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arXiv:1206.3339 · Physical Review A

Domain wall suppression in trapped mixtures of Bose-Einstein condensates

Francesco Vincenzo Pepe, Paolo Facchi A, Giuseppe Florio, Saverio Pascazio

Published Aug 22, 2012• 12 citations
arXivHTMLPDF

Abstract

The ground-state energy of a binary mixture of Bose-Einstein condensates can be estimated for large atomic samples by making use of suitably regularized Thomas-Fermi density profiles. By exploiting a variational method on the trial densities the energy can be computed by explicitly taking into account the normalization condition. This yields analytical results and provides the basis for further improvement of the approximation. As a case study, we consider a binary mixture of ${}^{87}$Rb atoms in two different hyperfine states in a double-well potential and discuss the energy crossing between density profiles with different numbers of domain walls, as the number of particles and the interspecies interaction vary.

DOI
10.1103/physreva.86.023629

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The ground-state energy of a binary mixture of Bose-Einstein condensates can be estimated for large atomic samples by making use of suitably regularized Thomas-Fermi density profiles. By exploiting a variational method on the trial densities the energy can be computed by explicitly taking into account the normalization condition. This yields analytical results and provides the basis for further improvement of the approximation. As a case study, we consider a binary mixture of 87{}^{87}87Rb atoms in two different hyperfine states in a double-well potential and discuss the energy crossing between density profiles with different numbers of domain walls, as the number of particles and the interspecies interaction vary.
We study a binary mixture of Bose–Einstein condensates, confined in a generic potential, in the Thomas–Fermi approximation. We search for the zero-temperature ground state of the system, both in the case of fixed numbers of particles and fixed chemical potentials. For generic potentials, we analyze the transition from mixed to separated ground-state configurations as the inter-species interaction increases. We derive a simple formula that enables one to determine the location of the domain walls. Finally, we find criteria for the energetic stability of separated configurations, depending on the number and the position of the domain walls separating the two species.
In the presence of a magnetic field, multicomponent ground states appear in trapped spin-1 Bose-Einstein condensates for both ferromagnetic and antiferromagnetic types of spin-spin interaction. We aim to produce an accurate analytical description of the multicomponent states which is of fundamental importance. Despite being in the so-called regime of the Thomas-Fermi approximation (condensates with large particle number), the scenario of multicomponent states is problematic under this approximation due to the large variation in densities of the subcomponents. We generalize the variational method that we have introduced [P. K. Kanjilal and A. Bhattacharyay, Eur. Phys. J. Plus 137, 547 (2022)] to overcome the limitations of the Thomas-Fermi approximation. We demonstrate that the variational method is crucial in identifying multicomponent ground states. A comparison of the results of the variational method, which is multimodal by construction, with that of the single-mode approximation is also presented in this paper to demonstrate a marked improvement in accuracy over the single-mode approximation. We have also looked into the phase transition between phase-matched and polar states in a trapped condensate using the variational method and have identified substantial change in the phase boundary. The correspondence of the phase diagram of the trapped case with the homogeneous one identifies other limitations of the Thomas-Fermi approximation as opposed to the more accurate variational method.
We show that binary mixtures of Bose condensates of alkali atoms have a great variety of ground state and vortex structures which can be accessed experimentally by varying the particle numbers of different alkalis. We have constructed a simple algorithm to determine the density profiles of the mixtures within Thomas-Fermi approximation. Many structures of the alkali binary contain a coexisting region, which is the analog of the long sought 3He{}^{3}\mathrm{He}3He- 4He{}^{4}\mathrm{He}4He interpenetrating superfluids in ultralow temperature physics.
We show that binary mixtures of Bose-condensates of alkali atoms have a great variety of ground state and vortex structures which can be accessed experimentally by varying the particle numbers of different alkalis. We have constructed a simple algorithm to determine the density profiles of these states, and have worked out their phase diagrams within Thomas-Fermi approximation. Many structures of the alkali binary contain a coexisting region, which is the analog of the long sought 3^{3}3He-4^{4}4He interpenetrating superfluids in ultra-low temperature physics.
Recently, coupled systems of nonlinear Schrödinger equations have been used extensively to describe mixtures Bose–Einstein condensates. In this paper, we study the distribution of two different hyperfine spin states of a binary mixture of three dimensional Bose–Einstein condensates. In a double condensate, an interface may occur due to large intraspecies and interspecies scattering lengths. We prove that there is an asymptotic separation of different phases in the strong coupling (Thomas–Fermi) limit.
Abstract Investigation of ground state structures and phase separation under confinement is of great interest in spinor Bose–Einstein condensates. In this paper we show that, in general, within the Thomas–Fermi approximation, the phase separation scenario of stationary states can be obtained including all the mixed states on an equal footing for a spin-1 condensate under any confinement. According to the process used here, the density of each and every stationary states can be determined exactly in terms of the system parameters. This allows to write the expression for energy density of all states in a form which are not an explicit function of densities of those states. An energy density comparison therefore, among all the allowed stationary states can be done which will reveal domain structures depending on the system parameters. We study here, in details, a particular case of spherically symmetric harmonic confinement as an example and show a wide range of potential phase separation scenario for anti-ferromagnetic and ferromagnetic interactions.