Recently there has been renewed interest in second sound in superfluid Bose and Fermi gases. By using two-fluid hydrodynamic theory, we review the density response $\chi_{nn}(\bq,\omega)$ of these systems as a tool to identify second sound in experiments based on density probes. Our work generalizes the well-known studies of the dynamic structure factor $S(\bq,\omega)$ in superfluid
4He in the critical region. We show that, in the unitary limit of uniform superfluid Fermi gases, the relative weight of second vs. first sound in the compressibility sum rule is given by the Landau--Placzek ratio $\lp\equiv (\bar{c}_p-\bar{c}_v)/\bar{c}_v$ for all temperatures below
Tc. In contrast to superfluid
4He, $\lp$ is much larger in strongly interacting Fermi gases, being already of order unity for
T∼0.8Tc, thereby providing promising opportunities to excite second sound with density probes. The relative weights of first and second sound are quite different in $S(\bq,\omega)$ (measured in pulse propagation studies) as compared to $\mathrm{Im}\chi_{nn}(\bq,\omega)$ (measured in two-photon Bragg scattering). We show that first and second sound in $S(\bq,\omega)$ in a strongly interacting Bose-condensed gas are similar to those in a Fermi gas at unitarity. However, in a weakly interacting Bose gas, first and second sound are mainly uncoupled oscillations of the thermal cloud and condensate, respectively, and second sound has most of the spectral weight in $S(\bq,\omega)$. We also discuss the behaviour of the superfluid and normal fluid velocity fields involved in first and second sound.
Recently, there has been renewed interest in second sound in superfluid Bose and Fermi gases. By using two-fluid hydrodynamic theory, we review the density response χ nn ( q , ω) of these systems as a tool to identify second sound in experiments based on density probes. Our work generalizes the well-known studies of the dynamic structure factor S ( q , ω) in superfluid 4 He in the critical region. We show that, in the unitary limit of uniform superfluid Fermi gases, the relative weight of second versus first sound in the compressibility sum rule is given by the Landau–Placzek ratio for all temperatures below T c . In contrast to superfluid 4 He, LP is much larger in strongly interacting Fermi gases, being already of order unity for T ∼0.8 T c , thereby providing promising opportunities to excite second sound with density probes. The relative weights of first and second sound are quite different in S ( q , ω) (measured in pulse propagation studies) as compared with Imχ nn ( q , ω) (measured in two-photon Bragg scattering). We show that first and second sound in S ( q , ω) in a strongly interacting Bose-condensed gas are similar to those in a Fermi gas at unitarity. However, in a weakly interacting Bose gas, first and second sound are mainly uncoupled oscillations of the thermal cloud and condensate, respectively, and second sound has most of the spectral weight in S ( q , ω). We also discuss the behaviour of the superfluid and normal fluid velocity fields involved in first and second sound.
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.
Abstract We theoretically investigate sound modes in a weakly-interacting collisional Bose gas in D dimensions. Using the Landau’s two-fluid hydrodynamics and working within the Bogoliubov theory, we observe the hybridization of the first and second sound modes for D ⩾ 2. To model the recent measurements of the sound velocities in 2D, obtained in the weakly-interacting regime and around the Berezinskii–Kosterlitz–Thouless transition temperature, we derive a refined calculation of the superfluid density, finding a fair agreement with the experiment. In the 1D case, for which experimental results are currently unavailable, we find no hybridization, triggering the necessity of future investigations. Our analysis provides a systematic understanding of sound propagation in a collisional weakly-interacting Bose gas in D dimensions.
We theoretically investigate sound modes in a weakly-interacting collisional Bose gas in
D dimensions. Using the Landau's two-fluid hydrodynamics and working within the Bogoliubov theory, we observe the hybridization of the first and second sound modes for
D≥2. To model the recent measurements of the sound velocities in 2D, obtained around the Berezinskii-Kosterlitz-Thouless transition temperature and outside the very weakly-interacting regime, we derive a refined calculation of the superfluid density, finding a fair agreement with the experiment. In the 1D case, for which experimental results are currently unavailable, we find no hybridization, triggering the necessity of future experimental investigations. Our analysis provides a systematic understanding of sound propagation in a collisional weakly-interacting Bose gas in
D dimensions.
We have recently derived two-fluid hydrodynamic equations for a trapped weakly interacting Bose gas. In this paper we use these equations to discuss first and second sound in a uniform Bose gas. These results are shown to agree with the predictions of the usual two-fluid equations of Landau when the thermodynamic functions are evaluated for a weakly interacting gas. In a uniform gas, second sound mainly corresponds to an oscillation of the superfluid (the condensate) and is the low-frequency continuation of the Bogoliubov-Goldstone symmetry-breaking mode.