Analysis beyond the Thomas-Fermi approximation of the density profiles of a miscible two-component Bose-Einstein condensate

Abstract

. (2015) 'Analysis beyond the Thomas-Fermi approximation of the density proles of a miscible two-component Bose-Einstein condensate.', Physical review A., 91 (5). 053626.Further information on publisher's website:http://dx.doi.org/10.1103/PhysRevA.91.053626Publisher's copyright statement:Reprinted with permission from the American Physical Society: Physical Review A 91, 053626 c 2015 by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modied, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We investigate a harmonically trapped two-component Bose-Einstein condensate within the miscible regime, close to its boundaries, for different ratios of effective intra-and interspecies interactions. We derive analytically a universal equation for the density around the different boundaries in one, two, and three dimensions, for both the coexisting and spatially separated regimes. We also present a general procedure to solve the Thomas-Fermi approximation in all three spatial dimensionalities, reducing the complexity of the Thomas-Fermi problem for the spatially separated case in one and three dimensions to a single numerical inversion. Finally, we analytically determine the frontier between the two different regimes of the system.

Singularity in the matrix of the coupled Gross-Pitaevskii equations and the related state-transitions in three-species condensates

“…Since N A , N B and N C are considered to be large, TFA has been adopted. The applicability of this approximation has been evaluated via a numerical approach given in [22,35] and will be discussed later. Under the TFA, the CGP become…”

“…Accompanying the progress in techniques, the research into the 2-species Bose-Einstein condensates (2-BEC) is gaining an increasing attention in recent years in both the experimental aspect [1][2][3][4][5][6][7] and theoretical aspect [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Many distinguished features have been found, say, the existence of various phases, the critical value in the inter-species interaction and the related instability, the emergence of asymmetric ground state (g.s.)…”

Dispersive hydrodynamics of nonlinear polarization waves in two-component Bose-Einstein condensates

“…The soliton solution found in [16] is reproduced from Eqs. (39) and (46) if we consider the situation where the two components have equal background densities (w 0 = 0), and no relative velocity (v 0 = 0). In this case, one gets from Eq.…”

Coherent quantum phase slip in two-component bosonic atomtronic circuits

“…The total number of particles N is fixed, in such a way that * Analytical expressions can be obtained within the Thomas-Fermi approach in order to study the ground state properties of the condensate in the regime of large interactions. In the case without Raman coupling [40][41][42], the Thomas-Fermi wavefunction is the same for both components:…”