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Physical Review A

Dynamics of a cold atom cloud in an anharmonic trap

Andréa D Bertoldi, Leonardo Ricci

Published Jun 17, 2010• 9 citations
Publisher

Abstract

A combined gravitomagnetic trap was used to measure how the anharmonicity of a trapping potential affects the dynamics of a cold atomic cloud. A displacement of the effective potential minimum as a function of the ensemble temperature was observed. The effect is a direct consequence of the thermal nature of the atomic sample. The results of both a theory approach to the dynamical evolution of the atomic cloud and a numerical simulation are in very good agreement with the experimental observations. The effect can be exploited to devise a novel measurement technique for the temperature of a trapped atomic cloud, as well as to separate thermal and condensed phases in Bose-Einstein condensation experiments.

DOI
10.1103/physreva.81.063415

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A combined gravitomagnetic trap was used to measure how the anharmonicity of a trapping potential affects the dynamics of a cold atomic cloud. A displacement of the effective potential minimum as a function of the ensemble temperature was observed. The effect is a direct consequence of the thermal nature of the atomic sample. The results of both a theory approach to the dynamical evolution of the atomic cloud and a numerical simulation are in very good agreement with the experimental observations. The effect can be exploited to devise a novel measurement technique for the temperature of a trapped atomic cloud, as well as to separate thermal and condensed phases in Bose-Einstein condensation experiments.
We have investigated experimentally the finite-temperature properties of a Bose-Einstein condensed cloud of 87Rb{}^{87}\mathrm{Rb}87Rb atoms in a harmonic trap. Focusing primarily on condensed fraction and expansion energy, we measure unambiguous deviations from ideal-gas thermodynamics and obtain good agreement with a Hartree-Fock description of the mixed cloud. Our results offer clear evidence of the mutual interaction between the condensed and thermal components. To probe the low-temperature region unaccessible to the usual time-of-flight technique, we use coherent Bragg scattering as a filtering technique for the condensate. This allows us to separate spatially the condensed and normal components in time of flight and to measure reliably temperatures as low as 0.2Tc00.2{T}_{c}^{0}0.2Tc0​ and thermal fractions as low as 10%. Finally, we observe evidence for the limitations of the usual image analysis procedure, pointing out to the need for a more elaborate model of the expansion of the mixed cloud.
We present a method for measuring nonharmonic contributions to the trapping potential of a cold atomic gas by measuring the dynamics of the cloud. This method can be used to minimize the anharmonicity of a trap, or to tune the quartic anharmonicity to some desired level in a sufficiently tunable trap. We present an approximate solution to the dynamics of a classical noninteracting cloud of thermal atoms in a cigar-shaped harmonic trap with a quartic perturbation along the weakly confined axis which is analytical and closed form. We calculate the first and second moments of position along the weak axis as functions of time, which is sufficient to characterize the trap. The dynamics of the thermal cloud differ notably from those of a single particle, with an offset to the oscillation frequency that persists even as the oscillation amplitude approaches zero. We also present some numerical results that describe the effects of time of flight on the behavior of the cloud in order to better understand the results of a hypothetical experimental realization of this system.
The dynamics of a trapped Bose-condensed gas at finite temperatures is described by a generalized Gross-Pitaevskii equation for the condensate order parameter and a semiclassical kinetic equation for the thermal cloud, solved using N-body simulations. The two components are coupled by mean fields as well as collisional processes that transfer atoms between the two. We use this scheme to investigate scissors modes in anisotropic traps as a function of temperature. Frequency shifts and damping rates of the condensate mode are extracted, and are found to be in good agreement with recent experiments.
Finite-temperature simulations are used to study quadrupole excitations of a trapped Bose-Einstein condensate. We focus specifically on the m = 0 mode, where a long-standing theoretical problem is to account for an anomalous variation of the mode frequency with temperature. We explain this behavior in terms of the excitation of two separate modes, corresponding to the coupled motion of the condensate and the thermal cloud. The relative amplitude of the modes depends sensitively on the temperature and on the frequency of the harmonic drive used to excite them. Good agreement with experiment is found for appropriate drive frequencies.