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arXiv:cond-mat/0203021 · Journal of Physics B Atomic Molecular and Optical Physics

Evolution of a coherent array of Bose Einstein condensates in a magnetic trap

Hongwei Xiong, Shujuan Liu, Guoxiang Huang, Zhijun Xu

Published Nov 19, 2002• 22 citations
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Abstract

We investigate the interference pattern evolution process for a coherent array of Bose–Einstein condensates in a magnetic trap after the optical lattices are switched off. It is shown that there is a decay and revival of the density oscillation for the condensates confined in the magnetic trap. We find that, due to the confinement of the magnetic trap, the interference effect is much stronger than that found in the experiment performed by Pedri et al (Pedri P et al 2001 Phys. Rev. Lett. 87 220401), where the magnetic trap is also switched off. The interaction correction to the interference effect is also discussed for the density distribution of the central peak.

DOI
10.1088/0953-4075/35/23/310

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We investigate the interference pattern evolution process for a coherent array of Bose–Einstein condensates in a magnetic trap after the optical lattices are switched off. It is shown that there is a decay and revival of the density oscillation for the condensates confined in the magnetic trap. We find that, due to the confinement of the magnetic trap, the interference effect is much stronger than that found in the experiment performed by Pedri et al (Pedri P et al 2001 Phys. Rev. Lett. 87 220401), where the magnetic trap is also switched off. The interaction correction to the interference effect is also discussed for the density distribution of the central peak.
We report experimental results on the dynamics and phase evolution of Bose-Einstein condensates in 1D optical lattices. The dynamical behaviour is studied by adiabatically loading the condensate into the lattice and subsequently switching off the magnetic trap. In this case, the condensate is free to expand inside the periodic structure of the optical lattice. The phase evolution of the condensate, on the other hand, can be studied by non-adiabatically switching on the periodic potential. We observe decays and revivals of the interference pattern after a time-of-flight.
For the Bose-condensed gas confined in a magnetic trap and in a two-dimensional optical lattice, the non-uniform distribution of atoms in different lattice sites is considered based on Gross-Pitaevskii equation. A propagator method is used to investigate the time evolution of 2D interference patterns after (i)only the optical lattice is swithed off, and (ii)both the optical lattice and the magnetic trap are swithed off. An analytical description on the motion of side peaks in the interference patterns is presented by using the density distribution in a momentum space.
We investigate the phase diffusion of a Bose–Einstein condensate (BEC) confined in the combined potential of a magnetic trap and a one-dimensional optical lattice. We show that the phase diffusion of the condensate in the whole optical lattice is evident and can be measured from the interference pattern of expanding subcondensates after the optical lattice is switched off. The maximum density of the interference pattern decreases significantly due to the mixing of the phase diffusion that appears in different subcondensates. This suggests a way to detect experimentally the notable phase diffusion of BECs.
Based on the Gross-Pitaevskii equation and by using the effective chemical poten tial,we study the distribution of the Bose-condensed gas in the combined potenti als (magnetic trap and three-dimensional optical lattices).The normalized ground-state wave function is given from the distribution of the Bose-condensed gas.The analytical expression of the density distribution of the Bose-condensed gas is given by using the propagator method when the combined potentials and only the optical lattices are switched off,respectively.When the combined potentials are switched off,the theoretical results of this work agree well with the experiment by Greiner et al.When only the optical lattices are switched off,it is show n that the interference pattern will oscillate in the magnetic trap.In addition,the evolution of the interference pattern is also investigated in the case of an isotropic magnetic trap.
We investigate the properties of a coherent array containing about 200 Bose-Einstein condensates produced in a far detuned 1D optical lattice. The density profile of the gas, imaged after releasing the trap, provides information about the coherence of the ground-state wave function. The measured atomic distribution is characterized by interference peaks. The time evolution of the peaks, their relative population, as well as the radial size of the expanding cloud are in good agreement with the predictions of theory. The 2D nature of the trapped condensates and the conditions required to observe the effects of coherence are also discussed.