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The Journal of Chemical Physics

Stochastic Schrödinger equation. II. A study of the coherence seen in pump-probe experiments that use a strong pump laser

Dmitrii E. Makarov, Horia I. Metiu

Published Dec 8, 1999• 6 citations
Publisher

Abstract

We use the stochastic Schrödinger equation approach to examine an experiment performed by Scherer, Jonas, and Fleming [J. Chem. Phys. 99, 153 (1993)]. They have excited I2 molecules dissolved in n-hexane with a strong, ultrashort pump pulse. This creates moving wave packets on both the excited and the ground electronic states. The coherent motion of these packets is studied by measuring the absorption of a weak probe pulse, as a function of the delay time between the pulses. We show how the oscillations in the signal are connected to different excitation mechanisms and to the interference between various packets created by the lasers. Our purpose is to clarify the dynamics of the packets and to show that the stochastic Schrödinger equation approach can be used to study their decoherence. We did not intend to try to develop a realistic model for the I2 dynamics and its interaction with the solvent and do not perform a detailed comparison with the experiment. Nevertheless, the calculations reproduce, semiquantitatively, the observations.

DOI
10.1063/1.480364

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We use the stochastic Schrödinger equation approach to examine an experiment performed by Scherer, Jonas, and Fleming [J. Chem. Phys. 99, 153 (1993)]. They have excited I2 molecules dissolved in n-hexane with a strong, ultrashort pump pulse. This creates moving wave packets on both the excited and the ground electronic states. The coherent motion of these packets is studied by measuring the absorption of a weak probe pulse, as a function of the delay time between the pulses. We show how the oscillations in the signal are connected to different excitation mechanisms and to the interference between various packets created by the lasers. Our purpose is to clarify the dynamics of the packets and to show that the stochastic Schrödinger equation approach can be used to study their decoherence. We did not intend to try to develop a realistic model for the I2 dynamics and its interaction with the solvent and do not perform a detailed comparison with the experiment. Nevertheless, the calculations reproduce, semiquantitatively, the observations.
The process of decoherence of vibrational states of I2 in a dense helium environment is studied theoretically using the mixed quantum/classical method based on the Bohmian formulation of quantum mechanics [E. Gindensperger, C. Meier, and J. A. Beswick, J. Chem. Phys. 113, 9369 (2000)]. Specifically, the revival of vibrational wave packets is a quantum phenomena which depends sensitively on the coherence between the vibrational states excited by an ultrafast laser pulse. Its detection by a pump-probe setup as a function of rare gas pressure forms a very accurate way of detecting vibrational dephasing. Vibrational revivals of I2 in high pressure rare gas environments have been observed experimentally, and the very good agreement with the simulated spectra confirms that the method can accurately describe decoherence processes of quantum systems in interaction with an environment.
The mixed quantum-classical method based on the Bohmian formulation of quantum mechanics [J. Chem. Phys. 113, 9369 (2000)]] is applied to study the process of vibrational decoherence of I2 in a dense helium environment. Specifically, the revival of vibrational wave packets, detectable by pump-probe spectroscopy, is a quantum phenomena which depends sensitively on the coherence between the vibrational levels excited by the pump pulse. The time-dependent pump-probe revival signal is a very sensitive way of detecting vibrational dephasing induced by an environment. The very good agreement between previous experimental signals and calculations presented in ths work confirms the theoretical approach and provides a promising basis for the prediction and interpretation of future experiments exploiting quantum revivals as a probe of decoherence.
Pump-probe, four-wave, and six-wave mixing measurements of I2 isolated in solid argon are used to provide a clear experimental measure for the onset of vibrational quantum decoherence on the excited electronic state. The electronically resonant, six-wave mixing measurements bypass the rapid electronic dephasing, and measure the quantum cross-correlation between two packets launched on the B-state. The vibrational quantum coherence survives one period of motion, 400 fs, during which approximately 2000 cm(-1) of energy is transferred to the lattice. The decoherence occurs during the second cycle of motion, while classically coherent motion measured via pump-probe spectroscopy using the same electronic resonances continues for approximately 15 periods. This is contrasted with vibrational dephasing on the ground electronic surface, which lasts for 10(2) periods, as measured through time-resolved coherent anti-Stokes Raman scattering. The measurements and observables are discussed through time-circuit diagrams, and a mechanistic description of decoherence is derived through semiclassical analysis and simulations that reproduce the experiments.
The dependence of the electronic absorption spectrum of a dye molecule on the time of delay between the excitation of the molecule by a pump-laser pulse and the probing of the absorption by a test-laser pulse is studied. The effect of dephasing of the molecular transition arising from the interaction with dissipative systems is described by a stochastic modulation of the electronic transition frequency. It is shown that in the case when the two laser pulses are short compared with the correlation time of the frequency modulation and when the spectral linewidth of the pump-laser light is smaller than the bandwidth of the equilibrium absorption spectrum, hole burning appears although the molecules have equal mean transition frequencies. This effect arises from non-Markovian correlations between the dephasings of the molecule during the actions of the pump- and the test-laser pulse. With increasing delay time the holes are smoothed out and disappear when the delay time exceeds the correlation time. Such effects were found in recent femtosecond absorption experiments by Shank et al. [in Ultrafast Phenomena V, dited by G. R. Fleming and A. E. Siegman (Springer, Berlin, 1986), p. 179].
Two atoms in an ultracold gas are correlated at short interatomic distances due to threshold effects in which the potential energy of their interaction dominates the kinetic energy. The correlations manifest themselves in a distinct nodal structure of the density matrix at short interatomic distances. Pump-probe spectroscopy has recently been suggested [Phys. Rev. Lett. 103, 260401 (2009)] to probe these pair correlations: A suitably chosen, short photoassociation laser pulse depletes the ground-state pair density within the photoassociation window, creating a nonstationary wave packet in the electronic ground state. The dynamics of this nonstationary wave packet is monitored by time-delayed probe and ionization pulses. Here we discuss how the choice of the pulse parameters affects the experimental feasibility of this pump-probe spectroscopy of two-body correlations.
This work presents expressions for the excited population resulting from a Ramsey pump-probe interferometric experiment in the short-weak-pulse limit. It describes time-resolved measurements, which have no direct frequency-resolved analogy, in terms of the eigenenergies, amplitudes, and lifetimes of the excited wave packet. An interferometric phase cross correlation is shown to affect wave packet dynamics by shifting the dispersion of a Rydberg-like wave packet with respect to zero delay. This work phenomenologically introduces eigenstate lifetimes into the expression for the excited population in the Ramsey pump-probe interferometric measurement. An interferometric intensity cross correlation is shown to produce an excited population that, as a function of the delay between pump and probe pulses, is asymmetric about zero delay when the excited eigenstate decays.