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Physical Review A

Second-order Monte Carlo wave-function approach to the relaxation effects on ringing revivals in a molecular system interacting with a strongly squeezed coherent field

Masayoshi Nakano, Ryohei Kishi, Tomoshige Nitta, Kizashi Yamaguchi

Published Sep 22, 2004• 9 citations
Publisher

Abstract

We investigate the relaxation effects on the quantum dynamics in a two-state molecular system interacting with a single-mode strongly amplitude-squeezed coherent field using the second-order Monte Carlo wave-function method. The molecular population inversion (collapse-revival behavior of Rabi oscillations) is known to show the echoes after each revival, which are referred to as ringing revivals, in the case of strongly squeezed coherent fields with oscillatory photon-number distributions due to the phase-space interference effect. Two types of relaxation effects, i.e., cavity relaxation (the dissipation of an internal single mode to outer mode) and molecular coherent (phase) relaxation caused by nuclear vibrations on ringing revivals are investigated from the viewpoint of the quantum-phase dynamics using the quasiprobability ($Q$ function) distribution of a single-mode field and the off-diagonal molecular density matrix $\ensuremath{\mid}{\ensuremath{\rho}}_{\mathrm{elec}\phantom{\rule{0.3em}{0ex}}1,2}(t)\ensuremath{\mid}$. It turns out that the molecular phase relaxation attenuates both the entire revival-collapse behavior and the increase in $\ensuremath{\mid}{\ensuremath{\rho}}_{\mathrm{elec}\phantom{\rule{0.3em}{0ex}}1,2}(t)\ensuremath{\mid}$ during the quiescent region, whereas a very slight cavity relaxation particularly suppresses the echoes in ringing revivals more significantly than the first revival but hardly changes a primary variation in envelope of $\ensuremath{\mid}{\ensuremath{\rho}}_{\mathrm{elec}\phantom{\rule{0.3em}{0ex}}1,2}(t)\ensuremath{\mid}$ in the nonrelaxation case.

