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arXiv:1004.1541 · Physical Review A

Quantum particle-number fluctuations in a two-component Bose gas in a double-well potential

Paweł Zin, Bartłomiej Oleś, Krzysztof Sacha

Published Sep 14, 2011• 8 citations
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Abstract

A two-component Bose gas in a double-well potential with repulsive interactions may undergo a phase separation transition if the interspecies interactions outweigh the intraspecies ones. We analyze the transition in the strong interaction limit within the two-mode approximation. Numbers of particles in each potential well are equal and constant. However, at the transition point, the ground state of the system reveals huge fluctuations of numbers of particles belonging to the different gas components; that is, the probability for observation of any mixture of particles in each potential well becomes uniform.

DOI
10.1103/physreva.84.033614

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A two-component Bose gas in a double-well potential with repulsive interactions may undergo a phase separation transition if the interspecies interactions outweigh the intraspecies ones. We analyze the transition in the strong interaction limit within the two-mode approximation. Numbers of particles in each potential well are equal and constant. However, at the transition point, the ground state of the system reveals huge fluctuations of numbers of particles belonging to the different gas components; that is, the probability for observation of any mixture of particles in each potential well becomes uniform.
The ground state and spectral properties of Bose gases in double-well potentials are studied in two different scenarios: (i) an interacting atomic Bose gas, and (ii) a mixture of an atomic gas interacting with diatomic molecules. A ground state second-order quantum phase transition is observed in both scenarios. For large attractive values of the atom-atom interaction, the ground state is degenerate. For repulsive and small attractive interaction, the ground state is not degenerate and is well approximated by a boson coherent state. Both systems depict an excited state quantum phase transition. In both cases, a critical energy separates a region in which all the energy levels are degenerate in pairs, from another region in which there are no degeneracies. For the atomic system, the critical point displays a singularity in the density of states, whereas this behavior is largely smoothed for the mixed atom-molecule system.
We discuss the mean-field theories obtained from the leading order in a large-NNN approximation for one- and two-component dilute Bose gases. For a one-component Bose gas, this approximation has the following properties: the Bose-Einstein condensation (BEC) phase transition is second order but the critical temperature Tc{T}_{c}Tc​ is not shifted from the noninteracting gas value T0{T}_{0}T0​. The spectrum of excitations in the BEC phase resembles the Bogoliubov dispersion with the usual coupling constant replaced by the running coupling constant which depends on both temperature and momentum. We then study two-component Bose gases with both inter- and intraspecies interactions and focus on the stability of the mixture state above Tc{T}_{c}Tc​. Our mean-field approximation predicts an instability from the mixture state to a phase-separated state when the ratio of the interspecies interaction strength to the intraspecies interaction strength (assuming equal strength for both species) exceeds a critical value. At high temperature this is a structural transition and the global translational symmetry is broken. Our work complements previous studies on the instability of the mixture phase in the presence of BEC.
The coherent nonlinear tunneling dynamics of a boson-fermion mixture in a double-well potential is studied in this paper. Four types of phase are found for the mixture. The first one is two species localizing in different potential wells. The second one is two species coexisting in the same well. The third one is two species equally populated in two wells. The fourth one is one species equally populated in two wells while the other species is in one well. The phase transitions among these four states have been investigated. The interspecies and intraspecies interactions as well as bosonic and fermionic numbers can dramatically affect these phase transitions.
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.
Multicomponent quantum gases are ideal platforms to study fundamental phenomena arising from the mutual interaction between different constituents. Particularly, due to the repulsive interactions between two species, the system may exhibit a phase separation. We develop a mean-field-based theory for a two-component Bose mixture, which is equivalent to the Hartree-Fock-Bogoliubov approximation, and derive analytical expressions for the phase boundary and miscibility. The majority of existing theories, which are valid only for weakly interacting Bose gases, predict that the phase boundary is determined by the criterion ${g}_{ab}\ensuremath{\leqslant}\sqrt{{g}_{aa}{g}_{bb}}$ (where gab{g}_{ab}gab​ is a coupling constant between the components aaa and bbb). We show that in the Bose-Einstein condensation phase ($T\ensuremath{\leqslant}{T}_{c}$) the system may remain in a stable and miscible phase also for larger values of gab{g}_{ab}gab​, depending on the gas parameter $\ensuremath{\gamma}$ and temperature.
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.