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Femtosecond electronic dephasing in large molecules in solution using mode suppression
Volume203,number 5,6
CHEMICAL PHYSICS LETTERS
5 March1993
Femtosecond electronic dephasing in large molecules in solution using mode suppression C.J. Bardeen and C.V. Shank MaterialSciences Division, Lawrence Berkeley Laboratory. Berkeley, CA 94720, USA and Department of Chemistry, Universityof California,Berkeley, CA 94720, USA
Received3 December 1992
The femtosecond electronic depbasing oflarge molecules in solution is measured using a three-pulse photon echo mode cancellation technique. We have demonstrated the suppression of the quantum interference in the echo decay caused by the dominant ring breathing mode at 590 cm-’ found in oxazine dyes. We have calculated the echo decay including the entire manifold of vibronic levels and have determined the dephasing time I-, to be in the range of 30 to 70 fs for the dye molecules nile blue and LD690.
The nature of spectral broadening of electronic transitions of large molecules in solution has been a subject of recent interest, as it is hoped that it may shed some light on the dynamics of solvent-solute interactions. Several nonlinear optical techniques, including coherent and incoherent transients [ l-41, holeburning [ 51, resonance Raman [ 61, and Rayleigh scattering [ 7 1, have been used to elucidate the mechanisms of the spectral broadening observed in liquid solutions. In general the manifold of vibronic levels in large molecules complicates the i.nterpretation of these measurements. In this Letter, we describe three-pulse photon echo measurements using a new mode suppression technique [ 81 which greatly reduces the effect of quantum interference from a dominant vibrational mode. Previous threepulse photon echo experiments on large molecules in solution have not addressed the complexity of the multi-level interactions [ 11. Results will be discussed for two oxazine molecules, nile blue (NB) and LD690 (LD), for which we have determined the polarization dephasing time T2 to be in the range of 30 to 70 fs. The three-pulse photon echo measurement is performed with a sequence of three pulses having a duration short compared to the dephasing time, T2.The first pulse in the sequence excites a polarization in the sample at time zero which interferes with the sec-
ond pulse at ~~2,creating a population grating. A third pulse, arriving at t13,scatters from this grating in a phase-matched direction. With rhe third pulse placed at a fixed delay, the scattered energy is measured as a function of the relative time delay between the first two pulses. Contributions to spectral broadening can be divided according to time scale into an inhomogeneous component (corresponding to processes slow compared to the time scale of the measurement) and a homogeneous component (processes fast compared to the time scale of the measurement )_ In the two extremes, and assuming a simple two-level system, a largely inhomogeneously broadened line will result in a signal asymmetric about f12=0 and exponentially decaying for tlz> 0 with a time constant of a T,, while a homogeneously broadened line will give rise to a symmetric signal with a time constant of 4T2. A dye molecule is a multi-level system. A short light pulse can coherently excite vibrational modes having a period longer than the pulse duration [ 91. In the three-pulse echo, the first two pulses create a coherent population which undergoes time-dependent oscillatory motion, If we consider a single coherently excited mode, it is possible to time the third pulse such that it samples the nonstationary population in or out of phase with the vibrational mode. If the echo is measured out of phase with the vibration, the echo
0009-2614/93/$ 06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.
