Analytical limits for cold atom Bose gases with tunable interactions

Abstract

We discuss the equilibrium properties of dilute Bose gases using a non-perturbative formalism based on auxiliary fields related to the normal and anomalous densities. We show analytically that for a dilute Bose gas of weakly-interacting particles at zero temperature, the leading-order auxiliary field (LOAF) approximation leads to well-known analytical results. Close to the critical point the LOAF predictions are the same as those obtained using an effective field theory in the large-N approximation. We also report analytical approximations for the LOAF results in the unitarity limit, which compare favorably with our numerical results. LOAF predicts that the equation of state for the Bose gas in the unitarity limit is E / (p V) = 1, unlike the case of the Fermi gas when E / (p V) = 3/2.

11 pages, 7 figures

References in corpus (14)

• Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates
• Tomographic RF Spectroscopy of a Trapped Fermi Gas at Unitarity
• Quantum versus classical statistical dynamics of an ultracold Bose gas
• Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Seven Loops
• Particle-hole fluctuations in the BCS-BEC Crossover
• Functional renormalization for Bose-Einstein Condensation
• Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Six Loops
• Non-perturbative predictions for cold atom Bose gases with tunable interactions
• Four-point vertex in the Hubbard model and partial bosonization
• Conserving Gapless Mean-Field Theory for Weakly Interacting Bose Gases
• Auxiliary field approach to dilute Bose gases with tunable interactions
• Auxiliary field formalism for dilute fermionic atom gases with tunable interactions
• Non-equilibrium dynamics of a Bose-Einstein condensate in an optical lattice
• Bose-Einstein Condensate Driven by a Kicked Rotor in a Finite Box

Cited by in corpus (9)

• The Josephson relation for the superfluid density and the connection to the Goldstone theorem in dilute Bose atomic gasses
• Quench Dynamics and Emergence of Phase Separation in Two-Component Atomic Bose Gases at Zero Temperature and above the BEC Critical Temperature
• Thermodynamics of the Bose-Hubbard model in a Bogoliubov+U theory
• 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
• Phase Transitions in Three-Dimensional Bosonic Systems in Optical Lattices
• $1/N$-expansion for the critical temperature of the Bose gas
• Leading-Order Auxiliary Field Theory of the Bose-Hubbard Model
• Addressing energy density functionals in the language of path-integrals II: Comparative study of functional renormalization group techniques applied to the (0+0)-D $O(N)$-symmetric ${\phi }^4$-theory
• Critical temperature of trapped interacting bosons from large-N based theories