Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1305.4678 · Physical Review A

Polytropic equilibrium and normal modes in cold atomic traps

Hugo Terças, José Tito Mendonça

Published Aug 9, 2013• 15 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.88.023412

Related papers

Satellite rings and normal modes in rotating clouds of ultra cold atoms

João D. Rodrigues, José Tito Mendonça, Rodrigues, J. A.

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.

arXiv:1406.6098•Jun 23, 2014•0 citations

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

Luiz Gustavo Ferreira Soares, Fernando Haas

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.

Physica Scripta•Jul 25, 2019•6 citations

Driven collective instabilities in magneto-optical traps: A fluid-dynamical approach

Hugo Terças, J. T. Mendonça, Robin Kaiser

We present a theoretical model to describe an instability mechanism in ultra-cold gases, where long-range interactions are taken into account. Focusing on the nonlinear coupling between the collective (plasma-like) and the center-of-mass modes, we show that the resulting dynamics is governed by a parametric equation of the generalized Mathieu type and compute the corresponding stability chart. We apply our model to typical ranges of magneto-optical traps (MOT) parameters and find a good agreement with previous experimental observations.

arXiv:0912.4318•Europhysics Letters (EPL)•Mar 1, 2010•20 citations

Nonlinear Dynamics in Isotropic and Anisotropic Magneto-Optical Traps

Fernando Haas, Luiz Gustavo Ferreira Soares

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.

Atoms•Aug 12, 2022•0 citations

Classical rotons in cold atomic traps

Hugo Terças, José Tito Mendonça, Vasco Guerra

We predict the emergence of a roton minimum in the dispersion relation of elementary excitations in cold atomic gases in the presence of diffusive light. In large magneto-optical traps, multiple scattering of light is responsible for the collective behavior of the system, which is associated to an effective Coulomb-like interaction between the atoms. In optically thick clouds, the rescattered light undergoes diffusive propagation, which is responsible for a stochastic short-range force acting on the atoms. We show that the dynamical competition between these two forces is by the appearance of a roton minimum in the dispersion relation. Making use of the fluctuation-dissipation theorem, we show that the roton minimum is related to classical long-range order in the system.

arXiv:1201.0298•Physical Review A•Nov 29, 2012•12 citations

Long Range Interactions in MagnetoOptical Traps

G. Labeyrie, G. L. Gattobigio, Thomas Pohl +1 more

We present in this paper a review of our work on the impact of long-range interactions on the static and dynamic behaviors of magneto-optical traps (MOT) for neutral atoms. In such systems, all forces (confinement and interaction) are mediated by light. The most obvious signature of longrange interactions is the dependence of the MOT size with number  of trapped atoms. We study in detail the scaling laws for the MOT size versus  , in a range of large N '3> 10^. We then show that the competition between confinement and repulsive interaction can lead, for  large, to a new dynamical instability characterized by spontaneous, self-sustained oscillations of the MOT. This instability is investigated experimentally and theoretically, using both a simple analytical model and a more refined numerical one.

•Jan 1, 2013•0 citations
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.
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 present a theoretical model to describe an instability mechanism in ultra-cold gases, where long-range interactions are taken into account. Focusing on the nonlinear coupling between the collective (plasma-like) and the center-of-mass modes, we show that the resulting dynamics is governed by a parametric equation of the generalized Mathieu type and compute the corresponding stability chart. We apply our model to typical ranges of magneto-optical traps (MOT) parameters and find a good agreement with previous experimental observations.
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.
We predict the emergence of a roton minimum in the dispersion relation of elementary excitations in cold atomic gases in the presence of diffusive light. In large magneto-optical traps, multiple scattering of light is responsible for the collective behavior of the system, which is associated to an effective Coulomb-like interaction between the atoms. In optically thick clouds, the rescattered light undergoes diffusive propagation, which is responsible for a stochastic short-range force acting on the atoms. We show that the dynamical competition between these two forces is by the appearance of a roton minimum in the dispersion relation. Making use of the fluctuation-dissipation theorem, we show that the roton minimum is related to classical long-range order in the system.
We present in this paper a review of our work on the impact of long-range interactions on the static and dynamic behaviors of magneto-optical traps (MOT) for neutral atoms. In such systems, all forces (confinement and interaction) are mediated by light. The most obvious signature of longrange interactions is the dependence of the MOT size with number  of trapped atoms. We study in detail the scaling laws for the MOT size versus  , in a range of large N '3> 10^. We then show that the competition between confinement and repulsive interaction can lead, for  large, to a new dynamical instability characterized by spontaneous, self-sustained oscillations of the MOT. This instability is investigated experimentally and theoretically, using both a simple analytical model and a more refined numerical one.