535
signal is diminished and driven down by quantum interference between the levels of that mode, or equivalently by the rapid motion of the wavepacket away from the Franck-Condon region. However if the measurement is made in phase with the vibration, the quantum interference will be suppressed [ 81. In contrast, the two-pulse photon echo will always be modulated by the quantum beating between the excited levels of the system, and this can lead to a fast apparent decay which is more indicative of vibronic congestion than of the pure dephasing time T,.The effectiveness of the quantum beat suppression technique relies on the vibrational coherence of the population and to a lesser extent on the degree of inhomogeneous broadening in the system. The experimental arrangement is identical to that described previously [ 11. Briefly, the output of a CPM dye laser is amplified at an 8 kHz repetition rate and focused into a single-mode optical fiber, whose spectrally broadened output is then compressed by gratings and prisms. A typical pulse spectrum is shown in fig. 1, along with the absorption spectra of nile blue and LD690 for comparison. The pulse spectrum shown in fig. 1 has both the red and blue edges clipped to improve the temporal and spatial quality of the pulses, which can be degraded by excess spectrum resulting from processes other than self-phase modulation in the fiber. The typical pulsewidth measured by non-collinear second harmonic generation is 9-l 0 fs, assuming a sech’ pulse shape. The ultrashort pulses are split into three beams of
550
570
590 610 Wavelength
630 650 [nm)
670
690
Fig. 1. Absorption of nile blue (single dashed line) and of LD690 (double dashed line) and the power spectrum of the femtosecond pulses used in the experiment.
536
5 March 1993
CHEMICAL PHYSICS LETTERS
Volume 203, number 5,6
parallel polarization and focused onto a flowing jet of the dye dissolved in ethylene glycol and a small amount of methanol to aid solubility. The scattered light in the -k,+k2+k3 phase-matched direction is collected using an iris and a collimating lens, and detected by a PMT. The jet thickness is approximately 50 pm, with a dye concentration such that the transmittance of the beam is 30% or more. Thermal effects are eliminated by flowing the jet rapidly enough to have complete replacement of the active spot between laser shots. The experimental pulse energy is approximately 0.5 nJ, a factor 5 below the level at which the signal was observed to depart from an I3 dependence. No change in the signal decay is observed at energies as low as 0.05 nJ. Possible nonresonant contributions from the neat solvent were checked for: none were found. We apply the mode suppression technique to the problem of determining the pure dephasing time T2 of the molecules NB and LD, taking advantage of the fact that both have a dominant ring breathing mode at 590 cm-‘, corresponding to a period of about 60 fs. This can be seen most easily in fig. 2, which is the signal obtained by setting the delay of the first two pulses, f12,to zero and scanning fL3,the delay of the third. This corresponds to a transmission correlation experiment, which essentially measures the population dynamics integrated over all pulse wavelengths. In both cases oscillations with a period of approximately 60 fs are clearly in evidence and are the result of the 590 cm-’ ring breathing mode.
I -50
/ 50
43
150
delay
250
Ifs)
350
Fig. 2. Experimental signal for setting f12to zero and scanning t,,, the delay of the third pulse, showing the population dynamics of (a) LD690, and (b) bile blue.
Volume 203, number 5,6
CHEMICAL PHYSICS LETTERS
The data in fig. 3 shows three-pulse echo signals (thick lines) measured as a function of tr2 with t,,=60 fs and t,,=90 fs. It is immediately apparent from the data that the echo decay is different at these two time delays. The measurement at 60 fs delay is in phase with the vibration and is clearly asymmetric and shifted in time with a slower decay than the 90 fs measurement. The difference between the two third-pulse delays demonstrates that the 590 cm-’ mode plays a significant role in determining the observed decay and must be taken into account for any quantitative interpretation of the echo signal. In addition the asymmetry in the echo is indicative of inhomogeneous broadening [2]. Results for LD are plotted in fig. 4, where the suppression effect is even more dramatic. In order to get an idea of what processes are contributing to the observed signal, it is necessary to calculate the photon echo in the perturbation limit. This involves evaluating the four time correlation functions for a multi-level system that result from a perturbative solution of the optical Bloch equations. We use Mukamel’s semi-classical Liouville space formalism and the resulting integrals are evaluated numerically [ 101. For NB the frequencies and excited state displacements of the forty Raman active modes as determined by Lawless et al. [ 61 are used in the calculation. For the molecule LD, such detailed mode data were not available and an approximate model that fits the linear absorption spectrum of LD is used
0 _
-1
;;) -2 & -3 ._ LI) 4 5 -5 -6 -7
, -20
40
Fig. 3. Experimental (thick) and calculated (thin ) three-p Ill! ie echo signals, scanning the second pulse (fJ, for third-pulse delays oft,,=60 fs (solid) and t,,=90 fs (dotted) in nile blue. For the calculated signal a T2 of 70 fs and an inhomogeneous hwhm of 450 cm-’ have been assumed.
