The Josephson relation for the superfluid density and the connection to the Goldstone theorem in dilute Bose atomic gasses

Abstract

We derive the Josephson relation for a dilute Bose gas in the framework of an auxiliary-field resummation of the theory in terms of the normal- and anomalous-density condensates. The mean-field phase diagram of this theory features two critical temperatures, T_c and $T^*, associated with the presence in the system of the Bose-Einstein condensate (BEC) and superfluid state, respectively. In this context, the Josephson relation shows that the superfluid density is related to a second order parameter, the square of the anomalous-density condensate. This is in contrast with the corresponding result in the Bose gas theory without an anomalous condensate, which predicts that the superfluid density is proportional to the BEC condensate density. Our findings are consistent with the prediction that in the temperature range between T_c and T^* a fraction of the system is in the superfluid state in the absence of the BEC condensate. This situation is similar to the case of dilute Fermi gases, where the superfluid density is proportional to the square of the gap parameter. The Josephson relation relies on the existence of zero energy and momentum excitations showing the intimate relationship between superfluidity and the Goldstone theorem.

13 pages, 1 figure

References in corpus (4)

• Pairing fluctuations and the superfluid density through the BCS-BEC crossover
• Non-perturbative predictions for cold atom Bose gases with tunable interactions
• The Josephson relation for the superfluid density in the BCS-BEC crossover
• Composite-Field Goldstone States and Higgs Mechanism in Dilute Bose Gases

Cited by in corpus (7)

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• Mean-field description of pairing effects, BKT physics, and superfluidity in 2D Bose gases
• Generalized Josephson relation for conserved charges in multi-component bosons
• 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
• Superfluid density, Josephson relation and pairing fluctuations in a multi-component fermion superfluid
• 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