Large-N approximation for single- and two-component dilute Bose gases

Abstract

We discuss the mean-field theories obtained from the leading order in a large-$N$ 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 $T_c$ is not shifted from the non-interacting gas value $T_0$. 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 intra- species interactions and focus on the stability of the mixture state above $T_c$. Our mean-field approximation predicts an instability from the mixture state to a phase-separated state when the ratio of the inter-species interaction strength to the intra-species 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.

10 pages, 3 figures

References in corpus (21)

• Many-Body Physics with Ultracold Gases
• Feshbach Resonances in Ultracold Gases
• Spin domains in ground state spinor Bose-Einstein condensates
• Phase separation of Bose-Einstein condensates
• Superflow in a toroidal Bose-Einstein condensate: an atom circuit with a tunable weak link
• Theory of the Weakly Interacting Bose Gas
• Quantum Field Theory in the Large N Limit: a review
• Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates
• Quantum magnetism and criticality
• The transition temperature of the dilute interacting Bose gas
• Controlling phase separation of binary Bose-Einstein condensates via mixed-spin-channel Feshbach resonance
• Quantum simulation of cosmic inflation in two-component Bose-Einstein condensates
• Efimov Physics in Cold Atoms
• Spin gradient thermometry for ultracold atoms in optical lattices
• T_c for dilute Bose gases: beyond leading order in 1/N
• Superfluid phase diagrams of trapped Fermi gases with population imbalance
• The O(N) vector model in the large N limit revisited: multicritical points and double scaling limit
• Non-perturbative predictions for cold atom Bose gases with tunable interactions
• On the Convergence of the Linear Delta Expansion for the Shift in T_c for Bose-Einstein Condensation
• Auxiliary field approach to dilute Bose gases with tunable interactions
• An O(N) symmetric extension of the Sine-Gordon Equation

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• Mean-field description of pairing effects, BKT physics, and superfluidity in 2D Bose gases
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• Quench Dynamics and Emergence of Phase Separation in Two-Component Atomic Bose Gases at Zero Temperature and above the BEC Critical Temperature
• Large-$N$ expansion for condensation and stability of Bose-Bose mixtures at finite temperatures
• Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Thermodynamics and structural transition of binary atomic Bose-Fermi mixtures in box or harmonic potentials: A path-integral study
• Large-$N$ properties of a non-ideal Bose gas
• Condensation and superfluidity of $SU(N)$ Bose gas
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• Bosonic binary mixtures with Josephson-type interactions