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Temperature-dependent electronic dephasing of molecules in polymers in the range 30 to 300 K
28 November 1997
Chemical Physics Letters 280 Ž1997. 127–133
Temperature-dependent electronic dephasing of molecules in polymers in the range 30 to 300 K C.J. Bardeen
a,b,1
, G. Cerullo
a,b,2
, C.V. Shank
a,b
a
b
Department of Chemistry, UniÕersity of California, Berkeley, CA 94720, USA Materials Sciences DiÕision, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Received 1 May 1997; in final form 13 August 1997
Abstract The ultrafast electronic dephasing of the molecules LD690 and LDS750 dissolved in amorphous polymer hosts is examined in the temperature range 30–300 K. The polarization decay time of LD690 in PMMA and PVA varies from about 40 fs at room temperature to 160 fs at 28 K, while the decay of LDS750 in PMMA is close to pulsewidth-limited at all temperatures. The difference between the dynamics observed in these two molecules shows how the molecular nature of the solute can affect the observed dephasing dynamics. q 1997 Published by Elsevier Science B.V.
1. Introduction Recent advances in the generation of ultrashort laser pulses have made it possible to directly observe the electronic dephasing of molecules in room-temperature liquid solutions w1–8x. The same solvent– solute interactions that cause this dephasing are also responsible for the solvation of charged species, and thus it is hoped that these studies will provide insight into the ultrafast dynamics of solvation. On the femtosecond timescale, where molecular motions are essentially frozen, one might suppose that a roomtemperature liquid resembles an amorphous solid. Thus, the study of solute molecules in such hosts, where the temperature can be easily varied, may
1 Present address: Department of Chemistry 0339, University of California at San Diego, La Jolla, CA 92093-0339, USA. 2 Permanent address: Dipartimento di Fisica, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milan, Italy.
provide insight into the mechanisms of ultrafast dephasing in liquids as well. In order to overcome the strong inhomogeneous broadening often present in such systems, many types of 4-wave-mixing spectroscopies, using both coherent and incoherent light, have been used to determine the electronic dephasing time or T2 of various molecules in various hosts at low temperatures w9–13x. The femtosecond three-pulse photon echo Ž3PPE. has proved to be a valuable tool in the investigation of electronic dephasing and has been described in detail previously w14x. Briefly, three pulses Ž k 1 , k 2 , and k 3 ,. interrogate the sample and the time-integrated signal diffracted in the yk 1 q k 2 q k 3 direction is measured as a function of both the delay t 12 Žbetween pulses 1 and 2. and the delay t 13 Žbetween pulses 1 and 3.. The t 12 dependence directly measures the fast polarization dynamics and the t 13 dependence reflects longer time population dynamics and spectral diffusion. The electronic dephasing rate can be extracted from the slope of the
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C.J. Bardeen et al.r Chemical Physics Letters 280 (1997) 127–133
echo signal as a function of t 12 for t 12 ) 0; alternatively, if the echo decays within the time resolution of the experiment, the dephasing can be extracted from the echo peak shift w14,15x. The electronic dephasing depends on the coupling of the probe molecule with its host environment and occurs on several different timescales. In this Letter, we concentrate mainly on the fastest dephasing process which occurs on the femtosecond timescale, since it is this process which is the most difficult to characterize via the peak shift method w16x and should be the most relevant to studies in high-temperature liquids. We present measurements of the dephasing of two different probe molecules, LD690 and LDS750, in the organic polymers PMMA and PVA in the temperature range 30 to 300 K. In this temperature range we find that the LD690 data show a strong temperature dependence in both polymers consistent with the high temperature limit of a phonon-activated process. The LDS750 3PPE data, on the other hand, is largely insensitive to changes in the temperature and decays on a timescale of about 30 fs at all temperatures.
2. Experiment The probe molecules, laser dyes LD690 and LDS750, are used as received from Exciton, Inc. The polymers, polyŽmethyl methacrylate. ŽPMMA. and polyŽvinyl alcohol., 80% hydrolyzed ŽPVA., are also used as received from Aldrich, without further purification. Dye films are made by heating a polymerrsolvent mixture ŽPMMAracetone or PVArwater. and then adding a small quantity of dye solution ŽLD690 or LDS750 in acetone for PMMA, or LD690 in methanol for PVA.. The resulting solution is then spread onto a glass slide and allowed to dry overnight, resulting in thin films of high optical quality and variable optical density. The maximum peak absorption of the dye films used in these experiments was 0.7, and the 3PPE decays did not change with lower OD samples. Fig. 1 shows the room-temperature dye absorption spectra Žalong with the laser pulse spectrum., which are very similar to those observed in the neat solvents acetone and methanol and show no sign of aggregation. Absorption spectra for LD690 taken at lower temperatures showed a
., along with the Fig. 1. The laser spectrum < EŽ n .< Ž room temperature absorption spectra of LD690 in PVA ŽPPPPP., LD690 in PMMA Ž — P — . and LDS750 in PMMA Ž — — — ..