DOI
10.1103/physreva.70.033407

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We investigate the quantum-phase dynamics of a dissipative molecular system interacting with a single-mode amplitude-squeezed field (with a sub-Poissonian photon-number distribution) using the Monte Carlo wave-function method. As quantum dissipation, we consider molecular coherent (phase) and population relaxations, which are caused by nuclear vibration, and cavity relaxation (the dissipation of an internal single mode to outer mode). In this study, we elucidate the effects of these dissipations on the unique quantum dynamical behaviors of this coupled system, e.g., collapse-revival behavior of Rabi oscillations, using the quasiprobability (Q function) distribution of a single-mode field and the off-diagonal molecular density matrix. It is found that although the amplitude-squeezed field exhibits a distinct revival with larger amplitudes of molecular population in the presence of the molecular phase and population relaxations as compared to the coherent field, a very slight cavity relaxation suppresses the revival of molecular population and the increase in the magnitude of off-diagonal molecular density matrices during the quiescent region in the amplitude-squeezed field case more significantly than in the coherent field case. These features are shown to be closely related to the difference in the dynamics of Q function distributions between amplitude-squeezed and coherent fields.
Abstract We investigate the quantum dynamics of a dissipative molecular system interacting with a single‐mode coherent field (with an initial average photon number 8) using the Monte Carlo wave function (MCWF) method. As quantum dissipation, we consider cavity relaxation (the dissipation of an internal single mode to outer mode) and molecular population relaxation and molecular coherent (phase) relaxation caused by nuclear vibration. In this study, we elucidate the effects of these dissipations on the unique quantum dynamic behaviors of this coupled system, e.g., collapse–revival behavior of Rabi oscillations, using the diagonal and off‐diagonal molecular density matrices. It is found that although slight cavity relaxation suppresses the revival of molecular population similarly to other relaxation effects with larger decay rates the cavity relaxation hardly suppresses the increase in the off‐diagonal molecular density matrix (representing the degree of coherency between the ground and excited states) in the quiescent region, the feature of which is related to the generation of the Schrödinger cat state, in contrast to molecular phase and population relaxations. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003
We investigate the quantum dynamics for a molecular-state-model system interacting with a resonant two-mode squeezed coherent field, in which each mode is initially correlated. As an example, we consider a three-state molecular model, which mimics the electronic excited states of trans-octatetraene obtained by a full-configuration-interaction calculation using the Pariser-Parr-Pople Hamiltonian, interacting with a two-mode squeezed coherent field. For comparison, we also perform parallel studies, in which the initial fields are prepared in uncorrelated two-mode states, i.e., a two-mode coherent state and a two-mode thermal state. It is well known that the case of two-mode coherent field leads to the usual collapse-revival phenomena of the Rabi oscillations, while the case of a two-mode thermal state leads to an irregular evolution of them. Although the two-mode squeezed coherent field exhibits similar collapse-revival behavior to that for the two-mode coherent field, some differences are detected in the amplitudes and periods of collapse-revival oscillations. Further, the dynamics of off-diagonal molecular density matrices between the ground and second excited states for these two fields are found to be distinctively different from each other. Such attractive behavior is found to be closely associated with the two-mode photon-phase dynamics obtained by the Pegg-Barnett phase operator and the initial quasiprobability (Q function) distribution of photons. These differences in phase properties are also shown to significantly affect the dynamics of the information entropy for a molecule, i.e., molecular entropy, which represents the degree of entanglement between the molecule and photons.
It is well-known that the interaction among atoms/molecules and quantized electromagnetic fields with a small number of photons provides a peculiar quantum nature, i.e., collapses and revivals in the Rabi oscillations. In this study, we investigate the intermolecular interaction (dipole–dipole interaction) effect on the collapse-revival behavior using several dimer models (composed of two kinds of two-state monomers with slightly different excitation energies) with different intermolecular distances in the presence of a two-mode squeezed coherent field, in which each mode is initially correlated. It is found that although the collapse-revival behavior is fairly overlapped and indistinct in the case of a noninteracting dimer under the present two-mode squeezed coherent field, the decrease in the intermolecular distance (the increase in the intermolecular interaction) resurrects relatively distinct collapse-revival behavior with longer collapse and revival times. By analyzing the quantum behavior from the viewpoint of the dynamics of two-mode Pegg–Barnett photon-phase distributions and off-diagonal dimer density matrices, this feature is found to closely relate to a significant change in the degree of contribution between one- and two-photon processes caused by the variation in the intermolecular interaction.
The Jaynes–Cummings interaction of a two-level atom with the radiation field is studied when the radiation is initially in a strongly squeezed coherent state. The dynamic response of the atomic inversion shows echoes after each revival when the squeezed coherent state exhibits an oscillatory photon-counting distribution due to the phase-space interference effect. The sensitivity of the dynamic behavior to approximations used in computing the atomic inversion is discussed. Comparison is made with the intensity-dependent interaction model of Buck and Sukumar [ Phys. Lett.81A, 132 ( 1981)]; this model does not exhibit echoes. The mean, variance, and entropy for the photon-number distribution are calculated and found to show behavior similar to that of the atomic inversion.
From the viewpoints of photon-phase and information-entropy dynamics, we investigate the dynamical behavior of initially one-mode amplitude- and phase-squeezed photon fields interacting with a two-state molecular system. A peculiar behavior of these systems is known to be the collapses and revivals of Rabi oscillation of the molecular population. As shown in previous studies, significant differences are observed in the amplitude and the period of the collapse−revival behavior for these fields. These differences are found to be well-described by the dynamical behavior of the photon phase (the Pegg−Barnett phase and the quasiprobability ( Q function) distributions). The features of these photon-phase dynamics are also found to provide significant influence on the time evolution of the information entropy of the molecule, which characterizes the degree of the entanglement between the molecule and the field.