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Physica Scripta

Nonlinear oscillations of ultra-cold atomic clouds in a magneto-optical trap

Luiz Gustavo Ferreira Soares, Fernando Haas

Published Jul 25, 2019• 6 citations
Publisher

Abstract

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.

DOI
10.1088/1402-4896/ab34c2

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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.
We briefly review some recent advances in the field of nonlinear dynamics of atomic clouds in magneto-optical traps. A hydrodynamical model in a three-dimensional geometry is applied and analyzed using a variational approach. A Lagrangian density is proposed in the case where thermal and multiple scattering effects are both relevant, where the confinement damping and harmonic potential are both included. For generality, a general polytropic equation of state is assumed. After adopting a Gaussian profile for the fluid density and appropriate spatial dependencies of the scalar potential and potential fluid velocity field, a set of ordinary differential equations is derived. These equations are applied to compare cylindrical and spherical geometry approximations. The results are restricted to potential flows.
The three-dimensional nonlinear dynamics of atomic clouds in a magneto-optical trap is analyzed in terms of a self-consistent fluid formulation using a variational approach.A Lagrangian density is proposed in the case where thermal and multiple-scattering effects are both relevant, in addition to damping.For closure, an adiabatic equation of state is assumed.After adopting a Gaussian profile for the fluid density and appropriated spatial dependencies of the scalar potential and potential fluid velocity field, a set of ordinary differential equations is derived.The linear stability analysis and the prominent features of the associated normal modes are characterized.Unlike previous treatments found in the literature, the current analysis applies to non-spherically symmetric trapped atomic gases.In addition, the use of a variational approach for a dissipative system is a further distinctive feature of the work.The paper is restricted to potential flows.
The compressibility limit of a cold gas confined in a magneto-optical trap due to multiple scattering of light is a long-standing problem. This scattering mechanism induces long-range interactions in the system, which are responsible for the occurrence of plasma-like phenomena. In the present paper, we investigate the importance of the long-range character of the mediated atom-atom interaction in the equilibrium and dynamical features of a magneto-optical trap. Making use of a hydrodynamical formulation, we derive a generalized Lane-Emden equation modeling the polytropic equilibrium of a magneto-optical trap, allowing us to describe the crossover between the two limiting cases: temperature-dominated and multiple-scattering-dominated traps. The normal collective modes of the system are also computed.
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.
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 have observed self-sustained radial oscillations in a large magneto-optical trap, containing up to 10(10) Rb85 atoms. This instability is due to the competition between the confining force of the magneto-optical trap and the repulsive interaction associated with multiple scattering of light inside the cold atomic cloud. A simple analytical model allows us to formulate a criterion for the instability threshold, in fair agreement with our observations. This criterion shows that large numbers of trapped atoms N>10(9) are required to observe this unstable behavior.