echo experiments on the same ~ y s t e m . ' ~Such , ' ~ behavior is typical for organic mixed crystals at low temperatures and is interpreted by dephasing of the optical transition through coupling of a pseudolocal mode (libration).I6 From temperature-dependent line-width measurements on single terrylene molecules in p-terphenyl presented here, we also derive an exponentially activated process whose activation energy was found to be AE = 18 f 2 cm-I. To our knowledge, these are the first temperature-dependent data available in this system. *I
To whom correspondence should be sent. Abstract published in Aduunce ACS Ahsrrucrr, November 1, 1995
0022-3654/95/2099- 17078$09.00/0
The fluorescence photons emitted by a single molecule are strongly correlated reflecting the dynamical processes undergone by the molecule. Photon bunching due to the temporal shelving of the molecule in the triplet statet7or photon antibunching due to the vanishing joint probability for the emission of two fluorescence photons at the same time'* are typical effects that can be observed in the fluorescence intensity autocorrelation function of a single dye molecule. When a molecule is excited at high intensity, the correlation function besides the anticorrelation at short times shows coherent Rabi oscillations that may be damped by energy and phase relaxation processes.'8 Coherence damping of transient spin nutations of single pentacene molecules in the microsecond time regime has also been reported re~ent1y.I~For single terrylene molecules in p-terphenyl we find that at 2 K the Rabi oscillations are damped by T I processes 3 K) an additional only, while at higher temperatures ( T damping attributable to pure optical dephasing ( T 3 is observed. The measurements presented here show the feasibility of studying single-molecule optical dephasing by the observation of coherent optical transients in the correlation function in the nanosecond time regime.
Experimental Section Single crystals of zone-refined p-terphenyl doped with terrylene were grown by cosublimation of a mixture of the two compounds. As was reported recently? terrylene in p-terphenyl possesses four electronic origins which were attributed to four different crystalline sites. The single molecules investigated in this study stem from site X? because we found the molecules to be very photostable in this site. The concentration of terrylene was so low that typically only three to five molecules were observed in a 30 GHz frequency range centered at the transition frequency of site X2 (578.48 nm). The samples were mounted at constant pressure in a He-flow cryostat, and temperatures between 2 and 7.2 K were adjusted by controlling the heat flow at the exchanger. The temperature accuracy was estimated to be better than 0.02 K. The experimental setup for SMS can be found in the literature. l 2 For the line-width measurements, fluorescence excitation spectra were recorded by scanning a single-frequency rhodamine 6G dye laser over the molecular resonance line while detecting the Stokes-shifted fluorescence with a photomultiplier. To measure the fluorescence intensity autocorrelation function 0 1995 American Chemical Society
Letters
J, Phys, Chem., Vol. 99,No. 47, 1995 17079
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Figure 1. Temperature dependence of the homogeneous line width (fwhm) of a single tenylene molecule in p-terphenyl as derived from fluorescence excitation spectra (U). The drawn line is the result of a fit of eq 2 to the data (AE = 18 f 2 cm-I). The circles at 2, 3, and 4 K represent the homogeneous line widths as computed from the correlation data (see text). Inset: fluorescence excitation spectra of the terrylene molecule at 2 and 5 K. (0 MHz 578.515 nm.)
for a single molecule simultaneously from nanoseconds up to seconds as was done here, two different correlation schemes had to be used. The photon stream emitted by the single molecule was first divided by a beam splitter (50/50)and the number distribution of the time separation of consecutive photon pairs in the nanosecond time regime was measured by a startstop technique. In our setup the output pulses of two phototubes were normalized by constant-fraction discriminators and activated the start and stop inputs of a time-to-amplitude converter (TAC). The voltage pulses from the TAC were stqred in a multichannel analyzer. Under the experimental conditions (low count rates and short separation times) the resulting distribution of start-stop pairs is indistinguishable from the full correlation function. The (full) correlation function for times > 1 ps was measured simultaneously by a digital logarithmic correlator fed by the second output channel of one of the discriminators. Summarizing, the start-stop technique covers the time range 1 ns < t 1 ps while the digital correlator works for longer times from 1 ps up to 1000 s.