slight shift of the absorption peak but no appreciable narrowing of the spectrum. The laser system has been described in detail elsewhere w17,18x. Briefly, the output of an 8 kHz amplified CPM system is used to generate a chirped continuum in a single mode optical fiber which is then reamplified in a broadband dye amplifier pumped by a copper vapor laser. After phase compensation this amplified short pulse has a duration of about 12 fs assuming a sech2 intensity profile. These short pulses are split into three beams, k 1 , k 2 , and k 3 , each with a pulse energy of about 1 nJ at the sample, which are focused onto the sample with a 75 mm lens. The signal in the yk 1 q k 2 q k 3 direction was found to vary as the cube of the intensity, the expected behavior in the perturbative Žsmall flip angle. limit. The thin film itself is mounted on the coldfinger of a closed cycle Helium gas cryostat ŽAPD DMX-20..
3. Experimental results Fig. 2 shows the 3PPE data for LD690 in PMMA, with the delay of pulse 3 relative to pulse 1 Ž t 13 . set at 233 fs and scanning t 12 , the delay of pulse 2. This experiment directly measures the decay of the polarization induced by pulse 1 as long as t 12 - t 13 . The delay of pulse 3 is chosen to be 233 fs because this corresponds to four periods of the dominant 586 cmy1 vibrational mode and suppresses the influence
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of this mode on the observed signal w19,20x. We choose t 13 in order to maximize both the mode suppression effect and the size of the observation window so that we observe the full polarization decay. We observe no change in the echo decays for t 13 delays of up to 1 ps. Both the signal and its natural logarithm are shown in Fig. 2, and the decay is asymmetric around t 12 s 0 and changes by a factor of about 5 over this temperature range. The data for LD690 in PVA look very similar to those in Fig. 2, although the decays are slightly faster at all temperatures. While the 3PPE data at t 13 s 233 fs show no great difference between the dephasing of LD690 in PMMA as opposed to PVA, the experiment with t 23 s 0 fs does show a small but significant difference. Overlapping pulses 2 and 3 and scanning pulse 1 is the equivalent of performing a two-pulse photon echo Ž2PPE., and these data for LD690 in PMMA and PVA at 28 K are shown in Fig. 3. The polarization decay is strongly modulated by the 586 cmy1 mode which obscures the true polarization decay at higher temperatures. Although
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the two signals are similar at early times, there is a small long-lived component in the PMMA 2PPE data that is absent in PVA, where the signal disappears completely after the second oscillation. There are at least two extra oscillations in the PMMA data, and although they are close to the noise level they are reproducible from day to day. We have also measured the temperature-dependent 3PPE signal from the molecule LDS750 in PMMA. LDS750 is considerably more complex than LD690 in terms of its spectroscopy due to its optical transition being strongly coupled to a larger number of vibrations w21x. Since there is no single dominant mode as there is in LD690, the mode suppression technique is not very useful in determining polarization decay rates. The differences between LD690 and LDS750 extend to the temperature dependence of their electronic dephasing in PMMA, as can be seen from Fig. 4. Here we show the 2PPE data because it is in these data that the fast dephasing of LDS750 is most clearly resolved. LDS750’s signal undergoes a considerably faster decay at all temperatures than
Fig. 2. The 3PPE signals for LD690 in PMMA at various temperatures, and their natural logarithms, scanning t12 with t13 s 233 fs.
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C.J. Bardeen et al.r Chemical Physics Letters 280 (1997) 127–133
Fig. 3. The 2PPE Ž t13 s 0, scanning t12 . data for LD690 in PMMA and PVA at 28 K, and natural logarithms.
does LD690, and even decays faster at 28 K than LD690 at 240 K. Lowering the temperature by almost an order of magnitude produces hardly any change in the LDS750 signal, while decay of
LD690’s signal slows dramatically. The polarization decay of LDS750 becomes even faster for finite third-pulse delays at all temperatures, becoming pulsewidth limited by about t 13 s 100 fs.
Fig. 4. The natural logarithms of LD690 and LDS750 2PPE signals at 28 K Ž
. and 240 K ŽPPPPP . in PMMA.
