arXiv:cond-mat/9805144

Bosons with attractive interactions in a trap: Is the ground state fragmented ?

Ø. Elgarøy, C. J. Pethick

Published May 12, 1998• 0 citations

Abstract

Possible fragmentation of a Bose-Einstein condensate with negative scattering length is investigated using a simple two-level model. Our results indicate that fragmentation does not take place for values of the coupling for which the system is metastable. We also comment on the possibility of realizing a fragmented condensate in trapping potentials other than an harmonic one.

DOI: 10.48550/arxiv.cond-mat/9805144

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arXiv:cond-mat/9805144

Bosons with attractive interactions in a trap: Is the ground state fragmented ?

Ø. Elgarøy, C. J. Pethick

Published May 12, 1998• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.cond-mat/9805144

Related papers

Absence of fragmentation of the condensate in a model for bosons in a trap

Ø. Elgarøy, C. J. Pethick

Physical Review AFeb 1, 199910 citations

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The fragmentation of the ground state of a repulsive condensate immersed into a double-trap potential is found to be a general and critical phenomenon. It takes place for a given number of bosons if their scattering length is larger than some critical value or for a given value of the scattering length if the number of bosons is above some critical number. We demonstrate that the geometry of the inner trap determines these critical parameters while the number of the fragments and the fraction of bosons in the various fragments can be manipulated by the outer trap. There is also a maximal number of bosons for which the ground state is fragmented. If this number is exceeded, the fragmented state becomes a very low-lying excited state of the condensate. This maximal number of bosons can be substantially manipulated by varying the inner and outer traps. To study threefold fragmentation we have chosen a potential well with two barriers as the inner trap and embedded in two types of outer ones. A manifold fragmentation is also addressed.The fragmentation of the ground state of a repulsive condensate immersed into a double-trap potential is found to be a general and critical phenomenon. It takes place for a given number of bosons if their scattering length is larger than some critical value or for a given value of the scattering length if the number of bosons is above some critical number. We demonstrate that the geometry of the inner trap determines these critical parameters while the number of the fragments and the fraction of bosons in the various fragments can be manipulated by the outer trap. There is also a maximal number of bosons for which the ground state is fragmented. If this number is exceeded, the fragmented state becomes a very low-lying excited state of the condensate. This maximal number of bosons can be substantially manipulated by varying the inner and outer traps. To study threefold fragmentation we have chosen a potential well with two barriers as the inner trap and embedded in two types of outer ones. A manifold fragmentation is also addressed.

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Amplifying on a proposal by O'Dell et al. for the realization of Bose-Einstein condensates of neutral atoms with attractive

1∕r

interaction, we point out that the instance of self-trapping of the condensate, without an external trap potential, is physically best understood by introducing appropriate ``atomic'' units. This reveals a remarkable scaling property: the physics of the condensate depends only on the two parameters

{N}^{2}a∕{a}_{u}

and $\ensuremath{\gamma}∕{N}^{2}$, where

N

is the particle number,

a

the scattering length,

{a}_{u}

the ``Bohr'' radius, and $\ensuremath{\gamma}$ the trap frequency in atomic units. We calculate accurate numerical results for self-trapping wave functions and potentials, and for energies, sizes, and peak densities, and compare with previous variational results. We point out the existence of a second solution of the extended Gross-Pitaevskii equation for negative scattering lengths, with and without trapping potential, which is born together with the ground state in a tangent bifurcation. This indicates the existence of an unstable collectively excited state of the condensate for negative scattering lengths.

{a}_{\mathrm{ij}}

for scattering of boson i with j,

i,j=1,2,

are negative representing an attractive interaction. Depending on the parameters of the problem a single or both components of the condensate may experience collapse.