experiment. This would not be the case in line-narrowing spectroscopy with large ensembles of molecules when investigating materials that do not show hole buming. For a system as the XZsite of tenylene in p-terphenyl where the hole-buming yield is negligible, the homogeneous line width would be typically determined by the photon-echo technique, which however gives no hint on the line shift. The latter would be accessible only in a rather crude manner by shifting the whole inhomogeneous line. The line widths (fwhm)in Figure 1 were determined by fitling Lorentzians to the excitation spectra at different temperatures. Below 2.5 K the line width is almost constant (Avhom= 43 MHz) and close to the lifetime-limited value (42 MHz), one would expect from the fluorescence lifetime of terrylene in polyethylene.20 The line width increases rapidly with temperature above 2.5 K, and in analogy to pentacene in p-terphenyl we fitted the temperature dependence of the line width with the following expression which serves as a good approximation for the description of optical dephasing by a pseudolocal mode in the weak coupling limit:I4
Avhom= -- -+Aexp(-AE/kr) nT2 2nT, It is seen in Figure 1 that the data can be very well approximated by eq 2 with AE = 18 f 2 cm-I. For several other single terrylene molecules we also found the same exponentially activated behavior. The line shift for this molecule follows the same temperature dependence, but this subject will be discussed in more detail in a forthqoming publication.2' In analogy with similar results for pentacene in p-terphenyl we interpret AE to be the energy of a pseudolocal mode (libration) of the terrylene molecule. The preexponential factor A relates to the lifetime and energy of the local mode in the electronic ground and excited state.I6 Having gained knowledge about the optical dephasing process by measuring the homogeneous line width at various temperatures, we now proceed to demonstrate how the dephasing rate can be extracted from the fluorescence correlation function of a single molecule. In general, the normalized fluorescence intensity autocorrelation function g(2)(z)for a single molecule is given by the following expression:
Results and Discussion The homogeneous optical line width (fwhm) of an impurity electronic transition in a solid is given by the following equation: 1 1 1 Avhom= -= nT2 2 n T , + where T2 is the dephasing time, T I the fluorescence lifetime, and TT the pure dephasing time. At low temperatures, TF becomes very large and the line width is dominated by the lifetime contribution. This result holds for molecular crystals in the absence of spectral diffusion. The temperature dependence of the optical line width between 2 and 7.2 K of a single terrylene molecule in p-terphenyl is shown in Figure 1. In the inset of Figure 1 fluorescence excitation spectra of the same terrylene molecule are displayed at temperatures of 2 and 5 K, respectively. By raising the temperature, the line broadens appreciably and shifts to the red with respect to the low-temperature spectrum. These data nicely demonstrate that from single-molecule spectra the homogeneous line width and line shift can be extracted readily in a single
where If is the fluorescence intensity. In the correlation measurement pairs of photons separated by time z are detected under stationary conditions by illuminating the molecule with continuous-wave laser radiation. The time evolution of the correlation function has been related to the dynamics of the molecule by solving the Bloch equations for the density matrix of an electronic three-level system representing a typical organic dye m ~ l e c u l e . ' ~ ~ ' ~ In Figure 2, g@)(t)is shown for a single terrylene molecule. First, we want to point out that the time axis in Figure 2 is logarithmic and covers 9 orders of magnitude. The time range between 40 ns and 1 ps not covered in Figure 2 would be easily accessible with the start-stop technique. Second, there are different time regimes in the correlation function which contain valuable information about the molecular dynamics. The-in the case of terrylene-biexponential decay of the Correlation function around 1 ms is caused by photon bunching through shelving of the optical electron in the long-lived triplet-state sublevels of t e ~ y l e n e .The ~ anticorrelation at short times is attributed to the nonclassical effect of photon antibunching.I8
17080 J. Phys, Chem., Vol, 99,No. 47, 1995 1.2
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Figure 2. Normalized fluorescence intensity autocorrelation function g(*)(t)for a single tenylene molecule in p-terphenyl at 2 K measured over 9 orders of magnitude in time ( 0 ) .The drawn line is a simulation of the correlation function according to the solution of the optical Bloch equations for a three-level system using appropriate photophysical parameters. Here we are interested in the oscillatory behavior (Rabi oscillations) of the correlation function appearing around 10 ns in Figure 2. Neglecting the triplet state, g(2)(z)at short times can be approximated by the following expression:
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g ( 2 ) ( t at ) short times for the same single terrylene molecule having been the source of the data shown in Figure 1. The drawn lines are fits of eq 4 to the data ( 0 ) :(a) 2 K; (b) 4 K. It is clearly seen that by raising the temperature the Rabi oscillationsbecome subject to stronger damping caused by pure dephasing.