C.J. Bardeen et al.r Chemical Physics Letters 280 (1997) 127–133
Since the 3PPE decays in LD690 are fairly linear on a log scale, it is reasonable to define the slope of these decays as the ‘dephasing rate’. In the traditional Bloch equation description of dephasing, assuming strong inhomogeneous broadening, this rate would correspond to 4rT2 . The assumption of a large Žseveral hundred wavenumbers. inhomogeneous component is justified by the observed asymmetry of the 3PPE signal w14x and the fact that we do not observe significant narrowing of the absorption spectrum as the temperature is lowered. A plot of the dephasing rate versus temperature is shown in Fig. 5 for LD690 in both PMMA and PVA. The rates in Fig. 5 are obtained from linear least squares fits to the data in Fig. 2. In both PVA and PMMA the dephasing rate varies linearly with temperature over the range studied. An average of the slopes of the data in Fig. 5, along with other data sets, yields a slope of Ž1.9 " 0.2. = 10y4 fsy1rK for PMMA and a slope of 2.2 = 10y4 fsy1 rK for PVA. Finally, we note that the 3PPE can also probe population relaxation by setting t 12 s 0 and scanning t 13 , which becomes the analog of the delay between pump and probe pulses in a conventional pump– probe experiment. LD690 exhibits strong oscillations at the 586 cmy1 frequency, similar to those observed in room-temperature liquids w19x, while LDS750 has a more complicated population behavior, with a signal modulated by several different oscillation frequencies. These many vibrational modes render the
Fig. 5. Temperature dependence of the dephasing rate for LD690 in PMMA ŽB. and in PVA Žl., with linear least squares fits. In the Markovian limit this rate corresponds to 4r T2 .
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mode suppression technique used for LD690 ineffective for LDS750. The observed population dynamics for both LD690 and LDS750 are independent of temperature.
4. Discussion LDS750’s optical dephasing rate is close to pulsewidth-limited and is almost completely insensitive to the temperature of the PMMA host. Furthermore, in contrast to LD690, LDS750’s dephasing rate depends strongly on t 13 , becoming pulsewidthlimited by t 13 s 100 fs. In other words, LDS750 is subject to a very large perturbation very quickly upon excitation which leads to rapid loss of polarization memory or spectral diffusion. This perturbation may be the result of some fast intramolecular relaxation or isomerization w22x. The spectroscopy of LDS750 is considerably more complex than that of LD690; resonance Raman data, which will be published elsewhere w21x, indicate that the optical transition is strongly coupled to many vibrational modes. A temperature-independent multimode decay of the initial polarization w4,19x which obscures slower processes due to the environment would also explain the apparent insensitivity of LDS750’s optical dephasing to temperature. A third explanation for the strong, nearly temperature-independent, dephasing in LDS750 could be that LDS750, unlike LD690, undergoes a large charge redistribution upon excitation. In the simplest picture of solvation Žand thus dephasing., the strength of the interaction of the solute with its environment is proportional to the change in dipole and the solute radius via the quantity < D m < 2rR 3 w23x. In the n-alcohols, a plot of the Stokes shift versus the dielectric reaction field results in < D m < 2rR 3 being 2700 cmy1 for LD690 as opposed to 9700 cmy1 for LDS750 w21,24x. The large change in charge distribution in LDS750 could result in such a strong coupling to the environmental fluctuations that the temperature dependence is difficult to observe even with our time resolution w15,25x. In contrast to LDS750, LD690 seems to be a fairly well-behaved probe molecule, showing exponential polarization decays even at the lowest temperatures. The similarity of the LD690 data in PMMA and PVA, two chemically different polymers, sug-
C.J. Bardeen et al.r Chemical Physics Letters 280 (1997) 127–133
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gests that the ultrafast dephasing may result from an intramolecular process. On the other hand, previous work on LD690 in room-temperature liquids has shown that the dephasing is solvent dependent w8x, and there is a significant difference in the long time behaviors of the dephasing in PMMA and PVA at the lowest temperatures as shown in Fig. 3. These observations show that at least some component of LD690’s electronic dephasing must be due to intermolecular interactions. The next question concerns the origin of the dephasing. The molecular absorption spectrum consists of many intramolecular transitions, with each transition consisting of a zero-phonon line ŽZPL. and a phonon sideband ŽPSB. due to coupling with the host polymer w26x. Our broadband pulse spans almost the entire absorption spectrum and excites many transitions simultaneously. Experiments by previous workers have observed two component photon echo decays, where the fast Žoften pulsewidth-limited. decay reflects the PSB contribution and the slower one is due to the ZPL w27x. This two-component decay is consistent with the 2PPE data in PMMA at 28 K ŽFig. 3., but all other data show a single, femtosecond decay time. This, and the fact that other workers have shown that the PSB-induced dephasing increases rapidly above 20 K w28x indicates that we are observing predominantly the influence of the PSB. If the PSB is assumed to be primarily due to linear coupling of the phonons to the molecule, we can make contact with theoretical models currently used to analyze high-temperature liquid experiments w2,3,5,29x. The solvent–solute interaction can be written in terms of a coupling strength D 2 , and a correlation time tc for the decay of the fluctuations w29,30x. If tc is shorter than the timescale of observation, the dynamics appear Markovian and the observed polarization decay will be exponential with the Bloch equation dephasing time T2 . LD690 appears to be close to the Markovian limit even at the lowest temperatures. In this case, the dephasing rate is largely determined by the coupling to the phonon modes, parameterized by D 2 . In the multimode Brownian oscillator model w29–31x, for example, this quantity is related to the host phonons via
D2 s
`
H0 d v v
2
"v
coth
ž / 2 kT
rŽ v.,
Ž 1.