5 March 1993
0 -1
:: -2 E m -3 -n cn I -4 5 “5 -6 -7J’, -40
, -2Q
20 ti:
40
delay (fsl
Fig. 4. Experimental (thick) and calculated (thin) three-pulse echo signals, scanning the second pulse, for tlx= 60 fs (solid) and tIJ = 90 fs (dotted) in LD690. For the calculated signal a Tr of 30 fs and an inhomogeneous hwhm of 295 cm-’ have heen assumed.
for the calculation. A representation of the electric field of the pulse is obtained by Fourier transforming the square root of the experimentally measured power spectrum of the pulse. This assumes the optical pulse is transform limited, a reasonable approximation for the experiment which, unlike the two-pulse echo, is not very sensitive to the detailed phase structure of the pulse [ 21. Indeed, the calculation is found to be insensitive to the chirp of the pulse as long as the pulse is short compared to the coherent population dynamics. The results of the calculations are shown in figs. 3 and 4 (thin lines). For the case of NB a TXof 70 fs and a Gaussian inhomogeneous hwhm of 450 cm-’ are assumed for the calculation. There is good qualitative agreement with the essential features of the signal and a clear indication of inhomogeneous broadening and dephasing on a femtosecond time scale. The fit is not perfect, especially considering the absolute widths of the signal and the presence of the beginning of a recurrence of the 60 fs oscillation in the t,3=90 fs calculation. One possible reason for the discrepancy between theory and experiment is that we have assumed the molecule to be a simple harmonic system with undamped vibrational modes. In this case the difference in signals at ti,=60 fs and t,,=90 fs should also be observed at 120, 150, 180 fs, etc., as the third pulse is delayed in and out of phase with the coherent vibration. For NB the quantum beat suppression is fairly pronounced at 60 fs, is reduced at 120 fs, and no effect is observed by 180 fs. After three oscillations electronic transition ap537
Volume 203, number 5,6
CHEMICAL PHYSICS LETTERS
pears to be entirely homogeneously broadened. This effect implies the memory
that the system is undergoing of the polarization
a loss of
read into it by the
first two pulses and has often been termed spectral diffusion [ 2,111. Spectral diffusion arises from a change in level occupation and can result from random solvent modulations or from intramolecular energy redistribution. Supporting evidence for the latter process can be seen in fig. 2b for NB. Note that the oscillations undergo very rapid damping at early times and reach a steady state amplitude by about 200 fs. The calculated response, assuming 40 harmonic modes, shows undamped oscillations persisting for much longer, qualitatively different from what is observed. Such fast population dynamics have been inferred from previous pump-probe [ 121 and timeresolved fluorescence [ 131 measurements, suggesting that significant excited state intramolecular vibrational redistribution occurs on the femtosecond time scale. A theoretical model for NB that treats IVR in the condensed phase is beyond the scope of this Letter but is probably necessary if we are to obtain quantitative agreement with the experimental data. Such fast population processes apparently do not occur in LD, as can be seen in fig. 2a, and in this case the suppression effect disappears much more gradually. LD is a cationic oxazine dye similar to NB, but lacking a phenyl group and with different amino sidechains #‘. These structural differences lead to a spectrum that is slightly blue-shifted from that of NB. LD also possesses a strong mode at approximately 590 cm-‘. The calculation shown in fig. 3 was done assuming four Franck-Condon-connected modes (590, 1140, 1240, and 1640 cm-‘), similar to what