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Physical Review A

Giant oscillations in a magneto-optical trap

Andrea di Stefano, M. Fauquembergue, Philippe Verkerk, Daniel Hennequin

Published Mar 21, 2003• 23 citations
Publisher

Abstract

The present paper reports on the study of deterministic instabilities in the atomic cloud of a magneto-optical trap. Giant periodic and erratic self-oscillations are experimentally observed and analyzed through a simple original model taking into account the shadow effect and the spatial distribution of the atoms in the cloud. We show that giant oscillations are induced by a homoclinic orbit merging in the neighborhood of a Hopf bifurcation.

DOI
10.1103/physreva.67.033404

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Physical Review A•Sep 25, 2003•23 citations
The present paper reports on the study of deterministic instabilities in the atomic cloud of a magneto-optical trap. Giant periodic and erratic self-oscillations are experimentally observed and analyzed through a simple original model taking into account the shadow effect and the spatial distribution of the atoms in the cloud. We show that giant oscillations are induced by a homoclinic orbit merging in the neighborhood of a Hopf bifurcation.
The instabilities observed in the atomic cloud of a magneto-optical trap are experimentally studied through the dynamics of the center of mass location and the cloud population. Two dynamical components are identified: a slow, stochastic one affects both variables, and a fast, deterministic one affects only the center of mass location. A one-dimensional stochastic model taking into account the shadow effect is developed from these observations and reproduces the experimental behavior. It is shown that instabilities are driven by noise and present stochastic resonancelike characteristics.
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.
In this Thesis, we study the fundamental aspects of self-oscillating atomic clouds in a large, balanced Magneto-Optical Trap (MOT). These instabilities bear analogies with astrophysical systems such as Cepheid variable stars, whose self-oscillations depend on radiation pressure and gravity, as well as technological systems such as confined plasmas, where self-oscillations may arise due to interactions between the plasma particles and the confining magnetic field. We begin with an experimental study of self-oscillating balanced MOT instabilities, investigating first the instability threshold behavior versus various MOT parameters, including magnetic field gradient, atom number and laser intensity. We proceed then investigating the spatio-temporal properties of the unstable regime and identify distinct instability regimes. Different analysis techniques are employed that allow us to learn about the oscillation modes of clouds of these regimes as well as the size distribution of the structures developing in clouds of these regimes. In a theoretical approach, we develop a kinetic 3D model for the MOT with many-atom effects included and successfully use it in numerical simulations of our instabilities. We find qualitative agreements with the instability thresholds from the experiments as well as predict experimentally obtained instability regimes. We investigate the impact of our model’s physical ingredients on the instabilities, to aid the understanding of the complex physics at work. Finally, we show a preliminary simulated result for a self-oscillating instability in the misaligned MOT, known to experimentally exist, in that way demonstrating that our developed numerical tool can be employed beyond the balanced MOT.
Large clouds of atoms in a magneto-optical trap (MOT) are known to exhibit spatiotemporal instabilities when the frequency of the trapping lasers comes close to the atomic resonance. Such instabilities possess similarities with stars and confined plasmas, where corresponding nonlinearities may give rise to spontaneous oscillations. In this paper, we describe the kinetic model that has recently been employed in three-dimensional (3D) simulations of spatiotemporal instabilities in a MOT, yielding qualitative agreements with experimentally observed instability thresholds and regimes. Details surrounding its implementation are included, and the impact of its physical effects on the instabilities is investigated to improve the understanding of the complex mechanism at work.
We have made a nonlinear dynamics study of a parametrically driven magneto-optical trap. When the trapping potential is modulated at around twice the trap frequency above a threshold, the limit cycle is manifested as two separate collective atomic packets oscillating with opposite phases and finite amplitudes, determined by the balance of the nonlinearity and the damping of the trap. In particular, we directly observe in situ the subcritical Hopf bifurcation, which suddenly converts the combined motions of a limit cycle and a stable attractor into a limit cycle motion. The experimental results are in quantitative agreement with the numerical results based on the simple Doppler cooling theory.