where r Ž v . is the phonon density of states. This analysis is valid both if the phonon bath is due to interactions with the environment and if it is intramolecular in origin. To obtain a linear dependence of D 2 , and thus the dephasing rate, on temperature, the inequality kT )) " v must be satisfied for all the phonons of interest. The linear temperature dependence of the dephasing rate thus implies that lowfrequency modes are responsible for the dephasing. This is in accord with previous experiments which have shown that the optical dephasing of different dye molecules in PMMA, for temperatures lower than 12.5 K, is due to a process with an activation energy of 15 cmy1 w32,33x. On the other hand, the polarization decays appear Markovian even with the very high temporal resolution in the present experiments, and preliminary modeling of our data using a linear coupling model w8,34x suggests that tc must be less than 50 fs. Such a small value for tc implies that modes with frequencies greater than several hundred wavenumbers must play a role in the dephasing. There is therefore a contradiction between the Markovian appearance of the polarization decays, which suggests the correlation time tc must be very short, and the linear temperature dependence of the dephasing rates, which implies coupling to lowfrequency modes and thus a relatively long tc . This contradiction indicates that a more complete model for optical dephasing in this temperature range is needed to explain the experimental data, possibly involving quadratic and higher order coupling terms w10,35x. Acknowledgements GC acknowledges support from a NATO fellowship. This research was supported under DOE Contract No. DE-AC0376SF00098. References w1x T. Joo, Y. Jia, G.R. Fleming, J. Chem. Phys. 102 Ž1995. 4063. w2x T. Joo, Y. Jia, J.-Y. Yu, M.J. Lang, G.R. Fleming, J. Chem. Phys. 104 Ž1996. 6089. w3x T.-S. Yang, P. Vohringer, D.C. Arnett, N.F. Scherer, J. Chem. Phys. 103 Ž1995. 8346. w4x E.T.J. Nibbering, D.A. Wiersma, K. Duppen, Chem. Phys. 183 Ž1994. 167.
C.J. Bardeen et al.r Chemical Physics Letters 280 (1997) 127–133 w5x W.P. De Boeij, M.S. Pshenichnikov, D.A. Wiersma, J. Chem. Phys. 105 Ž1996. 2953. w6x J. Yu, T.J. Kang, M. Berg, J. Chem. Phys. 94 Ž1991. 5787. w7x P. Cong, Y.J. Yan, H.P. Deuel, J.D. Simon, J. Chem. Phys. 100 Ž1994. 7855. w8x C.J. Bardeen, C.V. Shank, Chem. Phys. Lett. 226 Ž1994. 310. w9x D.W. Pack, L.R. Narasimhan, M.D. Fayer, J. Chem. Phys. 92 Ž1990. 4125. w10x T. Reinot, W.-H. Kim, J.M. Hayes, G.J. Small, J. Chem. Phys. 104 Ž1996. 793. w11x Y. Zhang, S.R. Hartmann, F. Moshary, J. Chem. Phys. 104 Ž1996. 4371. w12x S. De Silvestri, A.M. Weiner, J.G. Fujimoto, E.P. Ippen, Chem. Phys. Lett. 112 Ž1984. 195. w13x J. Yu, M. Berg, J. Chem. Phys. 96 Ž1992. 8741. w14x A.M. Weiner, S. De Silvestri, E.P. Ippen, J. Opt. Soc. Am. B 2 Ž1985. 654. w15x Y. Nagasawa, S.A. Passino, T. Joo, G.R. Fleming, J. Chem. Phys. 106 Ž1996. 4840. w16x W.P. De Boeij, M.S. Pshenichnikov, D.A. Wiersma, Chem. Phys. Lett. 253 Ž1996. 53. w17x R.L. Fork, C.H. Brito Cruz, P.C. Becker, C.V. Shank, Opt. Lett. 12 Ž1987. 483. w18x S.L. Dexheimer, Q. Wang, L.A. Peteanu, W.T. Pollard, R.A. Mathies, C.V. Shank, Chem. Phys. Lett. 188 Ž1992. 61. w19x C.J. Bardeen, C.V. Shank, Chem. Phys. Lett. 203 Ž1993. 535.