has been observed in other oxazines [ 6,141, a T, of 30 fs, and a Gaussian inhomogeneous hwhm of 295 cm-‘. It is interesting to note that although the experimentally observed decay of the photon echo of LD is slower than that of NB, the data can actually be reproduced with a shorter T2. These results illustrate the complex dynamics inherent in a multi-level system, where the observed polarization decay results both from the destructive interference of the levels excited by the pulses and from the pure dephasing represented by T2. In the case of LD where we have assumed a small number of Franck-Con$’Exciton, Inc., Laser Dye Catalog. 538
5 March I993
don-connected modes for the calculation, much of the damping has to come from T2 itself and thus T, must be short in order to model the data. A more realistic model of LD would probably include more modes and result in a proportionately longer T2, so our value of 30 fs is most likeiy a lower bound. In short, a complete description of the Franck-Condon allowed transitions must be known to accurately model the echo decay and separate multi-level effects from that of pure dephasing, which presumably contains information on the time scale of the solvent chromophore interaction. In conclusion we have demonstrated that by using an appropriately timed pulse sequence it is possible to suppress the influence of the 590 cm-’ ring breathing mode on the photon echo from large oxazine molecules in solution. We have calculated the echo using the known manifold of vibrational modes, the measured optical pulse, and with T, as a free parameter, and have reproduced the qualitative features of the data. Our results clearly indicate inhomogeneous broadening on the femtosecond time scale with a T, in the range 30 to 70 fs, and that in NB the echo information is lost on the order of a few hundred femtoseconds, perhaps due to intramolecular energy redistribution. We thank Dr. R.W. Schoenlein, Dr. W.T. Pollard, Dr. J.-Y. Bigot and M.K. Lawless for enlightening discussions. This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences of the US Department of Energy under Contract No. DE-AC03-76SF00098. CJB acknowledges a DOED fellowship.
References [I ] J.Y. Bigot, M.T. Portella, R.W. Schoenlein, C.J. Bardeen, A. Migus and C.V. Shank, Phys. Rev. Letters 66 (I 991) 1138; PC. Becker, H.L. Fragnito, J.Y. Bigot, C.H. BritoCrnz, R.L. Fork and C.V. Shank, Phys. Rev. Letters 63 ( 1989) 505. [2 ] A.M. Weiner, S. De Silvestri and E.P. Ippcn, J. Opt. Sot. Am.B2(1985)654; S. De Silvcstri, A.M. Weiner, J.G. Fujimoto and E.P. Ippen, Chem. Phys. Letters I1 2 ( 1984) 195. [ 3 ] E.T.J. Nibbering, D. Wiersma and K. Duppen, Phys. Rev. Letters 66 (1991) 2465. [4] F. Moshary, M. Arend, R. Friedberg and S.R. Hartmann, Phys. Rev. A 46 (1992) R33.
Volume 203, number 5,6
CHEMICAL PHYSICS LETTERS
[5] C.H. Brito Cruz, R.L. Fork, W.H. Knox and C.V. Shank, Chem. Phys. Letters 132 (1986) 341. [6] M.K. Lawless and R.A. Mathies, J. Chem. Phys. 96 ( 1992) 8037. [7] T. Yajima, H. Souma and Y. Isbida, Phys. Rev. A 17 (1978) 324. [S] R.W. Schoenlein, D.M. Mittleman, J.J. Shiang, A.P. Alivisatos and C.V. Shank, Phys. Rev. Letters, submitted for publication. [9] H.L. Fragnito, J.Y. Bigot, P.C. Becker and C.V. Shank, Chem. Phys. Letters 160 (1989) 101.
5 March 1993
[IO] Y.J. Yan and S. Mukamel, J. Chem. Phys. 89 (1988) 5160; 94 (1991) 179; W.T. Pollard, S.L. Dexheimer, Q. Wang, L.A. Peteanu, C.V. Shankand R.A. Math&, J. Phys. Chem. 96 (1992) 6147. [ 111C. Morou, IEEE I. Quantum. Electron. 11 ( 1975) I. [ 12JA.M. Weiner and E.P. Ippen, Chem. Phys. Letters I14 (1985) 456. [ 131A. Mokhtari, J. Chesnoy and A. Lauberau, Chem. Phys. Letters 155 (1989) 593. [ 141R. van den Berg and S. Volker, Chem. Phys. 128 (1988) 257.
