arXiv:1103.2684 · Physical Review A

Attractive Bose-Einstein condensates in three dimensions under rotation: Revisiting the problem of stability of the ground state in harmonic traps

Marios C. Tsatsos

Published Jun 14, 2011• 4 citations

Abstract

We study harmonically trapped ultracold Bose gases with attractive interparticle interactions under external rotation in three spatial dimensions and determine the critical value of the attraction strength where the gas collapses as a function of the rotation frequency. To this end, we examine the stationary ground state in the corotating frame with a many-body approach as well as within the Gross-Pitaevskii theory of systems in traps with different anisotropies. In contrast to recently reported results [N. A. Jamaludin, N. G. Parker, and A. M. Martin, Phys. Rev. A 77, 051603(R) (2008)], we find that the collapse is not postponed in the presence of rotation. Unlike repulsive gases, the properties of the attractive system remain practically unchanged under rotation in isotropic and slightly anisotropic traps.

DOI: 10.1103/physreva.83.063615

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arXiv:1103.2684 · Physical Review A

Attractive Bose-Einstein condensates in three dimensions under rotation: Revisiting the problem of stability of the ground state in harmonic traps

Marios C. Tsatsos

Published Jun 14, 2011• 4 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreva.83.063615

Related papers

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L

We consider a system of

N

interacting bosons in a rotating harmonic trap in

\mathbb{R}^2

, where the two-body interaction is attractive and scaled as

N^{2α}U(N^αx)

with

0<α<1/12

, and the three-body interaction is repulsive and scaled as

N^{4β}W(N^βx,N^βy)

with

0<β<1/24

. In the mean-field limit, the ground state energy is effectively described by a rotating cubic-quintic nonlinear Schrödinger functional. We analyze the collapse regime where the two-body coupling

a

approaches the critical value

a_*

and the three-body coupling

b

tends to zero. The NLS ground states blow up with a universal profile given by the optimizer of the Gagliardo-Nirenberg inequality, and the energy satisfies

E^{\mathrm{NLS}} = (1-ζ/4+o(1))\mathcal{Q}{\rm{pot}}\ell_n^2

with

ζ\geqslant0

determined by the relative rates of

a_n\to a_*

and

b_n\searrow0

. From the many-body theory, we rigorously justify this effective description: the quantum ground state energy converges to the NLS energy with the same asymptotic expansion in the collapse regime, and the many-body ground states exhibit complete Bose-Einstein condensation onto the universal blow-up profile.

{N}_{c}{=0.55(l}_{0}/|a|).

Our results also show that, by exchanging the frequencies ${\ensuremath{\omega}}_{z}$ and ${\ensuremath{\omega}}_{\ensuremath{\rho}},$ the geometry with ${\ensuremath{\omega}}_{\ensuremath{\rho}}<{\ensuremath{\omega}}_{z}$ favors the condensation of larger number of particles. We also simulate the time evolution of the condensate when changing the ground state from

a=0

a<0

using a 200 ms ramp. A conjecture on higher-order nonlinear effects is also added in our analysis with an experimental proposal to determine its signal and strength.