We provide an overview of the recent theoretical and experimental advances in the study of second sound in ultracold atomic gases. Starting from the Landau two fluid hydrodynamic equations we develop the theory of first and second sound in various configurations characterized by different geometries and quantum statistics. These include the weakly interacting 3D Bose gas, the strongly interacting Fermi gas at unitarity in the presence of highly elongated traps and the dilute 2D Bose gas, characterized by the Berezinskii-Kosterlitz-Thouless transition. An explicit comparison with the propagation of second sound in liquid Helium is carried out to elucidate the main analogies and differences. We also make an explicit comparison with the available experimental data and point out the crucial role played by the superfluid density in determining the temperature dependence of the second sound speed.We provide an overview of the recent theoretical and experimental advances in the study of second sound in ultracold atomic gases. Starting from the Landau two fluid hydrodynamic equations we develop the theory of first and second sound in various configurations characterized by different geometries and quantum statistics. These include the weakly interacting 3D Bose gas, the strongly interacting Fermi gas at unitarity in the presence of highly elongated traps and the dilute 2D Bose gas, characterized by the Berezinskii-Kosterlitz-Thouless transition. An explicit comparison with the propagation of second sound in liquid Helium is carried out to elucidate the main analogies and differences. We also make an explicit comparison with the available experimental data and point out the crucial role played by the superfluid density in determining the temperature dependence of the second sound speed.

arXiv:1510.01306Cambridge University Press eBooksOct 4, 201815 citations

SECOND SOUND IN A WEAKLY IDEAL BOSE GAS

Yu. A. Tserkovnikov, N. N. Bogolyubov

Dec 21, 19640 citations

First and Second Sound Modes of a Bose-Einstein Condensate in a Harmonic Trap

Vivek B. Shenoy, Tin-Lun Ho

We have calculated the first and second sound modes of a dilute interacting Bose gas in a spherical trap for temperatures $(0.6<{T/T}_{c}<1.2)$ and for systems with ${10}^{4}$ to ${10}^{8}$ particles. The second sound modes (which exist only below ${T}_{c}$ ) generally have a stronger temperature dependence than the first sound modes. The puzzling temperature variations of the sound modes near ${T}_{c}$ recently observed at JILA in systems with ${10}^{3}$ particles match surprisingly well with those of the first and second sound modes of much larger systems.We have calculated the first and second sound modes of a dilute interacting Bose gas in a spherical trap for temperatures $(0.6<{T/T}_{c}<1.2)$ and for systems with ${10}^{4}$ to ${10}^{8}$ particles. The second sound modes (which exist only below ${T}_{c}$) generally have a stronger temperature dependence than the first sound modes. The puzzling temperature variations of the sound modes near ${T}_{c}$ recently observed at JILA in systems with ${10}^{3}$ particles match surprisingly well with those of the first and second sound modes of much larger systems.

arXiv:cond-mat/9710274Physical Review LettersMay 4, 199827 citations

First and second sound in a uniform Bose gas

Adam Griffin, E. Zaremba

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.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.

arXiv:cond-mat/9707058Physical Review ADec 1, 199763 citations

We have calculated the first and second sound modes of a dilute interacting Bose gas in a spherical trap for temperatures

(0.6<{T/T}_{c}<1.2)

and for systems with

{10}^{4}

{10}^{8}

particles. The second sound modes (which exist only below

{T}_{c}

) generally have a stronger temperature dependence than the first sound modes. The puzzling temperature variations of the sound modes near

{T}_{c}

recently observed at JILA in systems with

{10}^{3}

particles match surprisingly well with those of the first and second sound modes of much larger systems.