TABLE 1: Values of TI and T $ at Two Different Temperatures As Calculated from Line-Width and Correlation Function Data
con function line width where r2 = UT2 = 1/2T1 l/T,*is the dephasing contribution, k21 = UTI the fluorescence rate, and R = Iji12E//hdenotes the on-resonance Rabi frequency. The factor B accounts for the background contribution caused by stray light which leads to a deviation of g(2)(0)from zero.i8 When pure dephasing can be neglected, the argument of the exponential reduces to -3/4k2~z and eq 4 becomes equivalent to the expression used to describe the correlation function of a single ion in a vacuum trap.22 Besides the antibunching near z = 0, the above equation describes the Rabi oscillations at short times (10 ns) and contains UT1 and UT: as damping terms. Including the triplet state would add a (bi-)exponentially decaying term at long times (milliseconds) and shift g(2)(r)along the ordinate (see Figure 2). In Figure 3, g(*)(z) is plotted at 2 and 4 K for the same molecule the data of which appeared in Figure 1. By adding a delay in the stop channel the correlation function could also be measured at “negative” times which helps to establish time zero. It is seen that by raising the temperature, the Rabi oscillations become subject to much stronger damping. This can be easily explained with reference to Figure 1. At elevated temperatures pure optical dephasing caused by coupling of the local mode to the electronic transition contributes to T2 and hence the Rabi oscillations are damped more strongly. In Table 1 the values for TI and Tf, as derived from the correlation and line-width measurements by fitting eqs 4 and 1, respectively, to the experimental data, are combined. The value of the Rabi frequency at 2 K used in the fitting procedure was shown to be consistent with that derived from light shift (dynamical Stark effect) measurements using similar intensity for the pump beam.’ This is important because we know neither the value
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of the transition dipole moment nor the exact electric field seen by the molecule. The free space peak intensity at the sample was estimated to be 100 W/cm2. Furthermore, the reasonable and for many systems experimentally verified assumption was made that TI remains constant over the investigated temperature range. The agreement of T : when comparing both measurements is satisfying and demonstrates that both techniques measure the same quantity. The homogeneous line widths calculated from the T2 values determined by the correlation measurements are also plotted in Figure 1. The coherent transient observed in the Correlation function can be interpreted as the single molecule analogue of an optical nutation experiment within an ensemble of molecules where the coherence of the ensemble would be established by a short laser pulse. In a single-molecule experiment coherence can be observed even under continuous excitation, and as justified by the ergodic hypothesis we treat time averages of a single quantum system with the density matrix description derived for an ensemble. As the optical nutation experiment does for ensembles, the correlation technique allows us to measure dephasing processes of a single molecule on a time scale of nanoseconds. It is clear that any reliable measurement with this technique requires the dynamics of the system to be stationary for the recording time of the correlation function. Additionally, it was demonstrated experimentally in this paper that by measurement of the fluorescence correlation function single-molecule dynamics can be investigated simultaneously over 9 orders of magnitude in time.
