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Journal of Mathematical Physics

Phase separation of two-component Bose–Einstein condensates

Zuhan Liu

Published Oct 1, 2009• 16 citations
Publisher

Abstract

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.

DOI
10.1063/1.3243875

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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.
This paper analyzes the properties of the two-component Bose–Einstein condensates (BECs) with long-range monopolar interaction by means of Thomas–Fermi approximation (TFA). The effects of long-range monopolar interaction, inter-component short-range s-wave scattering, and particle numbers on the density profiles and phase separation of BECs are investigated. It is shown that atoms with the small intra-component s-wave scattering length are squeezed out when the monopolar interaction of these atoms is not large enough, and the density profile will be compressed when corresponding monopolar interaction is increased. Effective zero interaction point that the s-wave scattering repulsive interaction is neutralized by monopolar attractive interaction, is found. Varying of particle numbers will cause the transformation between phase separation and faint phase separation (or mixture).
The phase separation and vortex states in a two-component Bose-Einstein condensate consisting of | F = 1, m f = 1〉 and |2, 1〉 internal spin states of 87 Rb atoms are considered in the framework of the Thomas-Fermi approximation. It is shown that in the nonrotating system, the atoms in the state |1, −1〉 form a shell around the atoms in the state |2, 1〉. The critical angular velocity for each state is calculated. These velocities depend drastically on the relative concentrations of the components, the critical angular velocity of the outer component being less than the angular velocity of the inner one. It is shown that the atoms in the |1, −1〉 state can form a rotating ring around the resting core of the atoms in the |2, 1〉 state.
The phase separation and vortex states in two-component Bose-Einstein condensate consisting of |F = 1,mf = −1> and |2,1> internal spin states of 87Rb atoms are considered in the framework of Thomas-Fermi approximation. It is shown that in nonrotating system the atoms in the state |1, −1> form a shell about the atoms in the state |2,1>. The critical angular velocity for each state is calculated. These velocities depend drastically on the relative concentrations of the components, the critical angular velocity of the outer component being less than the angular velocity of the inner one. It is shown that the atoms in the |1, −1> state can form a rotating ring about the resting core of the atoms in the state |2,1>. PACS:03.75.Fi; 05.30.Jp; 32.80.Pj. The realization of Bose-Einstein Condensation (BEC) in dilute atomic gases offers new opportunities for studying quantum degenerate fluids [1]. These condensates, which contain thousands of atoms confined to microscale clouds, have similarities to superfluidity and laser,
We study the quantum dynamics of a binary mixture of Bose-Einstein condensates (BEC) in a double-well potential starting from a two-mode Bose-Hubbard Hamiltonian. Focussing on the regime where the number of atoms is very large, a mapping onto a SU(2) spin problem together with a Holstein-Primakoff transformation is performed. The quantum evolution of the number difference of bosons between the two wells is investigated for different initial conditions, which range from the case of a small imbalance between the two wells to a coherent spin state. The results show an instability towards a phase-separation above a critical positive value of the interspecies interaction while the system evolves towards a coherent tunneling regime for negative interspecies interactions. A comparison with a semiclassical approach is discussed together with some implications on the experimental realization of phase separation with cold atoms.
Here we study the interaction and the configuration of spikes in a double condensate by analyzing least energy solutions of two coupled nonlinear Schrödinger equations which model Bose–Einstein condensates of two different hyperfine spin states. When the interspecies scattering length is positive and large enough, spikes of a double condensate repel each other and behave like two separate spikes. In contrast, spikes of a double condensate attract each other and behave like a single spike if the interspecies scattering length is negative and large enough. Our mathematical arguments can prove such physical phenomena. We first use Nehari's manifold to construct least energy solutions, and then use some techniques of singular perturbation problems to derive the asymptotic behavior of least energy solutions. It is shown that the interaction term determines the locations of the two spikes and the asymptotic shape of least energy solutions. Résumé Nous étudions l'interaction et la disposition des pics pour un condensat double. Notre méthode utilise l'analyse des solutions avec énergie minimale des deux équations de Schrödinger couplées non linéaires qui modèlent le condensat de Bose et Einstein pour deux états des spins différents hyperfinis. Si la longueur de dispersion entre espèces est positive et suffisamment gande, les pics pour un condensat double se repoussent, et se comportent comme deux pics séparés. En revanche pour un condensat double s'attirent et se comportent comme un seul pic ; la longueur de dispersion entre espèces est négative et suffisamment petite. Nos arguments mathématiques établissent rigoureusement ses phénomènes physiques. Nous utilisons d'une part la variété de Nehari pour la construction de solutions avec énergie minimale et d'autre part les techniques de problèmes de perturbation singulière pour la dérivation du comportement asymptotique de la solutions avec énergie minimale. Nous démontrons que le terme d'interaction détermine la position des pics et la forme asymptotique des solutions avec énergie minimale.
We study the interactions between two atomic species in a binary Bose-Einstein condensate to revisit the conditions for miscibility, oscillatory dynamics between the species, steady-state solutions, and their stability. By employing a variational approach for a quasi-one-dimensional, two-atomic species condensate, we obtain equations of motion for the parameters of each species: amplitude, width, position, and phase. A further simplification leads to a reduction of the dynamics into a simple classical Newtonian system where components oscillate in an effective potential with a frequency that depends on the harmonic trap strength and the interspecies coupling parameter. We develop explicit conditions for miscibility that can be interpreted as a phase diagram that depends on the harmonic trap's strength and the interspecies coupling parameter. We numerically illustrate the bifurcation scenario whereby nontopological, phase-separated states of increasing complexity emerge out of a symmetric state as the interspecies coupling is increased. The symmetry-breaking dynamical evolution of some of these states is numerically monitored and the associated asymmetric states are also explored.