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Physical Review A

Monte Carlo simulation of the atomic master equation for spontaneous emission

Ralph Dum, P. Zoller, Helmut Ritsch

Published Apr 1, 1992• 656 citations
Publisher

Abstract

A Monte Carlo simulation of the atomic master equation for spontaneous emission in terms of atomic wave functions is developed. Realizations of the time evolution of atomic wave functions are constructed that correspond to an ensemble of atoms driven by laser light undergoing a sequence of spontaneous emissions. The atomic decay times are drawn according to the photon count distribution of the driven atom. Each quantum jump of the atomic electron projects the atomic wave function to the ground state of the atom. Our theory is based on a stochastic interpretation and generalization of Mollow's pure-state analysis of resonant light scattering, and the Srinivas-Davies theory of continuous measurements in photodetection. An extension of the theory to include mechanical light effects and a generalization to atomic systems with Zeeman substructure are given. We illustrate the method by simulating the solutions of the optical Bloch equations for two-level systems, and laser cooling of a two-level atom in an ion trap where the center-of-mass motion of the atom is described quantum mechanically.

DOI
10.1103/physreva.45.4879

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A Monte Carlo simulation of the atomic master equation for spontaneous emission in terms of atomic wave functions is developed. Realizations of the time evolution of atomic wave functions are constructed that correspond to an ensemble of atoms driven by laser light undergoing a sequence of spontaneous emissions. The atomic decay times are drawn according to the photon count distribution of the driven atom. Each quantum jump of the atomic electron projects the atomic wave function to the ground state of the atom. Our theory is based on a stochastic interpretation and generalization of Mollow's pure-state analysis of resonant light scattering, and the Srinivas-Davies theory of continuous measurements in photodetection. An extension of the theory to include mechanical light effects and a generalization to atomic systems with Zeeman substructure are given. We illustrate the method by simulating the solutions of the optical Bloch equations for two-level systems, and laser cooling of a two-level atom in an ion trap where the center-of-mass motion of the atom is described quantum mechanically.
We discuss Monte Carlo simulation of the quantum master equation in terms of system wave functions undergoing a sequence of quantum jumps based on the delay function for the occurrence of the “next jump”.1-3 The formalism can be applied to calculate the density operator and correlation functions (spectra) in quantum systems with a large number of degrees of freedom. We present the formalism and applications to (i) a multilevel atom undergoing spontaneous emission including mechanical light effects (in particular, laser cooling in the quantum limit), (ii) coupling of an atomic system to a squeezed vacuum, and (iii) cavity QED problems with coupling to thermal and squeezed baths.
In this work Matlab simulation of the atomic Liouville equation for spontaneous emissions was developed for laser cooling of Radium atoms. The atomic decay time driven was determined according to the photon account. The theory includes the mechanical light effect for to atomic structure. The study followed the stimulating solution of Optical Bloch Equations (OBE’s) for four levels system in an atom trap, where the center of mass motion is described quantum mechanically. The results showed that the laser cooling approach to Maxwell’s law, the reduction of the velocity leads to new distribution of velocities and the atoms moving towards the light source will resonate the light field (crossing resonance).
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In this paper we consider the effects of spontaneous emission on the problem of atomic reflection from an optical evanescent travelling wave. The atoms are assumed to be travelling so slowly that the external degrees of freedom of the atom need to be treated quantum mechanically. Spontaneous emission is modelled using a fully quantum mechanical model based on the quantum Monte Carlo technique which includes the effects of atomic recoil. The results of the simulation are compared with a semi-classical Monte Carlo simulation in which the atomic motion is treated classically and the internal state of the atom is assumed to follow the light-induced quasipotentials adiabatically between spontaneous emission events. The spontaneous emission leads to a broadening of the momentum distribution of the outgoing wave packet and mechanisms for this broadening are discussed.
The spontaneous decay of an excited atom by photon emission is one of the most common and elementary physical process present in nature and in laboratories. The decay is random in time with constant probability density, as it can be inferred by the exponential law observed experimentally. Despite the simplicity of the process, in Quantum Mechanics the decay itself is considered a law of nature which is not further analyzed or explained. However it is legitimate to ask for the reason of its randomness and for the dynamics of the atom around the decay. The decay process of an isolated atom is usually assumed to be instantaneous, the so called Quantum jumps. Particular experimental arrangements can widen the duration of the transition from an excited state to the ground state to a finite time. In general this is due to the quantum back action of the detector. The development of Quantum Optics has enormously enriched the possibilities to study in detail the process, and new illuminating insights have been obtained, but the question is still valid and its answer is still elusive. In this paper we analyze the spontaneous decay within the new prospect introduced by a recent model that complete standard Quantum Mechanics in a formalism which is able to describe the dynamics of measurement and of spontaneous decay. Comparison is made with more phenomenological theories, the Quantum Mechanics of open system and the Stochastic wave function model. In the new model the stochastic photon emission by an excited atom is triggered by the vacuum fluctuations. It is suggested how to re-analyze three types of experiments, already realized in many laboratories, in order to reveal the presence and the effect of these fluctuations.