Superfluidity of non-condensate bosons in Bose–Einstein condensed systems

Abstract

We present a general theory for superfluidity of non-condensate bosons in Bose–Einstein condensed systems. Considering a system enclosed in a cylindrical vessel rotating about its axis, the superfluid density is determined by analyzing the response of the system to an inertial force field specified by a vector potential in the frame rotating together with the vessel. We derive a general formula for the superfluid density of non-condensate bosons expressed in terms of Green’s functions. It is shown that the superfluidity of non-condensate bosons is caused by the anomalous self-energy describing the pairing correlation between them. The total superfluid density is given by the sum of the condensate density and the superfluid density of non-condensate bosons, reducing to the Landau formula within mean-field approximations neglecting the damping of quasiparticles. We generalize the linear relation between the current and inertial vector potential to satisfy the gauge invariance, introducing the pairing wave function for the superfluid component of non-condensate bosons. We find that the phase of the pairing wave function is twice that of the condensate wave function and the circulation is still quantized in units of 2π∕m even in the presence of the pairing current of non-condensate bosons.