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arXiv:1712.05022 · Physical Review A

Second sound in a two-dimensional Bose gas: From the weakly to the strongly interacting regime

Miki Ota, S. Stringari

Published Mar 7, 2018• 24 citations
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Abstract

The temperature and interaction dependence of the first and second sound in a two-dimensional Bose gas is studied in the vicinity of the Berezinskii-Kosterlitz-Thouless transition, where it is found that the excitation of the second sound through a density perturbation becomes weaker as the interaction strength increases, as a consequence of the fast decrease of the thermal expansion coefficient.

DOI
10.1103/physreva.97.033604

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The temperature and interaction dependence of the first and second sound in a two-dimensional Bose gas is studied in the vicinity of the Berezinskii-Kosterlitz-Thouless transition, where it is found that the excitation of the second sound through a density perturbation becomes weaker as the interaction strength increases, as a consequence of the fast decrease of the thermal expansion coefficient.
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We calculate the temperature dependence of the first and second sound velocities in the superfluid phase of a 2D dilute Bose gas by solving Landau's two fluid hydrodynamic equations. We predict the occurrence of a significant discontinuity in both velocities at the critical temperature, as a consequence of the jump of the superfluid density characterizing the Berezinskii-Kosterlitz-Thouless transition. The key role of the thermal expansion coefficient is discussed. We find that second sound in this dilute Bose gas can be easily excited through a density perturbation, thereby making the perspective of the measurement of the superfluid density particularly favorable.
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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 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 theoretically investigate sound modes in a weakly-interacting collisional Bose gas in DDD 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≥2D\ge 2D≥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 DDD dimensions.