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Journal of Physics B Atomic Molecular and Optical Physics

Theory and simulation of the loss of coherence in thermal and nonequilibrium environments

Craig C. Martens

Published Jul 30, 2012• 12 citations
Publisher

Abstract

In this paper, we describe recent work on modelling the loss of quantum coherence in condensed phase systems. We review numerical methodology based on a semiclassical limit of the quantum Liouville equation for simulating quantum coherent processes using classical-like molecular dynamics simulation and ensemble averaging, and apply the approach to simulating vibrational dephasing of I 2 in cryogenic rare gas matrices and the quantum vibrations of OH stretches of HOD in D 2 O. We then describe a simple analytic and numerical model that highlights novel behaviour that can be exhibited by quantum coherent processes in the presence of a nonequilibrium environment.

DOI
10.1088/0953-4075/45/15/154008

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Coherent quantum processes in thermal and nonequilibrium environments

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In this paper, we describe recent work on modelling the loss of quantum coherence in condensed phase systems. We review numerical methodology based on a semiclassical limit of the quantum Liouville equation for simulating quantum coherent processes using classical-like molecular dynamics simulation and ensemble averaging, and apply the approach to simulating vibrational dephasing of I 2 in cryogenic rare gas matrices and the quantum vibrations of OH stretches of HOD in D 2 O. We then describe a simple analytic and numerical model that highlights novel behaviour that can be exhibited by quantum coherent processes in the presence of a nonequilibrium environment.
Abstract In this article, we describe recent work on investigating the role of the environment in influencing coherent quantum dynamics. We review numerical methodology based on a semiclassical limit of the quantum Liouville equation for simulating quantum coherent processes using classical‐like molecular dynamics simulation and ensemble averaging and apply the approach to simulate vibrational dephasing of I2 in cryogenic rare gas matrices and the quantum vibrations of OH stretches of HOD in D2O. We then describe a simple analytic and numerical model that highlights novel behavior that can be exhibited by quantum coherent processes in the presence of an environment that is not at thermal equilibrium. © 2012 Wiley Periodicals, Inc.
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.
In this paper we describe an application of the trajectory-based semiclassical Liouville method for modeling coherent molecular dynamics on multiple electronic surfaces to the treatment of the evolution and decay of quantum electronic coherence in many-body systems. We consider a model representing the coherent evolution of quantum wave packets on two excited electronic surfaces of a diatomic molecule in the gas phase and in rare gas solvent environments, ranging from small clusters to a cryogenic solid. For the gas phase system, the semiclassical trajectory method is shown to reproduce the evolution of the electronic-nuclear coherence nearly quantitatively. The dynamics of decoherence are then investigated for the solvated systems using the semiclassical approach. It is found that, although solvation in general leads to more rapid and extensive loss of quantum coherence, the details of the coupled system-bath dynamics are important, and in some cases the environment can preserve or even enhance quantum coherence beyond that seen in the isolated system.
Methods for simulating the dynamics of composite systems, where part of the system is treated quantum mechanically and its environment is treated classically, are discussed. Such quantum-classical sys- tems arise in many physical contexts where certain degrees of freedom have an essential quantum character while the other degrees of freedom to which they are coupled may be treated classically to a good approxi- mation. The dynamics of these composite systems are governed by a quantum-classical Liouville equation for either the density matrix or the dynamical variables which are operators in the Hilbert space of the quantum subsystem and functions of the classical phase space variables of the classical environment. Solutions of the evolution equations may be formulated in terms of surface-hopping dynamics involving ensembles of tra- jectory segments interspersed with quantum transitions. The surface-hopping schemes incorporate quantum coherence and account for energy exchanges between the quantum and classical degrees of freedom. Various simulation algorithms are discussed and illustrated with calculations on simple spin-boson models but the methods described here are applicable to realistic many- body environments.
This thesis develops mixed quantum-classical methods to model dynamical nonequilibrium quantum phenomena in condensed phase systems, and also explores properties of 2-d systems near a quantum critical point using field theoretic techniques and purely classical simulation. Mixed quantum-classical methods involve dividing the system into a quantum sub-system coupled to a classical bath, which is useful for examining the dynamics of systems in the condensed phase since the full quantum treatment of a large number of degrees of freedom is often computationally infeasible. Although the bath is treated classically, its coupling to the quantum system precludes a Newtonian description. We implement an approach that uses the quantum-classical Liouville equation to propagate the quantum subsystem density matrix, which results in an ensemble of surface-hopping trajectories. We test this method on model systems and compare with a linearized path-integral approach. We also develop a novel approach to propagating the reduced density matrix that incorporates ideas from both methods while
Abstract In the presence of strong dephasing noise the dynamics of Rydberg gases becomes effectively classical, due to the rapid decay of quantum superpositions between atomic levels. Recently a great deal of attention has been devoted to the stochastic dynamics that emerges in that limit, revealing several interesting features, including kinetically constrained glassy behaviour, self-similarity and aggregation effects. However, the non-equilibrium physics of these systems, in particular in the regime where coherent and dissipative processes contribute on equal footing, is yet far from being understood. To explore this we study the dynamics of a small one-dimensional Rydberg lattice gas subject to dephasing noise by numerically integrating the quantum master equation. We interpolate between the coherent and the strongly dephased regime by defining a generalised concept of a blockade length. We find indications that the main features observed in the strongly dissipative limit persist when the dissipation is not strong enough to annihilate quantum coherences at the dynamically relevant time scales. These features include the existence of a time-dependent Rydberg blockade radius, and a growth of the density of excitations which is compatible with the power-law behaviour expected in the classical limit.