539
CHEMICAL PHYSICS LETTERS
5 March1993
Femtosecond electronic dephasing in large molecules in solution using mode suppression C.J. Bardeen and C.V. Shank MaterialSciences Division, Lawrence Berkeley Laboratory. Berkeley, CA 94720, USA and Department of Chemistry, Universityof California,Berkeley, CA 94720, USA
Received3 December 1992
The femtosecond electronic depbasing oflarge molecules in solution is measured using a three-pulse photon echo mode cancellation technique. We have demonstrated the suppression of the quantum interference in the echo decay caused by the dominant ring breathing mode at 590 cm-’ found in oxazine dyes. We have calculated the echo decay including the entire manifold of vibronic levels and have determined the dephasing time I-, to be in the range of 30 to 70 fs for the dye molecules nile blue and LD690.
The nature of spectral broadening of electronic transitions of large molecules in solution has been a subject of recent interest, as it is hoped that it may shed some light on the dynamics of solvent-solute interactions. Several nonlinear optical techniques, including coherent and incoherent transients [ l-41, holeburning [ 51, resonance Raman [ 61, and Rayleigh scattering [ 7 1, have been used to elucidate the mechanisms of the spectral broadening observed in liquid solutions. In general the manifold of vibronic levels in large molecules complicates the i.nterpretation of these measurements. In this Letter, we describe three-pulse photon echo measurements using a new mode suppression technique [ 81 which greatly reduces the effect of quantum interference from a dominant vibrational mode. Previous threepulse photon echo experiments on large molecules in solution have not addressed the complexity of the multi-level interactions [ 11. Results will be discussed for two oxazine molecules, nile blue (NB) and LD690 (LD), for which we have determined the polarization dephasing time T2 to be in the range of 30 to 70 fs. The three-pulse photon echo measurement is performed with a sequence of three pulses having a duration short compared to the dephasing time, T2.The first pulse in the sequence excites a polarization in the sample at time zero which interferes with the sec-
ond pulse at ~~2,creating a population grating. A third pulse, arriving at t13,scatters from this grating in a phase-matched direction. With rhe third pulse placed at a fixed delay, the scattered energy is measured as a function of the relative time delay between the first two pulses. Contributions to spectral broadening can be divided according to time scale into an inhomogeneous component (corresponding to processes slow compared to the time scale of the measurement) and a homogeneous component (processes fast compared to the time scale of the measurement )_ In the two extremes, and assuming a simple two-level system, a largely inhomogeneously broadened line will result in a signal asymmetric about f12=0 and exponentially decaying for tlz> 0 with a time constant of a T,, while a homogeneously broadened line will give rise to a symmetric signal with a time constant of 4T2. A dye molecule is a multi-level system. A short light pulse can coherently excite vibrational modes having a period longer than the pulse duration [ 91. In the three-pulse echo, the first two pulses create a coherent population which undergoes time-dependent oscillatory motion, If we consider a single coherently excited mode, it is possible to time the third pulse such that it samples the nonstationary population in or out of phase with the vibrational mode. If the echo is measured out of phase with the vibration, the echo
0009-2614/93/$ 06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.
535
signal is diminished and driven down by quantum interference between the levels of that mode, or equivalently by the rapid motion of the wavepacket away from the Franck-Condon region. However if the measurement is made in phase with the vibration, the quantum interference will be suppressed [ 81. In contrast, the two-pulse photon echo will always be modulated by the quantum beating between the excited levels of the system, and this can lead to a fast apparent decay which is more indicative of vibronic congestion than of the pure dephasing time T,.The effectiveness of the quantum beat suppression technique relies on the vibrational coherence of the population and to a lesser extent on the degree of inhomogeneous broadening in the system. The experimental arrangement is identical to that described previously [ 11. Briefly, the output of a CPM dye laser is amplified at an 8 kHz repetition rate and focused into a single-mode optical fiber, whose spectrally broadened output is then compressed by gratings and prisms. A typical pulse spectrum is shown in fig. 1, along with the absorption spectra of nile blue and LD690 for comparison. The pulse spectrum shown in fig. 1 has both the red and blue edges clipped to improve the temporal and spatial quality of the pulses, which can be degraded by excess spectrum resulting from processes other than self-phase modulation in the fiber. The typical pulsewidth measured by non-collinear second harmonic generation is 9-l 0 fs, assuming a sech’ pulse shape. The ultrashort pulses are split into three beams of
550
570
590 610 Wavelength
630 650 [nm)
670
690
Fig. 1. Absorption of nile blue (single dashed line) and of LD690 (double dashed line) and the power spectrum of the femtosecond pulses used in the experiment.
