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Journal of Physics B Atomic Molecular and Optical Physics

Phase transition of the ground state for two-component Bose–Einstein condensates in a triple-well trap

Xin Yu Jiang, Libin Fu, Wen‐Shan Duan, Jie Liu

Published May 17, 2011• 1 citation
Publisher

Abstract

We consider the ground-state structure of two-component Bose–Einstein condensates trapped in a triple-well potential. We observe three structural phases of self-trapping, phase separation and symmetry state phase, which reflect the interplay of the intraspecies and interspecies interactions. We also show that the transitions from the self-trapping phase to the symmetry phase and from the phase separation to the symmetry phase are first-order phase transitions, while the transition from the self-trapping phase to the phase separation phase is a continuous one.

DOI
10.1088/0953-4075/44/11/115301

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We consider the ground-state structure of two-component Bose–Einstein condensates trapped in a triple-well potential. We observe three structural phases of self-trapping, phase separation and symmetry state phase, which reflect the interplay of the intraspecies and interspecies interactions. We also show that the transitions from the self-trapping phase to the symmetry phase and from the phase separation to the symmetry phase are first-order phase transitions, while the transition from the self-trapping phase to the phase separation phase is a continuous one.
We provide an in-depth characterization of a three-mode Bose-Einstein condensate trapped in a symmetric circular triple-well potential. We show how the purity related to the su (3) algebra scales for increasing number of atoms and signals the quantum phase transition between two dynamical regimes in a specific configuration. This measure, which is intrinsically related to particle entanglement, also depicts if some squeezing is occurring when we consider the system's ground state. Unlike the well-known double-well model, the triple-well model exhibits a first-order quantum phase transition, which could be investigated with the current trapping technology.
We address the possibility of realizing Bose-Einstein condensation as a first-order phase transition by admixture of particles of different species. To this aim we perform a comprehensive analysis of phase diagrams of two-component mixtures of bosons at finite temperatures. As a prototype model, we analyze a binary mixture of Bose particles interacting via an infinite-range (Kac-scaled) two-body potential. We obtain a rich phase diagram, where the transition between the normal and Bose-Einstein-condensed phases may be either continuous or first order. The phase diagram hosts lines of triple points, tricritical points, and quadruple points. We address the structure of the phase diagram depending on the relative magnitudes of the inter- and intraspecies interaction couplings. In addition, even for purely repulsive interactions, we identify a first-order liquid-gas-type transition between noncondensed phases characterized by different particle concentrations. In the obtained phase diagram, a surface of such first-order transitions terminates with a line of critical points.
Abstract We revisit the structure of the phase diagram of the two-component mean-field Bose mixture at finite temperatures, considering both the cases of attractive and repulsive interspecies interactions. In particular, we analyze the evolution of the phase diagram upon driving the system towards collapse and point out its distinctive features in this limit. We provide analytical insights into the global structure of the phase diagram and the properties of the phase transitions between the normal phase and the phases involving Bose–Einstein condensates. Inter alia we analytically demonstrate that for sufficiently weak interspecies interactions a 12 the system generically exhibits a line of quadruple points but has no triple nor tricritical points in the phase diagram spanned by the chemical potentials µ 1, µ 2 and temperature T. In contrast, for sufficiently large, positive values of a 12, the system displays both triple and tricritical points but no quadruple points. As pointed out in recent studies, in addition to the phase transitions involving condensation, the mixture may be driven through a liquid–gas type transition, and we clarify the conditions for its occurrence. We finally discuss the impact of interaction- and mass-imbalance on the phase diagram of the mixture.
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.
We investigate the properties of a three-dimensional (3D) dipolar Bose–Einstein condensate (BEC) in a triple-well potential. Symmetry breaking and self-trapping (SBST) phenomena are demonstrated for 52Cr atoms in the 3D triple-well potential using numerical solutions of the Gross–Pitaevskii (GP) equation. The results show that the ground-state density distributions are affected markedly by the long-range nature and anisotropy of the dipolar interaction and the isotropic s-wave contact interaction. In addition, the dynamical picture of the SBST induced by a gradual transformation of the single-well potential into a triple-well one is also illustrated. SBST phenomena are also presented by adjusting the height of the middle potential well when the dipole orientation is aligned in the dipole axis.
The effects of atom numbers on the miscibility-immiscibility transition of a harmonically trapped population imbalanced binary Bose-Einstein condensate are investigated. In two-dimensional parameter space expanded by the strength of interspecies interaction and the ratio of atom numbers between two components, we have mapped out the ground-state phase diagrams for the ideal model without intraspecies interactions, and for the $^{23}\mathrm{Na}\text{\ensuremath{-}}^{23}\mathrm{Na}$ mixture and the $^{87}\mathrm{Rb}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ mixture with experimentally accessible intraspecies scattering lengths, respectively. It is found that all the phase diagrams include the miscible, symmetric immiscible, and asymmetric immiscible phases, and there exists a tricritical point where those three different phases merge. Furthermore, the phase boundaries among those three phases show a strong dependence on the atom numbers of two components. These results can be observed in current experiments.