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Physical Review A

Quantum dynamics of a laser-cooled ideal gas

J. I. Cirac, Maciej Lewenstein, P. Zoller

Published Oct 1, 1994• 33 citations
Publisher

Abstract

We study a system of bosonic or fermionic atoms in a microscopic trap undergoing laser cooling. We derive a master equation governing the evolution of such a system, and show that the stationary state can be described by Bose-Einstein or Fermi-Dirac distributions. The quantum-statistical character of the atoms exhibits itself in the dynamical behavior of the system and in the statistical properties of fluorescence photons emitted in the stationary state.

DOI
10.1103/physreva.50.3409

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We study a system of bosonic or fermionic atoms in a microscopic trap undergoing laser cooling. We derive a master equation governing the evolution of such a system, and show that the stationary state can be described by Bose-Einstein or Fermi-Dirac distributions. The quantum-statistical character of the atoms exhibits itself in the dynamical behavior of the system and in the statistical properties of fluorescence photons emitted in the stationary state.
Abstract Chapter 11 presents a statistical mechanical treatment of the quantum ideal gases, i.e., the ideal Boltzmann, fermion, and boson gases. The discussion begins with the microscopic description and the solution of the eigenvalue problem for a quantum ideal gas. It is argued that calculating the partition function is most readily accomplished in the grand canonical ensemble using a second-quantized formulation. When the particles are distinguishable, the equation of state is identical to that of a classical ideal gas. For fermions and bosons, however, the problem of computing thermodynamic properties is significantly more complex and can only be solved exactly in certain limits. Away from these limits approximations are needed and are discussed in detail. The relevant distributions - the Fermi-Dirac and Bose-Einstein distributions are derived. The local density approximation of density functional theory is derived for the ideal electron gas. For the ideal boson gas, the phenomenon of Bose-Einstein condensation is discussed
A system of bosons in a harmonic trap is cooled via their interactions with a thermal reservoir. We derive the master equation that governs the evolution of the system and may describe diverse physical situations: laser cooling, sympathetic cooling, etc. We investigate in detail the dynamics of the gas in the Lamb-Dicke limit, whereby the size of the trap is small in comparison with the de Broglie wavelength of the reservoir quanta. In this case, the dynamics is characterized by two time scales. First, an equilibrium is reached on a fast time scale within the degenerated subspaces of the system. Then, an equilibrium between these subspaces is reached on a slow time scale .