Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0211118 · Physical Review A

Symmetric-asymmetric transition in mixtures of Bose-Einstein condensates

Anatoly A. Svidzinsky, S. T. Chui

Published May 27, 2003• 42 citations
arXivHTMLPDF

Abstract

We study a quantum phase transition in phase-separated mixtures of Bose-Einstein condensates. In this transition, the distribution of the two components changes from a symmetric to an asymmetric shape. We discuss the nature of the phase transition, the role of interface tension, and the phase diagram. The symmetric to asymmetric transition is the simplest quantum phase transition that one can imagine. Careful study of this problem should provide us insight into this burgeoning field of discovery.

DOI
10.1103/physreva.67.053608

Related papers

Normal modes and stability of phase-separated trapped Bose-Einstein condensates

Anatoly A. Svidzinsky, S. T. Chui

We study the normal modes and the stability of two component condensates in a phase separated regime. In such a regime, the system can undergo a quantum phase-transition upon the change of interaction strength between bosons of the same species or the variation of the trap frequencies. In this transition, the distribution of the two components changes from a symmetric to an asymmetric shape. We discuss the nature of the phase transition, the role of the interface tension, and the phase diagram. The symmetric to asymmetric transition is the simplest quantum phase transition that one can imagine. We found new branches of normal modes which are specific for trapped multicomponent condensates and are analogous to the waves at the interface between two layers of immiscible fluids under gravity. At the point of the phase transition, the frequencies of those modes go to 0 and become imaginary which causes an instability. The interface tension shifts the normal-mode frequencies and changes the stability region of the system.

arXiv:cond-mat/0212205•Physical Review A•Jul 28, 2003•48 citations

Phase diagram of two-component mean-field Bose mixtures

Oskar Stachowiak, Paweł Jakubczyk

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.

arXiv:2501.05910•Journal of Statistical Mechanics Theory and Experiment•Oct 1, 2025•1 citation

Quantum entanglement manifestation of transition to nonlinear self-trapping for Bose-Einstein condensates in a symmetric double well

Liu Fu, Jie Liu

We investigate the nonlinear self-trapping phenomenon of a Bose-Einstein condensate (BEC) in a symmetric double well, emphasizing its underlying dynamical phase transition. As the nonlinear parameter characterizing the interaction between the degenerate atoms increases, the BEC becomes self-trapped, manifesting an asymmetric distribution of the atomic density profile. The essence of this phenomenon is revealed to be a continuous phase transition and the underlying critical behavior is studied analytically and found to follow a logarithmic scaling law. We then go beyond the mean-field treatment and extend our treatment to discuss the effect of many-body quantum fluctuations on the transition. It is found that the transition point is shifted and the scaling law is broken. In particular, the quantum phase transition is accompanied by a change of the entanglement entropy, which is found to reach a maximum at the transition point. The underlying physics is revealed.

arXiv:cond-mat/0609337•Physical Review A•Dec 13, 2006•95 citations

Phase separation and dynamics of two-component Bose-Einstein condensates

R. Navarro, R. Carretero-González, P. G. Kevrekidis

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.

arXiv:0906.3316•Physical Review A•Aug 20, 2009•59 citations

First-order, continuous, and multicritical Bose-Einstein condensation in Bose mixtures

Paweł Jakubczyk, Krzysztof Myśliwy, Marek Napiórkowski

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.

arXiv:2312.05217•Physical Review A•Jan 12, 2024•4 citations

Phase separation of two-component Bose–Einstein condensates

Zuhan Liu

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.

Journal of Mathematical Physics•Oct 1, 2009•16 citations
We study a quantum phase transition in phase-separated mixtures of Bose-Einstein condensates. In this transition, the distribution of the two components changes from a symmetric to an asymmetric shape. We discuss the nature of the phase transition, the role of interface tension, and the phase diagram. The symmetric to asymmetric transition is the simplest quantum phase transition that one can imagine. Careful study of this problem should provide us insight into this burgeoning field of discovery.
We study the normal modes and the stability of two component condensates in a phase separated regime. In such a regime, the system can undergo a quantum phase-transition upon the change of interaction strength between bosons of the same species or the variation of the trap frequencies. In this transition, the distribution of the two components changes from a symmetric to an asymmetric shape. We discuss the nature of the phase transition, the role of the interface tension, and the phase diagram. The symmetric to asymmetric transition is the simplest quantum phase transition that one can imagine. We found new branches of normal modes which are specific for trapped multicomponent condensates and are analogous to the waves at the interface between two layers of immiscible fluids under gravity. At the point of the phase transition, the frequencies of those modes go to 0 and become imaginary which causes an instability. The interface tension shifts the normal-mode frequencies and changes the stability region of the system.
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 investigate the nonlinear self-trapping phenomenon of a Bose-Einstein condensate (BEC) in a symmetric double well, emphasizing its underlying dynamical phase transition. As the nonlinear parameter characterizing the interaction between the degenerate atoms increases, the BEC becomes self-trapped, manifesting an asymmetric distribution of the atomic density profile. The essence of this phenomenon is revealed to be a continuous phase transition and the underlying critical behavior is studied analytically and found to follow a logarithmic scaling law. We then go beyond the mean-field treatment and extend our treatment to discuss the effect of many-body quantum fluctuations on the transition. It is found that the transition point is shifted and the scaling law is broken. In particular, the quantum phase transition is accompanied by a change of the entanglement entropy, which is found to reach a maximum at the transition point. The underlying physics is revealed.
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 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.
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.