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Physical Review Letters

Atomic soliton in a traveling wave laser beam

Weiping Zhang, Daniel F. Walls, Barry C. Sanders

Published Jan 3, 1994• 125 citations
Publisher

Abstract

A vector quantum field theory is employed to study the propagation of an ultracold atomic wave packet in a traveling wave laser beam with a Gaussian intensity profile. The collective dipole-dipole correlation induced by photon exchanges between atoms produces a ``Kerr-type'' nonlinearity of atomic waves. We show that such an atomic nonlinearity could result in an atomic soliton under appropriate conditions.

DOI
10.1103/physrevlett.72.60

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 1, 1997•0 citations
A vector quantum field theory is employed to study the propagation of an ultracold atomic wave packet in a traveling wave laser beam with a Gaussian intensity profile. The collective dipole-dipole correlation induced by photon exchanges between atoms produces a ``Kerr-type'' nonlinearity of atomic waves. We show that such an atomic nonlinearity could result in an atomic soliton under appropriate conditions.
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.
An ultracold wave packet of bosonic atoms loaded into a travelling laser wave may form a many-atom soliton. This is disturbed by a homogeneous force field, for example by the inevitable gravitation. The wave packet is accelerated and therefore the laser frequency appears to be chirped in the rest frame of the atoms. We derive the effective nonlinear Schrödinger equation. It shows a time-dependent nonlinearity coefficient which amounts to a damping or antidamping, respectively. The accelerated packet solution remains a soliton which changes its shape adiabatically. Similarly, an active shaping can be obtained in the force-free case by chirping the laser frequency thus representing a way of coherent control of the soliton form. The experimental consequences are discussed.
The deleterious effects of dispersion on a propagating coherent atomic pulse, along the axis of a traveling-wave laser beam, can be ameliorated by the nonlinear self-interacting force due to dipole-dipole coupling between atoms. We show that a wide atomic pulse with a particular profile can retain its shape during propagation and, moreover, the momentum of the pulse increases due to photon absorption. For the wide soliton case, we demonstrate analytically that the self-interacting atomic force scales inversely with the third power of the pulse width.
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.