536
5 March 1993
CHEMICAL PHYSICS LETTERS
Volume 203, number 5,6
parallel polarization and focused onto a flowing jet of the dye dissolved in ethylene glycol and a small amount of methanol to aid solubility. The scattered light in the -k,+k2+k3 phase-matched direction is collected using an iris and a collimating lens, and detected by a PMT. The jet thickness is approximately 50 pm, with a dye concentration such that the transmittance of the beam is 30% or more. Thermal effects are eliminated by flowing the jet rapidly enough to have complete replacement of the active spot between laser shots. The experimental pulse energy is approximately 0.5 nJ, a factor 5 below the level at which the signal was observed to depart from an I3 dependence. No change in the signal decay is observed at energies as low as 0.05 nJ. Possible nonresonant contributions from the neat solvent were checked for: none were found. We apply the mode suppression technique to the problem of determining the pure dephasing time T2 of the molecules NB and LD, taking advantage of the fact that both have a dominant ring breathing mode at 590 cm-‘, corresponding to a period of about 60 fs. This can be seen most easily in fig. 2, which is the signal obtained by setting the delay of the first two pulses, f12,to zero and scanning fL3,the delay of the third. This corresponds to a transmission correlation experiment, which essentially measures the population dynamics integrated over all pulse wavelengths. In both cases oscillations with a period of approximately 60 fs are clearly in evidence and are the result of the 590 cm-’ ring breathing mode.
I -50
/ 50
43
150
delay
250
Ifs)
350
Fig. 2. Experimental signal for setting f12to zero and scanning t,,, the delay of the third pulse, showing the population dynamics of (a) LD690, and (b) bile blue.
Volume 203, number 5,6
CHEMICAL PHYSICS LETTERS
The data in fig. 3 shows three-pulse echo signals (thick lines) measured as a function of tr2 with t,,=60 fs and t,,=90 fs. It is immediately apparent from the data that the echo decay is different at these two time delays. The measurement at 60 fs delay is in phase with the vibration and is clearly asymmetric and shifted in time with a slower decay than the 90 fs measurement. The difference between the two third-pulse delays demonstrates that the 590 cm-’ mode plays a significant role in determining the observed decay and must be taken into account for any quantitative interpretation of the echo signal. In addition the asymmetry in the echo is indicative of inhomogeneous broadening [2]. Results for LD are plotted in fig. 4, where the suppression effect is even more dramatic. In order to get an idea of what processes are contributing to the observed signal, it is necessary to calculate the photon echo in the perturbation limit. This involves evaluating the four time correlation functions for a multi-level system that result from a perturbative solution of the optical Bloch equations. We use Mukamel’s semi-classical Liouville space formalism and the resulting integrals are evaluated numerically [ 101. For NB the frequencies and excited state displacements of the forty Raman active modes as determined by Lawless et al. [ 61 are used in the calculation. For the molecule LD, such detailed mode data were not available and an approximate model that fits the linear absorption spectrum of LD is used
0 _
-1
;;) -2 & -3 ._ LI) 4 5 -5 -6 -7
, -20
40
Fig. 3. Experimental (thick) and calculated (thin ) three-p Ill! ie echo signals, scanning the second pulse (fJ, for third-pulse delays oft,,=60 fs (solid) and t,,=90 fs (dotted) in nile blue. For the calculated signal a T2 of 70 fs and an inhomogeneous hwhm of 450 cm-’ have been assumed.
