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arXiv:0912.4420 · Physical Review A

Collective oscillations in ultracold atomic gas

José Tito Mendonça, Robin Kaiser, Hugo Terças, Jorge Loureiro

Published Jul 11, 2008• 59 citations
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Abstract

Using both fluid and kinetic descriptions, with repulsive forces between nearby atoms included, we discuss the basic oscillations and waves of a cloud of ultracold atoms confined in a magneto-optical trap. The existence of a hybrid mode, with properties similar to both plasma and acoustic waves, is described in detail. Tonks-Dattner resonances for confined hybrid modes in a spherical cloud are discussed, and the prediction of a nonlinear coupling between the dipole resonance and the hybrid modes is considered. Landau damping processes and quasilinear diffusion in velocity space are also discussed.

DOI
10.1103/physreva.78.013408

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Using both fluid and kinetic descriptions, with repulsive forces between nearby atoms included, we discuss the basic oscillations and waves of a cloud of ultracold atoms confined in a magneto-optical trap. The existence of a hybrid mode, with properties similar to both plasma and acoustic waves, is described in detail. Tonks-Dattner resonances for confined hybrid modes in a spherical cloud are discussed, and the prediction of a nonlinear coupling between the dipole resonance and the hybrid modes is considered. Landau damping processes and quasilinear diffusion in velocity space are also discussed.
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 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.
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Abstract Confined atomic clouds in a magneto-optical trap can be formally interpreted as a single component trapped plasma. A hydrodynamical model in a three-dimensional geometry with radial symmetry is applied. A general polytropic equation of state is assumed. For suitable initial conditions and velocity fields, the Lagrangian variables method reduces the problem to ordinary differential equations in the limiting cases according to the prevalence of thermal or multiple-scattering (MS) effects. The thermal, pressure dominated case with adiabatic equation of state leads to a dissipative nonlinear oscillator with an inverse cubic force, in the form of a damped Pinney equation. An accurate approximate analytic solution derived from Kuzmak–Luke perturbation theory allows the assessment of the fully nonlinear dynamics. The applicability conditions of the two regimes are discussed. The intermediate case where both thermal and MS effects are equally relevant is also analytically studied.
An ultracold Bose gas of two-level atoms can be thought of as a spin-1/2 Bose gas. It supports spin-wave collective modes due to the exchange mean field. Such collective spin oscillations have been observed in recent experiments at JILA with 87Rb{}^{87}\mathrm{Rb}87Rb atoms confined in a harmonic trap. We present a theory of the spin-wave collective modes based on the moment method for trapped gases. In the collisionless and hydrodynamic limits, we derive analytic expressions for the frequencies and damping rates of modes with dipole and quadrupole symmetry. We find that the frequency for a given mode is given by a temperature-independent function of the peak density n, and falls off as 1/n.1/n.1/n. We also find that, to a very good approximation, excitations in the radial and axial directions are decoupled. We compare our model to the numerical integration of a one-dimensional version of the kinetic equation and find very good qualitative agreement. The damping rates, however, show the largest deviation for intermediate densities, where one expects Landau damping---which is unaccounted for in our moment approach---to play a significant role.