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Physical Review A

Many-body quantum Monte Carlo wave-function approach to the dissipative atom-field interaction

Ataç İmamoğlu, Li You

Published Sep 1, 1994• 25 citations
Publisher

Abstract

We develop a many-body quantum Monte Carlo wave-function approach to analyze the dissipative interaction of ultracold free atoms with the radiation field reservoir. A Markovian master equation for the identical atoms that neglects the dipole-dipole interaction is derived within the framework of quantum field theory. The effective Hamiltonian obtained by a decomposition of the master equation explicitly depends on the quantum statistics.

DOI
10.1103/physreva.50.2642

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We develop a many-body quantum Monte Carlo wave-function approach to analyze the dissipative interaction of ultracold free atoms with the radiation field reservoir. A Markovian master equation for the identical atoms that neglects the dipole-dipole interaction is derived within the framework of quantum field theory. The effective Hamiltonian obtained by a decomposition of the master equation explicitly depends on the quantum statistics.
We present a wave-function approach to the study of the evolution of a small system when it is coupled to a large reservoir. Fluctuations and dissipation originate in this approach from quantum jumps that occur randomly during the time evolution of the system. This approach can be applied to a wide class of relaxation operators in the Markovian regime, and it is equivalent to the standard master-equation approach. For systems with a number of states N much larger than unity this Monte Carlo wave-function approach can be less expensive in terms of calculation time than the master-equation treatment. Indeed, a wave function involves only N components, whereas a density matrix is described by N2 terms. We evaluate the gain in computing time that may be expected from such a formalism, and we discuss its applicability to several examples, with particular emphasis on a quantum description of laser cooling.
Summary form only given. Nonlinear Schrodinger equations are ubiquitous in physics, and appear in problems ranging from Bose liquids and light propagation in nonlinear media to quantum chains, nonlinear atom optics, and atomic Bose condensation. A generic situation leading to a nonlinear Schrodinger equation description involves the effective single-particle dynamics of a many-particle system coupled by a two-body interaction, and with the manybody wave function truncated via a Hartree-Fock Ansatz. However, if this system is in addition coupled to one, or possibly several reservoirs, such a description is no longer appropriate, and must be superseded by a master equation.
Very recently there have been a number of papers discussing the applicability of stochastic methods as an alternative to the usual treatment of master equations in quantum mechanics.1-5 In this paper we present a wave function approach including a stochastic element to study the evolution of a small system when it is coupled to a reservoir. We show how fluctuations and dissipation originate from quantum jumps occuring randomly during the time evolution of the system, and we present a physical interpretation of the procedure. We demonstrate how this treatment may replace a wide class of master equations, and its use in problems with a large number of states N is discussed. Since the density matrix has N ×N elements, where a wave function is determined by only N variables, there is a computational advantage in using the wave function procedure. This is illustrated by calculations on cooling atoms in a laser field.
Here we study the dynamics of many-body quantum systems using the time-dependent quantum Monte Carlo method where the evolution is described by ensembles of particles and guide waves. The exponential time scaling inherent to the quantum many-body problem is reduced to polynomial-time computation by solving concurrently a set of coupled Schrodinger equations for the guide waves in physical space and a set of first-order equations for the Monte Carlo walkers. We use effective potentials to account for the local and nonlocal quantum correlations in time-varying fields, where for fermionic states an exchange "hole" is introduced explicitly through screened Coulomb potentials. The walker distributions for the ground states of para- and ortho-helium reproduce well the statistical properties, such as the electron-pair density function, of the real atoms. Our predictions for the dipole response and the ionization of an atom exposed to strong ultrashort optical pulse are in good agreement with the exact results.
We extend the quantum Monte Carlo wave-function method of quantum optics to non-Markovian system-reservoir interactions. The finite correlation time of the reservoir and the associated memory effects are incorporated into the dynamics by expanding the initial system using fictitious harmonic-oscillator modes, which have Markovian dissipative interactions. The underlying principle is the fact that a class of reservoir spectral functions can be approximated by a finite superposition of Lorentzian functions with positive coefficients.