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arXiv:1007.1534 · Physical Review A

Stability of an attractive bosonic cloud with van der Waals interaction

Anindya Biswas, Tapan Kumar Das, Luca Salasnich, Barnali Chakrabarti

Published Oct 11, 2010• 18 citations
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Abstract

We investigate the structure and stability of Bose-Einstein condensates of $^{7}\mathrm{Li}$ 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.

DOI
10.1103/physreva.82.043607

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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 \ensuremathδ\ensuremath{\delta}\ensuremathδ-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.
We investigate the form and stability of a cloud of atoms confined in a harmonic trap when the scattering length is negative. We find that, besides the known low-density metastable solution, a different branch of Bose condensate appears at higher density when nonlocality effects in the attractive part are taken into account. The transition between the two classes of solutions as a function of the number NNN of atoms can be either sharp or smooth according to the strength and range of the attractive interaction. Use of tight traps is favorable for investigating the evolution of the system, as the strength of the effective interaction increases with NNN.
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.
We study the properties of a Bose-Einstein condensed cloud of atoms with negative scattering length confined in a harmonic trap. When a realistic non local (finite range) effective interaction is taken into account, we find that, besides the known low density metastable solution, a new branch of Bose condensate appears at higher density. This state is self-bound but its density can be quite low if the number NNN of atoms is not too big. The transition between the two classes of solutions as a function of NNN can be either sharp or smooth according to the ratio between the range of the attractive interaction and the length of the trap. A tight trap leads to a smooth transition. In addition to the energy and the shape of the cloud we study also the dynamics of the system. In particular, we study the frequencies of collective oscillation of the Bose condensate as a function of the number of atoms both in the local and in the non local case. Moreover, we consider the dynamics of the cloud when the external trap is switched off.
We study the properties of Bose-Einstein condensates with the realistic van der Waals two-body interaction for large numbers of trapped atoms, solving the many-body Schr\"odinger equation by the potential harmonic expansion method. The effect of different C6{C}_{6}C6​ parameters has been critically examined, starting from very few to 14 000 atoms to analyze and justify the idea of a shape-independent approximation. It is found that the condensate properties almost remain unchanged when the number of atoms are quite small $(\ensuremath{\sim}100)$, in good agreement with earlier results of Blume and Greene [Phys. Rev. A 63, 063601 (2001)], but we observe the appreciable effect of a long attractive tail when NNN is large, even in the low-density limit. The above reference considered only 20 atoms which is far from a real experimental situation. Our calculation gives a realistic scenario which justifies the use of a shape-dependent two-body interaction in many-body theories.
We study the stability of a Bose-Einstein condensate of harmonically trapped atoms with negative scattering length, specifically 7Li.{}^{7}\mathrm{Li}.7Li. Our method is to solve the time-dependent nonlinear Schr\"odinger equation numerically. For an isolated condensate, with no gain or loss, we find that the system is stable (apart from quantum tunneling) if the particle number N is less than a critical number Nc.{N}_{c}.Nc​. For N>Nc,N>{N}_{c},N>Nc​, the system collapses to high-density clumps in a region near the center of the trap. The time for the onset of collapse is on the order of one trap period. Within numerical uncertainty, the results are consistent with the formation of a ``black hole'' of infinite density fluctuations, as predicted by Ueda and Huang [Phys. Rev. A (to be published)]. We numerically obtain ${N}_{c}\ensuremath{\approx}1251.$ We then include gain-loss mechanisms, i.e., the gain of atoms from a surrounding ``thermal cloud,'' and the loss due to two- and three-body collisions. The number N now oscillates in a steady state, with a period of about 145 trap periods. We obtain ${N}_{c}\ensuremath{\approx}1260$ as the maximum value in the oscillations.
It is well known that bosonic particles with attractive interaction in a uniform gas do not form a condensate. Here we investigate a dilute Bose gas and study stationary solutions of the Gross–Pitaevskii equation with attractive interaction. We have also used a higher order stabilising term in the presence of a harmonic confining potential. We show that there are three possible types of stationary solutions corresponding to stable, metastable and unstable phases. These results are discussed in relation to a 7Li condensate.