5 March 1993
0 -1
:: -2 E m -3 -n cn I -4 5 “5 -6 -7J’, -40
, -2Q
20 ti:
40
delay (fsl
Fig. 4. Experimental (thick) and calculated (thin) three-pulse echo signals, scanning the second pulse, for tlx= 60 fs (solid) and tIJ = 90 fs (dotted) in LD690. For the calculated signal a Tr of 30 fs and an inhomogeneous hwhm of 295 cm-’ have heen assumed.
for the calculation. A representation of the electric field of the pulse is obtained by Fourier transforming the square root of the experimentally measured power spectrum of the pulse. This assumes the optical pulse is transform limited, a reasonable approximation for the experiment which, unlike the two-pulse echo, is not very sensitive to the detailed phase structure of the pulse [ 21. Indeed, the calculation is found to be insensitive to the chirp of the pulse as long as the pulse is short compared to the coherent population dynamics. The results of the calculations are shown in figs. 3 and 4 (thin lines). For the case of NB a TXof 70 fs and a Gaussian inhomogeneous hwhm of 450 cm-’ are assumed for the calculation. There is good qualitative agreement with the essential features of the signal and a clear indication of inhomogeneous broadening and dephasing on a femtosecond time scale. The fit is not perfect, especially considering the absolute widths of the signal and the presence of the beginning of a recurrence of the 60 fs oscillation in the t,3=90 fs calculation. One possible reason for the discrepancy between theory and experiment is that we have assumed the molecule to be a simple harmonic system with undamped vibrational modes. In this case the difference in signals at ti,=60 fs and t,,=90 fs should also be observed at 120, 150, 180 fs, etc., as the third pulse is delayed in and out of phase with the coherent vibration. For NB the quantum beat suppression is fairly pronounced at 60 fs, is reduced at 120 fs, and no effect is observed by 180 fs. After three oscillations electronic transition ap537
Volume 203, number 5,6
CHEMICAL PHYSICS LETTERS
pears to be entirely homogeneously broadened. This effect implies the memory
that the system is undergoing of the polarization
a loss of
read into it by the
first two pulses and has often been termed spectral diffusion [ 2,111. Spectral diffusion arises from a change in level occupation and can result from random solvent modulations or from intramolecular energy redistribution. Supporting evidence for the latter process can be seen in fig. 2b for NB. Note that the oscillations undergo very rapid damping at early times and reach a steady state amplitude by about 200 fs. The calculated response, assuming 40 harmonic modes, shows undamped oscillations persisting for much longer, qualitatively different from what is observed. Such fast population dynamics have been inferred from previous pump-probe [ 121 and timeresolved fluorescence [ 131 measurements, suggesting that significant excited state intramolecular vibrational redistribution occurs on the femtosecond time scale. A theoretical model for NB that treats IVR in the condensed phase is beyond the scope of this Letter but is probably necessary if we are to obtain quantitative agreement with the experimental data. Such fast population processes apparently do not occur in LD, as can be seen in fig. 2a, and in this case the suppression effect disappears much more gradually. LD is a cationic oxazine dye similar to NB, but lacking a phenyl group and with different amino sidechains #‘. These structural differences lead to a spectrum that is slightly blue-shifted from that of NB. LD also possesses a strong mode at approximately 590 cm-‘. The calculation shown in fig. 3 was done assuming four Franck-Condon-connected modes (590, 1140, 1240, and 1640 cm-‘), similar to what