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arXiv:1811.02719 · Chinese Physics B

Expansion dynamics of a spherical Bose–Einstein condensate*

Rui-Zong Li, Tian-You Gao, Dong-Fang Zhang, Shi-Guo Peng, Ling-Ran Kong, Xing Shen, Kaijun Jiang

Published Sep 5, 2019• 6 citations

Abstract

We experimentally and theoretically observe the expansion behaviors of a spherical Bose–Einstein condensate. A rubidium condensate is produced in an isotropic optical dipole trap with an asphericity of 0.037. We measure the variation of the condensate size in the expansion process after switching off the trap. The free expansion of the condensate is isotropic, which is different from that of the condensate usually produced in the anisotropic trap. We derive an analytic solution of the expansion behavior based on the spherical symmetry, allowing a quantitative comparison with the experimental measurement. The interaction energy of the condensate is gradually converted into the kinetic energy during the expansion and after a long time the kinetic energy saturates at a constant value. We obtain the interaction energy of the condensate in the trap by probing the long-time expansion velocity, which agrees with the theoretical calculation. This work paves a way to explore novel quantum states of ultracold gases with the spherical symmetry.

DOI: 10.1088/1674-1056/ab4177

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The expansion of Bose-Einstein condensates with quantized vortices is studied by solving numerically the time-dependent Gross-Pitaevskii equation at zero temperature. For a condensate initially trapped in a spherical harmonic potential, we confirm previous results obtained by means of variational methods showing that, after releasing the trap, the vortex core expands faster than the radius of the atomic cloud. This could make the detection of vortices feasible, by observing the depletion of the density along the axis of rotation. We find that this effect is significantly enhanced in the case of anisotropic disk-shaped traps. The results obtained as a function of the anisotropy of the initial configuration are compared with the analytic solution for a noninteracting gas in three dimensions as well as with the scaling law predicted for an interacting gas in two dimensions.

The anisotropic density distribution of Bose particles after expansion from a magnetic trap has been taken as an important signature of the formation of Bose-Einstein condensate. In this letter we show that even for a non-condensed trapped gas one can get an anisotropic distribution due to anisotropic collision rates along radial and axial directions. We demonstrate that the mean energies along those directions, different from the energy in the trap, have opposite evolution tendencies with the expansion. This difference is particularly important for the case where a large number of bosons is trapped. We also show that the velocity distribution of the non-condensed gas in the trap, assumed initially isotropic and Gaussian, becomes anisotropic and with linewidth dependent on the expansion direction.

We report the observation of parametric down-conversion of phonons in a spherical Bose-Einstein condensate. The spherical symmetry, which is crucial for observing this phenomenon, is experimentally demonstrated by measuring the collective mode and expansion behavior of the condensate. The low-energy monopole mode is excited by coupling with a high-energy mode with a nearly twice eigen-frequency. The population of the low-energy mode becomes maximum only when the high-energy mode is resonantly excited. Furthermore, we directly observe the parametric down-conversion process in the driving process, through simultaneously probing the two coupling modes. The experimental observation is consistent with the perturbation theory including the gravity effect. This work opens the challenge in related study of the condensate beyond mean-field theory and has potential applications in quantum information.

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