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Physical Review A

Collective oscillations of ultracold matter

José Tito Mendonça

Published Feb 24, 2010• 19 citations
Publisher

Abstract

We consider the collective oscillations of an ultracold atomic cloud by using a wave kinetic description which retains phonon recoil effects. We derive an exact quantum-wave dispersion relation for hybrid plasma-acoustic oscillations and the associated atomic Landau damping. The quasilinear kinetic theory is also extended into the quantum regime, leading to a Boltzmann type of equation for the atoms in a collective force field. Comparison with our previous quasiclassical results is considered. Diffusion in velocity space due to density fluctuations is discussed in detail. This will us allow to establish an additional temperature limit, different from the usual Doppler limit, below which the laser cooling process is prevented by the density fluctuations. This work could also be useful to describe low-frequency Doppler instabilities, as well as collective phonon laser processes.

DOI
10.1103/physreva.81.023421

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We investigated hybrid modes and traveling wave propagation in an ultracold atomic gas. Using both fluid and kinetic plasma description models, we treat the nonlinear oscillation modes of a cloud of ultracold atoms confined in a magneto-optical trap (MOT). The effect of repulsive forces between nearby atoms is discussed, through the key parameterzeffqeffz_{\mathrm { eff }}q_{\mathrm { eff}}zeff​qeff​which ranges from10−5e10^{-5}e10−5eto10−3e10^{-3}e10−3e. The gas is treated as an effective plasma-like single species. We focused on wave propagation dynamics, considering only thermal pressure and effective Coulomb interaction effects. A small amplitude wave analysis revealed the existence of nonlinear plasma-like oscillations and cnoidal structure waves governed by the effective charge number (zeffz_{\mathrm { eff}}zeff​).
We consider Landau damping of elementary excitations in Bose-Einstein condensates (BECs) with dipolar interactions. We discuss quantum and quasiclassical regimes of Landau damping. We use a generalized wave-kinetic description of BECs which, apart from the long-range dipolar interactions, also takes into account the quantum fluctuations and the finite-energy corrections to short-range interactions. Such a description is therefore more general than the usual mean-field approximation. The present wave-kinetic approach is well suited for the study of kinetic effects in BECs, such as those associated with Landau damping, atom trapping, and turbulent diffusion. The inclusion of quantum fluctuations and energy corrections changes the dispersion relation and the damping rates, leading to possible experimental signatures of these effects. Quantum Landau damping is described with generality, and particular examples of dipolar condensates in two and three dimensions are studied. The occurrence of roton-maxon excitations, and their relevance to Landau damping, are also considered in detail. The present approach is mainly based on a linear perturbative procedure, but the nonlinear regime of Landau damping, which includes atom trapping and atom diffusion, is also briefly discussed.