has been observed in other oxazines [ 6,141, a T, of 30 fs, and a Gaussian inhomogeneous hwhm of 295 cm-‘. It is interesting to note that although the experimentally observed decay of the photon echo of LD is slower than that of NB, the data can actually be reproduced with a shorter T2. These results illustrate the complex dynamics inherent in a multi-level system, where the observed polarization decay results both from the destructive interference of the levels excited by the pulses and from the pure dephasing represented by T2. In the case of LD where we have assumed a small number of Franck-Con$’Exciton, Inc., Laser Dye Catalog. 538
5 March I993
don-connected modes for the calculation, much of the damping has to come from T2 itself and thus T, must be short in order to model the data. A more realistic model of LD would probably include more modes and result in a proportionately longer T2, so our value of 30 fs is most likeiy a lower bound. In short, a complete description of the Franck-Condon allowed transitions must be known to accurately model the echo decay and separate multi-level effects from that of pure dephasing, which presumably contains information on the time scale of the solvent chromophore interaction. In conclusion we have demonstrated that by using an appropriately timed pulse sequence it is possible to suppress the influence of the 590 cm-’ ring breathing mode on the photon echo from large oxazine molecules in solution. We have calculated the echo using the known manifold of vibrational modes, the measured optical pulse, and with T, as a free parameter, and have reproduced the qualitative features of the data. Our results clearly indicate inhomogeneous broadening on the femtosecond time scale with a T, in the range 30 to 70 fs, and that in NB the echo information is lost on the order of a few hundred femtoseconds, perhaps due to intramolecular energy redistribution. We thank Dr. R.W. Schoenlein, Dr. W.T. Pollard, Dr. J.-Y. Bigot and M.K. Lawless for enlightening discussions. This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences of the US Department of Energy under Contract No. DE-AC03-76SF00098. CJB acknowledges a DOED fellowship.
References [I ] J.Y. Bigot, M.T. Portella, R.W. Schoenlein, C.J. Bardeen, A. Migus and C.V. Shank, Phys. Rev. Letters 66 (I 991) 1138; PC. Becker, H.L. Fragnito, J.Y. Bigot, C.H. BritoCrnz, R.L. Fork and C.V. Shank, Phys. Rev. Letters 63 ( 1989) 505. [2 ] A.M. Weiner, S. De Silvestri and E.P. Ippcn, J. Opt. Sot. Am.B2(1985)654; S. De Silvcstri, A.M. Weiner, J.G. Fujimoto and E.P. Ippen, Chem. Phys. Letters I1 2 ( 1984) 195. [ 3 ] E.T.J. Nibbering, D. Wiersma and K. Duppen, Phys. Rev. Letters 66 (1991) 2465. [4] F. Moshary, M. Arend, R. Friedberg and S.R. Hartmann, Phys. Rev. A 46 (1992) R33.
Volume 203, number 5,6
CHEMICAL PHYSICS LETTERS
[5] C.H. Brito Cruz, R.L. Fork, W.H. Knox and C.V. Shank, Chem. Phys. Letters 132 (1986) 341. [6] M.K. Lawless and R.A. Mathies, J. Chem. Phys. 96 ( 1992) 8037. [7] T. Yajima, H. Souma and Y. Isbida, Phys. Rev. A 17 (1978) 324. [S] R.W. Schoenlein, D.M. Mittleman, J.J. Shiang, A.P. Alivisatos and C.V. Shank, Phys. Rev. Letters, submitted for publication. [9] H.L. Fragnito, J.Y. Bigot, P.C. Becker and C.V. Shank, Chem. Phys. Letters 160 (1989) 101.
5 March 1993
[IO] Y.J. Yan and S. Mukamel, J. Chem. Phys. 89 (1988) 5160; 94 (1991) 179; W.T. Pollard, S.L. Dexheimer, Q. Wang, L.A. Peteanu, C.V. Shankand R.A. Math&, J. Phys. Chem. 96 (1992) 6147. [ 111C. Morou, IEEE I. Quantum. Electron. 11 ( 1975) I. [ 12JA.M. Weiner and E.P. Ippen, Chem. Phys. Letters I14 (1985) 456. [ 131A. Mokhtari, J. Chesnoy and A. Lauberau, Chem. Phys. Letters 155 (1989) 593. [ 141R. van den Berg and S. Volker, Chem. Phys. 128 (1988) 257.
539