Hybridization of first and second sound in a weakly interacting Bose gas

¹ École normale supérieure, International Center for Fundamental Physics - Paris, France
² INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento - I-38123 Povo, Italy
³ Kapitza Institute for Physical Problems - Kosygina 2, 119334 Moscow, Russia

Received: 20 June 2015
Accepted: 6 August 2015

Abstract

Using Landau's theory of two-fluid hydrodynamics we investigate the sound modes propagating in a uniform weakly interacting superfluid Bose gas for values of temperature up to the critical point. In order to evaluate the relevant thermodynamic functions needed to solve the hydrodynamic equations, including the temperature dependence of the superfluid density, we use the Bogoliubov theory at low temperatures and the results of a perturbative approach based on the Beliaev diagrammatic technique at higher temperatures. Special focus is given on the hybridization phenomenon between first and second sound which occurs at low temperatures of the order of the interaction energy and we discuss explicitly the behavior of the two sound velocities near the hybridization point.