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w20x R.W. Schoenlein, D.M. Mittleman, J.J. Shiang, A.P. Alivisatos, C.V. Shank, Phys. Rev. Lett. 70 Ž1993. 1014. w21x C.J. Bardeen, S.J. Rosenthal, C.V. Shank, manuscript in preparation. w22x S.A. Kovalenko, N.P. Ernsting, J. Ruthmann, J. Chem. Phys. 106 Ž1997. 3504. w23x C.-P. Hsu, X. Song, R.A. Marcus, J. Phys. Chem. 101 Ž1997. 2546. w24x E.W. Castner, M. Maroncelli, G.R. Fleming, J. Chem. Phys. 86 Ž1987. 1090. w25x S.J. Rosenthal, B.J. Schwartz, P.J. Rossky, Chem. Phys. Lett. 229 Ž1994. 443. w26x K.K. Rebane, Chem. Phys. 189 Ž1994. 139. w27x S. Saikan, A. Imaoka, Y. Kanematsu, K. Sakoda, K. Kominami, M. Iwamoto, Phys. Rev. B. 41 Ž1990. 3185. w28x Y.G. Vainer, N.V. Gruzdev, Opt. Spec. 76 Ž1994. 226. w29x Y.J. Yan, S. Mukamel, J. Chem. Phys. 94 Ž1991. 179. w30x M. Aihara, Phys. Rev. B. 25 Ž1982. 53. w31x T.H. Keil, Phys. Rev. 140 Ž1965. A601. w32x S.R. Greenfield, Y.S. Bai, M.D. Fayer, Chem. Phys. Lett. 170 Ž1990. 133. w33x A. Elschner, L.R. Narasimhan, M.D. Fayer, Chem. Phys. Lett. 171 Ž1990. 19. w34x W.T. Pollard, S.L. Dexheimer, Q. Wang, L.A. Peteanu, C.V. Shank, R.A. Mathies, J. Phys. Chem. 96 Ž1992. 6147. w35x J.T. Fourkas, M. Berg, J. Chem. Phys. 98 Ž1993. 7773.
Chemical Physics Letters 280 Ž1997. 127–133
Temperature-dependent electronic dephasing of molecules in polymers in the range 30 to 300 K C.J. Bardeen
a,b,1
, G. Cerullo
a,b,2
, C.V. Shank
a,b
a
b
Department of Chemistry, UniÕersity of California, Berkeley, CA 94720, USA Materials Sciences DiÕision, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Received 1 May 1997; in final form 13 August 1997
Abstract The ultrafast electronic dephasing of the molecules LD690 and LDS750 dissolved in amorphous polymer hosts is examined in the temperature range 30–300 K. The polarization decay time of LD690 in PMMA and PVA varies from about 40 fs at room temperature to 160 fs at 28 K, while the decay of LDS750 in PMMA is close to pulsewidth-limited at all temperatures. The difference between the dynamics observed in these two molecules shows how the molecular nature of the solute can affect the observed dephasing dynamics. q 1997 Published by Elsevier Science B.V.
1. Introduction Recent advances in the generation of ultrashort laser pulses have made it possible to directly observe the electronic dephasing of molecules in room-temperature liquid solutions w1–8x. The same solvent– solute interactions that cause this dephasing are also responsible for the solvation of charged species, and thus it is hoped that these studies will provide insight into the ultrafast dynamics of solvation. On the femtosecond timescale, where molecular motions are essentially frozen, one might suppose that a roomtemperature liquid resembles an amorphous solid. Thus, the study of solute molecules in such hosts, where the temperature can be easily varied, may
1 Present address: Department of Chemistry 0339, University of California at San Diego, La Jolla, CA 92093-0339, USA. 2 Permanent address: Dipartimento di Fisica, Politecnico di Milano, Piazza L. da Vinci 32, 20133 Milan, Italy.
