arXiv:1111.1079 · Physical Review A

Destruction of attractive bosonic cloud due to high spatial coherence in tight trap

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

Published Oct 20, 2011• 12 citations

Abstract

We study coherence of a trapped bosonic cloud with attractive finite-range interaction in a tight harmonic trap. One-body density and pair-distribution function in the ground state for different trap sizes are calculated. We also calculate healing length and the correlation length which signify the presence of high spatial coherence in a very tight trap leading to the destruction of the condensate for a fixed particle number. This is in marked variance with the usual collapse of the attractive metastable condensate when $N>{N}_{cr}$. Thus we investigate the critical frequency and critical size of the trap for the existence of attractive Bose-Einstein condensation. The finite-range interaction gives a nonlocal effect in the effective many-body potential, and we observe a high-density stable branch besides the known metastable branch. Moreover, the new branch shows universal behavior even in the very tight trap.

DOI: 10.1103/physreva.84.043631

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arXiv:1111.1079 · Physical Review A

Destruction of attractive bosonic cloud due to high spatial coherence in tight trap

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

Published Oct 20, 2011• 12 citations

arXiv HTML PDF

Abstract

N>{N}_{cr}

. Thus we investigate the critical frequency and critical size of the trap for the existence of attractive Bose-Einstein condensation. The finite-range interaction gives a nonlocal effect in the effective many-body potential, and we observe a high-density stable branch besides the known metastable branch. Moreover, the new branch shows universal behavior even in the very tight trap.

DOI: 10.1103/physreva.84.043631

Related papers

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N>{N}_{cr}

N

of atoms is not too big. The transition between the two classes of solutions as a function of

N

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 Bose-Einstein condensation for a cloud of

{}^{7}\mathrm{Li}

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.

N

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

N

We study the stability of a Bose-Einstein condensate of harmonically trapped atoms with negative scattering length, specifically

{}^{7}\mathrm{Li}.

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

{N}_{c}.

For

N>{N}_{c},

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.

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.