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arXiv:1009.4578 · Physical Review A

Resonance states and quantum tunneling of Bose-Einstein condensates in a three-dimensional shallow trap

Sudip Kumar Haldar, Barnali Chakrabarti, Tapan Kumar Das

Published Oct 20, 2010• 19 citations
arXivHTMLPDF

Abstract

A correlated quantum many-body method is applied to describe resonance states of atomic Bose-Einstein condensates (BEC) in a realistic shallow trap (as opposed to the infinite traps commonly used). The realistic van der Waals interaction is adopted as the interatomic interaction. We calculate experimentally measurable decay rates of the lowest quasibound state in the shallow trap. The most striking result is the observation of a metastable branch besides the usual one for attractive BEC in a pure harmonic trap. As the particle number increases the metastable branch appears and then gradually disappears, and finally the usual metastable branch (associated with the attractive BEC in a harmonic trap) appears, eventually leading to the collapse of the condensate.

DOI
10.1103/physreva.82.043616

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A correlated quantum many-body method is applied to describe resonance states of atomic Bose-Einstein condensates (BEC) in a realistic shallow trap (as opposed to the infinite traps commonly used). The realistic van der Waals interaction is adopted as the interatomic interaction. We calculate experimentally measurable decay rates of the lowest quasibound state in the shallow trap. The most striking result is the observation of a metastable branch besides the usual one for attractive BEC in a pure harmonic trap. As the particle number increases the metastable branch appears and then gradually disappears, and finally the usual metastable branch (associated with the attractive BEC in a harmonic trap) appears, eventually leading to the collapse of the condensate.
We study the Bose-Einstein condensation for a cloud of 7Li{}^{7}\mathrm{Li}7Li atoms with attractive nonlocal (finite-range) interaction in a harmonic trap. In addition to the low-density metastable branch, which is present also in the case of local interaction, a new stable branch appears at higher densities. For a large number of atoms, the size of the cloud in the stable high-density branch is independent of the trap size and the atoms are in a macroscopic quantum self-trapped configuration. We analyze the macroscopic quantum tunneling between the low-density metastable branch and the high-density one by using the instanton technique. Moreover, we consider the decay rate of the Bose condensate due to inelastic two- and three-body collisions.
The stability of Bose–Einstein condensates (BECs) loaded into a two-dimensional shallow harmonic potential well is studied. By using the variational method, the ground state properties for interacting BECs in the shallow trap are discussed. It is shown that the possible stable bound state can exist. The depth of the shallow well plays an important role in stabilizing the BECs. The stability of BECs in the shallow trap with the periodic modulating of atom interaction by using the Feshbach resonance is also discussed. The results show that the collapse and diffusion of BECs in a shallow trap can be controlled by the temporal modulation of the scattering length.
The mean-field dynamics of a Bose-Einstein condensate is studied in the presence of a microscopic trapping potential from which the condensate can escape via tunneling through finite barriers. We show that the method of complex scaling can be used to obtain a quantitative description of this decay process. A real-time propagation approach that is applied to the complex-scaled Gross-Pitaevskii equation allows us to calculate the chemical potentials and lifetimes of the metastably trapped Bose-Einstein condensate. The method is applied to a one-dimensional harmonic confinement potential combined with a Gaussian envelope, for which we compute the lowest symmetric and antisymmetric quasibound states of the condensate. A comparison with alternative approaches using absorbing boundary conditions as well as complex absorbing potentials shows good agreement.
We investigate the structure and stability of Bose-Einstein condensates of 7Li^{7}\mathrm{Li}7Li atoms with realistic van der Waals interactions by using the potential harmonic expansion method. Besides the known low-density metastable solution with a contact $\ensuremath{\delta}$-function interaction, we find a stable branch at a higher density which corresponds to the formation of an atomic cluster. Comparison with the results of a nonlocal effective interaction is also presented. We analyze the effect of trap size on the transition between the two branches of solutions. We also compute the loss rate of a Bose condensate due to two- and three-body collisions.
The quantized vortex states of a weakly interacting Bose-Einstein condensate of atoms with attractive interatomic interaction in an axially symmetric harmonic oscillator trap are investigated using the numerical solution of the time-dependent Gross-Pitaevskii equation obtained by the semi-implicit Crank-Nicholson method. The collapse of the condensate is studied in the presence of deformed traps with the larger frequency along either the radial or the axial direction. The critical number of atoms for collapse is calculated as a function of the vortex quantum number L. The critical number increases with increasing angular momentum L of the vortex state but tends to saturate for large L.