provide insight into the mechanisms of ultrafast dephasing in liquids as well. In order to overcome the strong inhomogeneous broadening often present in such systems, many types of 4-wave-mixing spectroscopies, using both coherent and incoherent light, have been used to determine the electronic dephasing time or T2 of various molecules in various hosts at low temperatures w9–13x. The femtosecond three-pulse photon echo Ž3PPE. has proved to be a valuable tool in the investigation of electronic dephasing and has been described in detail previously w14x. Briefly, three pulses Ž k 1 , k 2 , and k 3 ,. interrogate the sample and the time-integrated signal diffracted in the yk 1 q k 2 q k 3 direction is measured as a function of both the delay t 12 Žbetween pulses 1 and 2. and the delay t 13 Žbetween pulses 1 and 3.. The t 12 dependence directly measures the fast polarization dynamics and the t 13 dependence reflects longer time population dynamics and spectral diffusion. The electronic dephasing rate can be extracted from the slope of the
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C.J. Bardeen et al.r Chemical Physics Letters 280 (1997) 127–133
echo signal as a function of t 12 for t 12 ) 0; alternatively, if the echo decays within the time resolution of the experiment, the dephasing can be extracted from the echo peak shift w14,15x. The electronic dephasing depends on the coupling of the probe molecule with its host environment and occurs on several different timescales. In this Letter, we concentrate mainly on the fastest dephasing process which occurs on the femtosecond timescale, since it is this process which is the most difficult to characterize via the peak shift method w16x and should be the most relevant to studies in high-temperature liquids. We present measurements of the dephasing of two different probe molecules, LD690 and LDS750, in the organic polymers PMMA and PVA in the temperature range 30 to 300 K. In this temperature range we find that the LD690 data show a strong temperature dependence in both polymers consistent with the high temperature limit of a phonon-activated process. The LDS750 3PPE data, on the other hand, is largely insensitive to changes in the temperature and decays on a timescale of about 30 fs at all temperatures.
2. Experiment The probe molecules, laser dyes LD690 and LDS750, are used as received from Exciton, Inc. The polymers, polyŽmethyl methacrylate. ŽPMMA. and polyŽvinyl alcohol., 80% hydrolyzed ŽPVA., are also used as received from Aldrich, without further purification. Dye films are made by heating a polymerrsolvent mixture ŽPMMAracetone or PVArwater. and then adding a small quantity of dye solution ŽLD690 or LDS750 in acetone for PMMA, or LD690 in methanol for PVA.. The resulting solution is then spread onto a glass slide and allowed to dry overnight, resulting in thin films of high optical quality and variable optical density. The maximum peak absorption of the dye films used in these experiments was 0.7, and the 3PPE decays did not change with lower OD samples. Fig. 1 shows the room-temperature dye absorption spectra Žalong with the laser pulse spectrum., which are very similar to those observed in the neat solvents acetone and methanol and show no sign of aggregation. Absorption spectra for LD690 taken at lower temperatures showed a
., along with the Fig. 1. The laser spectrum < EŽ n .< Ž room temperature absorption spectra of LD690 in PVA ŽPPPPP., LD690 in PMMA Ž — P — . and LDS750 in PMMA Ž — — — ..
slight shift of the absorption peak but no appreciable narrowing of the spectrum. The laser system has been described in detail elsewhere w17,18x. Briefly, the output of an 8 kHz amplified CPM system is used to generate a chirped continuum in a single mode optical fiber which is then reamplified in a broadband dye amplifier pumped by a copper vapor laser. After phase compensation this amplified short pulse has a duration of about 12 fs assuming a sech2 intensity profile. These short pulses are split into three beams, k 1 , k 2 , and k 3 , each with a pulse energy of about 1 nJ at the sample, which are focused onto the sample with a 75 mm lens. The signal in the yk 1 q k 2 q k 3 direction was found to vary as the cube of the intensity, the expected behavior in the perturbative Žsmall flip angle. limit. The thin film itself is mounted on the coldfinger of a closed cycle Helium gas cryostat ŽAPD DMX-20..
3. Experimental results Fig. 2 shows the 3PPE data for LD690 in PMMA, with the delay of pulse 3 relative to pulse 1 Ž t 13 . set at 233 fs and scanning t 12 , the delay of pulse 2. This experiment directly measures the decay of the polarization induced by pulse 1 as long as t 12 - t 13 . The delay of pulse 3 is chosen to be 233 fs because this corresponds to four periods of the dominant 586 cmy1 vibrational mode and suppresses the influence
C.J. Bardeen et al.r Chemical Physics Letters 280 (1997) 127–133
of this mode on the observed signal w19,20x. We choose t 13 in order to maximize both the mode suppression effect and the size of the observation window so that we observe the full polarization decay. We observe no change in the echo decays for t 13 delays of up to 1 ps. Both the signal and its natural logarithm are shown in Fig. 2, and the decay is asymmetric around t 12 s 0 and changes by a factor of about 5 over this temperature range. The data for LD690 in PVA look very similar to those in Fig. 2, although the decays are slightly faster at all temperatures. While the 3PPE data at t 13 s 233 fs show no great difference between the dephasing of LD690 in PMMA as opposed to PVA, the experiment with t 23 s 0 fs does show a small but significant difference. Overlapping pulses 2 and 3 and scanning pulse 1 is the equivalent of performing a two-pulse photon echo Ž2PPE., and these data for LD690 in PMMA and PVA at 28 K are shown in Fig. 3. The polarization decay is strongly modulated by the 586 cmy1 mode which obscures the true polarization decay at higher temperatures. Although
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the two signals are similar at early times, there is a small long-lived component in the PMMA 2PPE data that is absent in PVA, where the signal disappears completely after the second oscillation. There are at least two extra oscillations in the PMMA data, and although they are close to the noise level they are reproducible from day to day. We have also measured the temperature-dependent 3PPE signal from the molecule LDS750 in PMMA. LDS750 is considerably more complex than LD690 in terms of its spectroscopy due to its optical transition being strongly coupled to a larger number of vibrations w21x. Since there is no single dominant mode as there is in LD690, the mode suppression technique is not very useful in determining polarization decay rates. The differences between LD690 and LDS750 extend to the temperature dependence of their electronic dephasing in PMMA, as can be seen from Fig. 4. Here we show the 2PPE data because it is in these data that the fast dephasing of LDS750 is most clearly resolved. LDS750’s signal undergoes a considerably faster decay at all temperatures than
Fig. 2. The 3PPE signals for LD690 in PMMA at various temperatures, and their natural logarithms, scanning t12 with t13 s 233 fs.
