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IEEE Transactions on Plasma Science

On the 1-D Plasma-Like Model for Studying Nonlinear Oscillations and Wave Propagation in Ultracold Gases

Elamine Benkhelifa, M. Djebli

Published Oct 1, 2024• 0 citations
Publisher

Abstract

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 parameter$z_{\mathrm { eff }}q_{\mathrm { eff}}$which ranges from$10^{-5}e$to$10^{-3}e$. 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 ($z_{\mathrm { eff}}$).

DOI
10.1109/tps.2024.3492000

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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.
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.
The multiple scattering of light in a gas of ultra cold atoms is responsible for many exciting features observed in magneto-optical traps including the collective behavior forced by a Coulomb like potential. This field also induces plasma like phenomena in the cloud which allows the treatment of the system as a one component trapped plasma. With a fluid description and casting the thermodynamical behavior in the form of a polytropic equation of state we investigate the equilibrium profiles of rotating clouds and its dependence on the experiment characteristics. Numerical solutions predict the formation of stable orbital modes both in rotating and non rotating clouds. We also investigate the normal modes on such rotating systems.
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Here we discuss collective processes and plasma effects that can be found in ultra‐cold matter. First, we consider the ultra‐cold atomic gas that can be produced in a magneto‐optical trap. Due to the existence of long‐range repulsive forces, new collective oscillation can take place, resembling sound waves but with a cut‐off frequency. We also examine new phenomena in Rydberg plasmas, resulting from laser ionization of the ultra‐cold gas. In these very low temperature plasmas a large amount of excited Rydberg states can exist, leading to a new dispersion relation for the electromagnetic waves. Enhanced magnetic field generation will also be considered. Finally, we discuss the collective properties of Bose Einstein condensates, showing a strong analogy with collective plasma processes. Two related examples are given as an illustration: Bogoliubov oscillations in the condensate, and two‐stream instabilities of counter‐streaming BECs.