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arXiv:1201.0298 · Physical Review A

Classical rotons in cold atomic traps

Hugo Terças, José Tito Mendonça, Vasco Guerra

Published Nov 29, 2012• 12 citations
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Abstract

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.

DOI
10.1103/physreva.86.053630

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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.
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.
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.
Atoms excited into high-lying Rydberg states and under strong dipole-dipole interactions exhibit phenomena associated with highly correlated and complex systems. We perform first-principles numerical simulations on the dynamics of such systems. The emergence of a roton minimum in the excitation spectrum, as expected in strongly correlated gases and accurately described by Feynman's theory of liquid helium, is shown to significantly inhibit particle transport, with a strong suppression of the diffusion coefficient, due to the emerging spatial order. We also demonstrate how the ability to temporally tune the interaction strength among Rydberg atoms can be used in order to overcome the effects of disorder-induced heating, allowing the study of unprecedented highly coupled regimes.
We have studied the behavior of clouds of neutral atoms contained in a spontaneous force optical trap. Because of the low temperatures of the atoms (<1 mK) we have observed a variety of new phenomena which involve both short and long range interactions between the atoms. The short range interactions are manifested in two body collisions which are notable because of the very long collision times. This time scale causes the dynamics to be profoundly affected by absorption and spontaneous emission during the collision. An interesting assortment of collective behaviors are observed when the trapped atom cloud contains more than 105 atoms. These include the expansion of the cloud as the number is increased and dramatic changes in the distribution of the atoms at higher numbers. We can explain much of the collective behavior using a simple model that includes a 1/r2 force between the atoms arising from the multiple scattering of photons. Finally, we discuss the optical trapping of atoms directly from a low pressure vapor in a small glass cell. We have used these optically trapped atoms to load a magnetostatic trap in the same cell. This provided a high density sample of atoms with a temperature of less than 2 μK.
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.
Large clouds of cold atoms prepared in a magneto-optical trap can develop spatiotemporal instabilities when the frequency of the trapping lasers is brought close to the atomic resonance. This system bears close similarities with trapped plasmas, whereby effective Coulomb interactions are induced by the exchange of scattered photons and lead to collective nonlinear dynamics of the trapped atoms. We report in this paper a detailed experimental study of the instability threshold, and comparisons with three-dimensional simulations of the interacting, laser-driven cloud.