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Fig. 3. The 2PPE Ž t13 s 0, scanning t12 . data for LD690 in PMMA and PVA at 28 K, and natural logarithms.
does LD690, and even decays faster at 28 K than LD690 at 240 K. Lowering the temperature by almost an order of magnitude produces hardly any change in the LDS750 signal, while decay of
LD690’s signal slows dramatically. The polarization decay of LDS750 becomes even faster for finite third-pulse delays at all temperatures, becoming pulsewidth limited by about t 13 s 100 fs.
Fig. 4. The natural logarithms of LD690 and LDS750 2PPE signals at 28 K Ž
. and 240 K ŽPPPPP . in PMMA.
C.J. Bardeen et al.r Chemical Physics Letters 280 (1997) 127–133
Since the 3PPE decays in LD690 are fairly linear on a log scale, it is reasonable to define the slope of these decays as the ‘dephasing rate’. In the traditional Bloch equation description of dephasing, assuming strong inhomogeneous broadening, this rate would correspond to 4rT2 . The assumption of a large Žseveral hundred wavenumbers. inhomogeneous component is justified by the observed asymmetry of the 3PPE signal w14x and the fact that we do not observe significant narrowing of the absorption spectrum as the temperature is lowered. A plot of the dephasing rate versus temperature is shown in Fig. 5 for LD690 in both PMMA and PVA. The rates in Fig. 5 are obtained from linear least squares fits to the data in Fig. 2. In both PVA and PMMA the dephasing rate varies linearly with temperature over the range studied. An average of the slopes of the data in Fig. 5, along with other data sets, yields a slope of Ž1.9 " 0.2. = 10y4 fsy1rK for PMMA and a slope of 2.2 = 10y4 fsy1 rK for PVA. Finally, we note that the 3PPE can also probe population relaxation by setting t 12 s 0 and scanning t 13 , which becomes the analog of the delay between pump and probe pulses in a conventional pump– probe experiment. LD690 exhibits strong oscillations at the 586 cmy1 frequency, similar to those observed in room-temperature liquids w19x, while LDS750 has a more complicated population behavior, with a signal modulated by several different oscillation frequencies. These many vibrational modes render the
Fig. 5. Temperature dependence of the dephasing rate for LD690 in PMMA ŽB. and in PVA Žl., with linear least squares fits. In the Markovian limit this rate corresponds to 4r T2 .
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mode suppression technique used for LD690 ineffective for LDS750. The observed population dynamics for both LD690 and LDS750 are independent of temperature.
