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Physical Review A

Phonon-induced quantum pair correlation in the diffraction of an ultracold atomic beam by a crystalline solid surface

Weiping Zhang, Daniel F. Walls

Published Nov 1, 1994• 4 citations
Publisher

Abstract

In this paper, a quantum-field theory is employed to study the diffraction of an ultracold atomic beam by a crystalline solid surface. We show that the crystalline solid surface acts as a nonlinear atomic grating for an ultracold atomic beam with a Bose condensate. The nonlinearity in such a mechanical atomic grating is due to the phonon exchange between the atoms in the ultracold atomic beam via the surface lattice vibration. Such a phonon exchange leads to an attractive interatom interaction in the ultracold atomic beam, which results in the generation of correlated atomic pairs in momentum space. Such correlated atomic pairs have similar properties to the conjugate photon pairs in nonclassical light.

DOI
10.1103/physreva.50.4069

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In this paper, a quantum-field theory is employed to study the diffraction of an ultracold atomic beam by a crystalline solid surface. We show that the crystalline solid surface acts as a nonlinear atomic grating for an ultracold atomic beam with a Bose condensate. The nonlinearity in such a mechanical atomic grating is due to the phonon exchange between the atoms in the ultracold atomic beam via the surface lattice vibration. Such a phonon exchange leads to an attractive interatom interaction in the ultracold atomic beam, which results in the generation of correlated atomic pairs in momentum space. Such correlated atomic pairs have similar properties to the conjugate photon pairs in nonclassical light.
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.
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.
Coherent scattering of light from ultracold atoms involves an exchange of energy and momentum introducing a wealth of nonlinear dynamical phenomena.As a prominent example, particles can spontaneously form stationary periodic configurations that simultaneously maximize the light scattering and minimize the atomic potential energy in the emerging optical lattice.Such self-ordering effects resulting in periodic lattices via bimodal symmetry breaking have been experimentally observed with cold gases and Bose-Einstein condensates (BECs) inside an optical resonator.Here, we study a new regime of periodic pattern formation for an atomic BEC in free space, driven by far off-resonant counterpropagating and noninterfering lasers of orthogonal polarization.In contrast to previous works, no spatial light modes are preselected by any boundary conditions and the transition from homogeneous to periodic order amounts to a crystallization of both light and ultracold atoms breaking a continuous translational symmetry.In the crystallized state the BEC acquires a phase similar to a supersolid with an emergent intrinsic length scale whereas the light field forms an optical lattice allowing phononic excitations via collective backscattering, which are gapped due to the infinte-range interactions.The system we study constitutes a novel configuration allowing the simulation of synthetic solid-state systems with ultracold atoms including long-range phonon dynamics.
We develop a theoretical model to investigate the Bragg diffraction of an elongated interacting Bose-Einstein condensate which is illuminated by a pair of laser beams. We find that the mean-field effect resulting from the atomic interaction plays an important role in modifying the atomic coherence. Our results show that both the repulsive and attractive interactions would dampen the momentum oscillation of the condensate; they establish surprisingly distinguishable equilibria for the atomic occupations among different diffraction orders. We also give an experimental proposal to observe this phenomenon.