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The Journal of Chemical Physics

Femtosecond pump-probe spectroscopy of I2 in a dense rare gas environment: A mixed quantum/classical study of vibrational decoherence

C. Meier, Juan Alberto Beswick

Published Aug 23, 2004• 31 citations
Publisher

Abstract

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.

DOI
10.1063/1.1774159

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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.
In this paper, we present simulations of the decay of quantum coherence between vibrational states of I(2) in its ground (X) electronic state embedded in a cryogenic Kr matrix. We employ a numerical method based on the semiclassical limit of the quantum Liouville equation, which allows the simulation of the evolution and decay of quantum vibrational coherence using classical trajectories and ensemble averaging. The vibrational level-dependent interaction of the I(2)(X) oscillator with the rare-gas environment is modeled using a recently developed method for constructing state-dependent many-body potentials for quantum vibrations in a many-body classical environment [J. M. Riga, E. Fredj, and C. C. Martens, J. Chem. Phys. 122, 174107 (2005)]. The vibrational dephasing rates gamma(0n) for coherences prepared between the ground vibrational state mid R:0 and excited vibrational state mid R:n are calculated as a function of n and lattice temperature T. Excellent agreement with recent experiments performed by Karavitis et al. [Phys. Chem. Chem. Phys. 7, 791 (2005)] is obtained.
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.
Revealing possible long-living coherence in ultrafast processes allows detecting genuine quantum mechanical effects in molecules. To investigate such effects from a quantum chemistry perspective, we have developed a method for simulating the time evolution of molecular systems based on ab initio calculations, which includes relaxation and environment-induced dephasing of the molecular wave function whose rates are external parameters. The proposed approach combines a quantum chemistry description of the molecular target with a real-time propagation scheme within the time-dependent stochastic Schrödinger equation. Moreover, it allows a quantitative characterization of the state and dynamics coherence through the l1-norm of coherence and the linear entropy, respectively. To test the approach, we have simulated femtosecond pulse-shaping ultrafast spectroscopy of terrylenediimide, a well-studied fluorophore in single-molecule spectroscopy. Our approach is able to reproduce the experimental findings [R. Hildner et al., Nat. Phys. 7, 172 (2011)], confirming the usefulness of the approach and the correctness of the implementation.
Electronic and vibrational coherences of Cl2 embedded in solid Ar are investigated by exciting to the B state with a phase-locked pulse pair from an unbalanced Michelson interferometer, where the chirp difference matches the B state anharmonicity. Recording the A' --> X fluorescence after relaxation is compared to probing to charge transfer states by a third pulse. The three-pulse experiment delivers more details on the decoherence processes. The signal modulation due to phase tuning up to the third vibrational round-trip time indicates that the electronic coherence in the B <-- X transition is preserved for more than 660 fs in the solid Ar environment where many body electronic interactions take place. Vibrational coherence lasts longer than 3 ps according to the observed half revival of the wavepacket. Control of the coupling between wavepacket motion and lattice oscillation is demonstrated by tuning the relative phase between the phase-locked pulses, preparing wavepackets predominantly composed of either zero-phonon lines or phonon side bands.