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arXiv:cond-mat/9711231 · Physical Review A

Phase dynamics in a binary-collision atom-laser scheme

O. Zobay, Pierre Meystre

Published Jun 1, 1998• 15 citations
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Abstract

Various aspects of the phase dynamics of an atom-laser scheme based on binary collisions are investigated. Analytical estimates of the influence of elastic atom-atom collisions on the laser linewidth are given, and linewidths achievable in a recently proposed atom-laser scheme [M. G. Moore and P. Meystre, Phys. Rev. A 56, 2989 (1997)] are evaluated explicitly. The extent to which a relative phase can be established between two interfering atom lasers as well as the properties of this phase are also investigated.

DOI
10.1103/physreva.57.4710

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Various aspects of the phase dynamics of an atom-laser scheme based on binary collisions are investigated. Analytical estimates of the influence of elastic atom-atom collisions on the laser linewidth are given, and linewidths achievable in a recently proposed atom-laser scheme [M. G. Moore and P. Meystre, Phys. Rev. A 56, 2989 (1997)] are evaluated explicitly. The extent to which a relative phase can be established between two interfering atom lasers as well as the properties of this phase are also investigated.
An atom laser is a device which would ideally produce a coherent excitation of a single mode of the Bose-atom field. That is to say, an atom laser field would have a well defined number of atoms, and a slow rate of phase diffusion. Here we consider an atom laser model recently proposed by Holland et al, based on evaporative cooling of atoms. We extend their model, and give approximate analytical results for the time-dependent intensity and phase statistics of the atom laser in different regimes. Although the intensity fluctuations may be relatively small, the laser linewidth is always in excess of the bare linewidth of the laser mode. Nevertheless, in one regime (weak collisions), the laser linewidth may be less than the output flux of atoms, which is a minimum requirement for considering the output to be coherent.
It was proposed by two of us (Wiseman H M and Collett M J 1995 Phys. Lett. A 202 246) that a device producing a coherent atomic wave (that is, an atom laser) could be built using dark-state cooling of atoms in a trap. Here we present a more complete analysis of this system, including the effects of atomic interactions through dipole-dipole coupling and hard-core collisions. We show that for reasonable physical parameters the dipole interactions have little contribution to the atomic dynamics. In contrast, the hard-core collisions are likely to dominate the laser linewidth. In fact, it would appear necessary to select (or produce) a species with a hard-core scattering radius of much less than one nm in order for the output of the device to be phase coherent.
In two recent papers [Blum and Lohmann, Phys. Rev. Lett. 116, 033201 (2016); Lohmann et al., Phys. Rev. A 94, 032331 (2016)], the possibility of continuously varying the degree of entanglement between an elastically scattered electron and the valence electron of an alkali-metal target was discussed. To estimate how well such a scheme may work in practice, we present results for elastic electron scattering from lithium in the energy regime of 1−−5eV1--5\phantom{\rule{4pt}{0ex}}\mathrm{eV}1−−5eV and the full range of scattering angles ${0}^{\ensuremath{\circ}}--{180}^{\ensuremath{\circ}}$. The most promising regime for Bell correlations in this particular collision system are energies between about 1.5 and 3.0 eV, in an angular range around ${110}^{\ensuremath{\circ}}\ifmmode\pm\else\textpm\fi{}{10}^{\ensuremath{\circ}}$. In addition to the relative exchange asymmetry parameter, we present the differential cross section that is important when estimating the count rate and hence the feasibility of experiments using this system.
We consider elastic scattering of atoms from elongated clouds taking into account an effective, finite duration of the collision due to the expansion of the condensates. We also include the quasicondensate nature of the degenerate quantum gas, due to a finite temperature of the system. We evaluate the pair-correlation function measured experimentally in Kheruntsyan et al. [Phys. Rev. Lett. 108, 260401 (2012)] and show that the finite duration of the collision is an important factor determining the properties of the correlations. Our analytic calculations are in agreement with the measurements. The analytical model we provide, useful for identifying physical processes that influence the correlations, is relevant for experiments with nonclassical pairs of atoms.