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Acta Physica Polonica A

Dynamics and Stability of Axially Symmetric Atomic Clouds in Magneto-Optical Trap

Luiz Gustavo Ferreira Soares, Fernando Haas

Published Jun 1, 2021• 1 citation
Publisher

Abstract

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.

DOI
10.12693/aphyspola.139.659

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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.
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.
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.
We investigate the dynamics of a weakly open Bose-Einstein condensate with attractive interaction in a magneto-optical double-well trap. A set of time-dependent ordinary differential equations describing the complex dynamics are derived by using a two-mode approximation. The stability of the stationary solution is analyzed and some stability regions on the parameter space are displayed. In the symmetric well case, the numerical calculations reveal that by adjusting the feeding from the nonequilibrium thermal cloud or the two-body dissipation rate, the system could transit among the periodic motions, chaotic self-trapping states of the Lorenz model, and the steady states with the zero relative atomic population or with the macroscopic quantum self-trapping (MQST). In the asymmetric well case, we find the periodic orbit being a stable two-sided limited cycle with MQST. The results are in good agreement with that of the direct numerical simulations to the Gross-Pitaevskii equation.
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 dynamics of weakly interacting three-dimensional Bose-Einstein condensates (BECs), trapped in external axially symmetric plus anharmonic distortion potential are studied. Within a variational approach and time-dependent Gross-Pitaevskii equation, the coupled condensate width equations are derived. By modulating anharmonic distortion of the trapping potential, nonlinear features are studied numerically and illustrated analytically, such as mode coupling of oscillation modes, and resonances. Furthermore, the stability of attractive interaction BEC in both repulsive and attractive anharmonic distortion is examined. We demonstrate that a small repulsive and attractive anharmonic distortion is effective in reducing (extending) the condensate stability region since it decreases (increases) the critical number of atoms in the trapping potential.