4. Discussion LDS750’s optical dephasing rate is close to pulsewidth-limited and is almost completely insensitive to the temperature of the PMMA host. Furthermore, in contrast to LD690, LDS750’s dephasing rate depends strongly on t 13 , becoming pulsewidthlimited by t 13 s 100 fs. In other words, LDS750 is subject to a very large perturbation very quickly upon excitation which leads to rapid loss of polarization memory or spectral diffusion. This perturbation may be the result of some fast intramolecular relaxation or isomerization w22x. The spectroscopy of LDS750 is considerably more complex than that of LD690; resonance Raman data, which will be published elsewhere w21x, indicate that the optical transition is strongly coupled to many vibrational modes. A temperature-independent multimode decay of the initial polarization w4,19x which obscures slower processes due to the environment would also explain the apparent insensitivity of LDS750’s optical dephasing to temperature. A third explanation for the strong, nearly temperature-independent, dephasing in LDS750 could be that LDS750, unlike LD690, undergoes a large charge redistribution upon excitation. In the simplest picture of solvation Žand thus dephasing., the strength of the interaction of the solute with its environment is proportional to the change in dipole and the solute radius via the quantity < D m < 2rR 3 w23x. In the n-alcohols, a plot of the Stokes shift versus the dielectric reaction field results in < D m < 2rR 3 being 2700 cmy1 for LD690 as opposed to 9700 cmy1 for LDS750 w21,24x. The large change in charge distribution in LDS750 could result in such a strong coupling to the environmental fluctuations that the temperature dependence is difficult to observe even with our time resolution w15,25x. In contrast to LDS750, LD690 seems to be a fairly well-behaved probe molecule, showing exponential polarization decays even at the lowest temperatures. The similarity of the LD690 data in PMMA and PVA, two chemically different polymers, sug-
C.J. Bardeen et al.r Chemical Physics Letters 280 (1997) 127–133
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gests that the ultrafast dephasing may result from an intramolecular process. On the other hand, previous work on LD690 in room-temperature liquids has shown that the dephasing is solvent dependent w8x, and there is a significant difference in the long time behaviors of the dephasing in PMMA and PVA at the lowest temperatures as shown in Fig. 3. These observations show that at least some component of LD690’s electronic dephasing must be due to intermolecular interactions. The next question concerns the origin of the dephasing. The molecular absorption spectrum consists of many intramolecular transitions, with each transition consisting of a zero-phonon line ŽZPL. and a phonon sideband ŽPSB. due to coupling with the host polymer w26x. Our broadband pulse spans almost the entire absorption spectrum and excites many transitions simultaneously. Experiments by previous workers have observed two component photon echo decays, where the fast Žoften pulsewidth-limited. decay reflects the PSB contribution and the slower one is due to the ZPL w27x. This two-component decay is consistent with the 2PPE data in PMMA at 28 K ŽFig. 3., but all other data show a single, femtosecond decay time. This, and the fact that other workers have shown that the PSB-induced dephasing increases rapidly above 20 K w28x indicates that we are observing predominantly the influence of the PSB. If the PSB is assumed to be primarily due to linear coupling of the phonons to the molecule, we can make contact with theoretical models currently used to analyze high-temperature liquid experiments w2,3,5,29x. The solvent–solute interaction can be written in terms of a coupling strength D 2 , and a correlation time tc for the decay of the fluctuations w29,30x. If tc is shorter than the timescale of observation, the dynamics appear Markovian and the observed polarization decay will be exponential with the Bloch equation dephasing time T2 . LD690 appears to be close to the Markovian limit even at the lowest temperatures. In this case, the dephasing rate is largely determined by the coupling to the phonon modes, parameterized by D 2 . In the multimode Brownian oscillator model w29–31x, for example, this quantity is related to the host phonons via
D2 s
`
H0 d v v
2
"v
coth
ž / 2 kT
rŽ v.,
Ž 1.
where r Ž v . is the phonon density of states. This analysis is valid both if the phonon bath is due to interactions with the environment and if it is intramolecular in origin. To obtain a linear dependence of D 2 , and thus the dephasing rate, on temperature, the inequality kT )) " v must be satisfied for all the phonons of interest. The linear temperature dependence of the dephasing rate thus implies that lowfrequency modes are responsible for the dephasing. This is in accord with previous experiments which have shown that the optical dephasing of different dye molecules in PMMA, for temperatures lower than 12.5 K, is due to a process with an activation energy of 15 cmy1 w32,33x. On the other hand, the polarization decays appear Markovian even with the very high temporal resolution in the present experiments, and preliminary modeling of our data using a linear coupling model w8,34x suggests that tc must be less than 50 fs. Such a small value for tc implies that modes with frequencies greater than several hundred wavenumbers must play a role in the dephasing. There is therefore a contradiction between the Markovian appearance of the polarization decays, which suggests the correlation time tc must be very short, and the linear temperature dependence of the dephasing rates, which implies coupling to lowfrequency modes and thus a relatively long tc . This contradiction indicates that a more complete model for optical dephasing in this temperature range is needed to explain the experimental data, possibly involving quadratic and higher order coupling terms w10,35x. Acknowledgements GC acknowledges support from a NATO fellowship. This research was supported under DOE Contract No. DE-AC0376SF00098. References w1x T. Joo, Y. Jia, G.R. Fleming, J. Chem. Phys. 102 Ž1995. 4063. w2x T. Joo, Y. Jia, J.-Y. Yu, M.J. Lang, G.R. Fleming, J. Chem. Phys. 104 Ž1996. 6089. w3x T.-S. Yang, P. Vohringer, D.C. Arnett, N.F. Scherer, J. Chem. Phys. 103 Ž1995. 8346. w4x E.T.J. Nibbering, D.A. Wiersma, K. Duppen, Chem. Phys. 183 Ž1994. 167.
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