Acknowledgment. Financial support by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie
Letters
is gratefully acknowledged. We would like to thank C. Brauchle for his continuing interest and support related to this work. References and Notes (1) Wiersma, D. A. In Photoselectiue Chemistry, Part 2; Adv. Chem. Phys.; Jortner, J., Levine, R. D., Rice, S. A., Eds.; Wiley: New York, 1981; Vol. 47. (2) See: Moerner, W. E., Ed. Persistent Spectral Hole-Burning: Science and Applications; Springer: Berlin, 1988. (3) See: Yen, W. M., Selzer, P. M., Eds. Laser Spectroscopy of Solids; Top. Appl. Phys.; Springer: New York, 1986; Vol. 49. (4) Friedrich, J.; Haarer, D. In Optical Spectroscopy of Glasses; Zschokke, I., Ed.; Reidel: Dordrecht, 1986. (5) Narasimhan, L. R.; Littau, K. A.; Pack, D. W.; Bai, Y. S.; Elschner, A.; Fayer, M. D. Chem. Rev. 1990, 90, 439. (6) Moemer, W. E.; Bascht, Th. Angew. Chem. 1993, 105,537; Angew. Chem., lnt. Ed. Engl. 1993, 32, 457. (7) Omt, M.; Bernard, J.; Personov, R. I. J . Phys. Chem. 1993, 97, 10256. (8) Moerner, W. E. Science 1994, 265, 46. (9) (a) Kummer, S.; BaschC, Th.; Brauchle, C. Chem. Phys. Lett. 1994, 229, 309. (b) Kummer, S.; Bascht, Th.; Brauchle, C. Chem. Phys. Lett. 1995, 232, 414. (10) Bascht, Th.; Kummer, S.; Brauchle, C. Nature 1995, 373, 132.
J. Phys. Chem., Vol. 99, No. 47, 1995 17081 (11) Tamarat, Ph.; Lounis, B.; Bernard, J.; Orrit, M.; Kummer, S.; Kettner, R.; Mais, S.; BaschB, Th. Phys. Rev. Lett. 1995, 75, 1514. (12) Ambrose, W. P.; BaschC, Th.; Moerner, W. E. J . Chem. Phys. 1991, 95, 7150. (13) Fleury, L.; Zumbusch, A.; Orrit, M.; Brown, R.; Bernard, J. J . Lumin. 1993, 56, 15. (14) Hesselink, W. H.; Wiersma, D. A. J . Chem. Phys. 1980, 73, 648. Wilson, W. L.; Lee, H. W. H.; Fayer, M. D. Chem. (15) Patterson, F. G.; Phys. Lett. 1984, 110, 7. (16) (a) Hsu, D.; Skinner, J. L. J . Chem. Phys. 1985, 83, 2097. (b) Hsu, D.; Skinner, J. L. J . Chem. Phys. 1985, 83, 2107. (17) Bernard, J.; Fleury, L.; Talon, H.; Onit, M. J . Chem. Phys. 1993, 98. 850. (18) Bascht, Th.; Moerner, W. E.; Orrit, M.; Talon, H. Phys. Rev. Lett. 1992, 69, 1516. (19) Wrachtrup, J.; von Borczyskowski, C.; Bernard, J.; Onit, M.; Brown, R. Phys. Rev. Lett. 1993, 71, 3565. (20) Moemer, W. E.; Plakhotnik, T.; Imgartinger, T.; Croci, M.; Palm, V.; Wild, U. P. J . Phys. Chem. 1994, 98, 7382. (21) Kummer, S.; Kettner, R.; BaschC, Th. J . Phys. Chem., to be published. (22) Diedrich, F.; Walther, H. Phys. Rev. Lett. 1987, 58, 203. JP95 19777
