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Physical Review A

Quantum field theory of interaction of ultracold atoms with a light wave: Bragg scattering in nonlinear atom optics

Weiping Zhang, Daniel F. Walls

Published May 1, 1994• 98 citations
Publisher

Abstract

A vector quantum field theory is developed to describe the interaction of an ultracold atomic ensemble with a laser field. The ultracold atomic ensemble is composed of either bosonic atoms or fermionic atoms. The photon exchanges between different ultracold atoms result in a long-range interatom interaction. Under appropriate conditions, such a many-body interaction leads to an effective ``Kerr-type'' nonlinearity of atomic waves. In terms of the nonlinearity, we construct a general formalism of nonlinear atom optics for an ultracold atomic beam. Applying the formalism to the diffraction of an ultracold atomic beam composed of bosonic atoms by a standing-wave laser field, we find that the many-body nonlinearity induces self-phase and cross-phase modulation of diffracted atomic waves. As a result, a standing-wave laser acts as a nonlinear atomic grating which diffracts atoms in the same way as a nonlinear periodic medium diffracts photons.

DOI
10.1103/physreva.49.3799

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A vector quantum field theory is developed to describe the interaction of an ultracold atomic ensemble with a laser field. The ultracold atomic ensemble is composed of either bosonic atoms or fermionic atoms. The photon exchanges between different ultracold atoms result in a long-range interatom interaction. Under appropriate conditions, such a many-body interaction leads to an effective ``Kerr-type'' nonlinearity of atomic waves. In terms of the nonlinearity, we construct a general formalism of nonlinear atom optics for an ultracold atomic beam. Applying the formalism to the diffraction of an ultracold atomic beam composed of bosonic atoms by a standing-wave laser field, we find that the many-body nonlinearity induces self-phase and cross-phase modulation of diffracted atomic waves. As a result, a standing-wave laser acts as a nonlinear atomic grating which diffracts atoms in the same way as a nonlinear periodic medium diffracts photons.
The recent experimental progress in laser cooling and trapping of neutral atoms brings the atomic samples into the ultracold regime where the bosonic atoms and fermionic atoms are expected to have different dynamic behaviours in the laser fields. In this paper we systematically introduce the theoretical study of interaction of an ultracold atomic ensemble with a light wave in the frame of a vector quantum field theory. The many-body quantum correlation in the ultracold regime of atom optics is studied in terms of vector quantum field theory. A general formalism of nonlinear atom optics for a coherent atomic beam is developed.
We employ a vector quantum field theory to describe the interaction of a coherent atomic beam with a standing-wave laser field. The coherent atomic beam is assumed to be composed of degenerate bosonic atoms. We derive a nonlinear Schr\"odinger equation to describe the diffraction of the coherent atomic beam through the standing-wave laser field in the adiabatic regime of interaction of atoms with a light wave. Under appropriate conditions, we find that the standing-wave laser field acts as a quantum nonlinear atomic beam splitter for a coherent atomic beam. The quantum correlations in the nonlinear atomic beam splitter are analyzed and the analogy to quantum correlations of nonclassical light in an optical Kerr-type medium is discussed.
We have developed the quantum theory of the interaction of ultracold atomic ensemble with the electromagnetic field of vacuum and laser photons. The main attention is paid to the consistent consideration of dynamical dipole-dipole interactions in the case of the second quantized matter. We show that the retardation effects significantly influence the behavior of atomic ensemble in the radiation field. We have derived the general system of equations, which can be used for the investigation of various linear and nonlinear phenomena in atom optics. As an example, we have considered the diffraction of ultracold atomic beam by the standard laser wave. We show that with the increase of the initial density of the intensities of diffractions modes decrease. We also show that the angles of diffraction for different modes depend on the density.
We study the scattering of an atomic beam slowly passing through a standing laser wave with an amplitude periodically modulated in time. The formal analysis of the problem involves the theory of interacting nonlinear resonances, developed earlier in the field of quantum chaos. Two different diffraction regimes are distinguished: a quasiregular regime, where the atoms are Bragg-like scattered by a primary or secondary nonlinear resonance, and a chaotic regime, where the scattering can be regarded as (quasi)random.