Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2003.06847

Second sound in the BEC-BCS crossover

Daniel Kai Hoffmann, Vijay Pal Singh, Thomas Paintner, Manuel Jäger, W. Limmer, Ludwig Mathey, Johannes Hecker Denschlag

Published Mar 15, 2020• 2 citations
arXivHTMLPDF

Abstract

Second sound is an entropy wave which propagates in the superfluid component of a quantum liquid. Because it is an entropy wave, it probes the thermodynamic properties of the quantum liquid which are determined, e.g., by the interaction strength between the particles of the quantum liquid and their temperature. Here, we study second sound propagation for a large range of interaction strengths within the crossover between a Bose-Einstein condensate (BEC) and the Bardeen-Cooper-Schrieffer (BCS) superfluid. In particular, we investigate the strongly-interacting regime where currently theoretical predictions only exist in terms of an interpolation between the BEC, BCS and unitary regimes. Working with a quantum gas of ultracold fermionic $^6$Li atoms with tunable interactions, we show that the second sound speed varies only slightly in the crossover regime. We gain deeper insights into sound propagation and excitation of second sound by varying the excitation procedure which ranges from a sudden force pulse to a gentle heating pulse at the cloud center. These measurements are accompanied by classical-field simulations which help with the interpretation of the experimental data. Furthermore, we determine the spatial extension of the superfluid phase and estimate the superfluid density. In the future, this may be used to construct the so far unknown equation of state throughout the crossover.

DOI
10.48550/arxiv.2003.06847

Related papers

Second sound in the crossover from the Bose-Einstein condensate to the Bardeen-Cooper-Schrieffer superfluid

Daniel Kai Hoffmann, Vijay Pal Singh, Thomas Paintner +4 more

Abstract Second sound is an entropy wave which propagates in the superfluid component of a quantum liquid. Because it is an entropy wave, it probes the thermodynamic properties of the quantum liquid. Here, we study second sound propagation for a large range of interaction strengths within the crossover between a Bose-Einstein condensate (BEC) and the Bardeen-Cooper-Schrieffer (BCS) superfluid, extending previous work at unitarity. In particular, we investigate the strongly-interacting regime where currently theoretical predictions only exist in terms of an interpolation in the crossover. Working with a quantum gas of ultracold fermionic 6Li atoms with tunable interactions, we show that the second sound speed varies only slightly in the crossover regime. By varying the excitation procedure, we gain deeper insight on sound propagation. We compare our measurement results with classical-field simulations, which help with the interpretation of our experiments.

Nature Communications•Dec 6, 2021•13 citations

Critical Velocity in the BEC-BCS Crossover

Wolf Weimer, Kai Morgener, Vijay Pal Singh +5 more

We map out the critical velocity in the crossover from Bose-Einstein condensation to Bardeen-Cooper-Schrieffer superfluidity with ultracold ^{6}Li gases. A small attractive potential is dragged along lines of constant column density. The rate of the induced heating increases steeply above a critical velocity v_{c}. In the same samples, we measure the speed of sound v_{s} by exciting density waves and compare the results to the measured values of v_{c}. We perform numerical simulations in the Bose-Einstein condensation regime and find very good agreement, validating the approach. In the strongly correlated regime our measurements of v_{c} provide a testing ground for theoretical approaches.

arXiv:1408.5239•Physical Review Letters•Mar 3, 2015•98 citations

Second sound in Fermi gases at the BCS-BEC crossover

H. Heiselberg

The thermodynamic potential is calculated for a uniform superfluid gas of fermi atoms from the mean field BCS equations including corrections from induced interactions, Hartree-Fock energies and quasiparticle selfenergies. The entropy, specific heat and sound modes are calculated as function of temperature, density and interaction strength from the BCS to the unitarity limit and around the BCS-BEC crossover. The second sound speed is of particular interest as it is a clear signal of a superfluid component and it determines the critical temperature.

arXiv:cond-mat/0409077•Sep 3, 2004•0 citations

Propagation of sound and supersonic bright solitons in superfluid Fermi gases in BCS-BEC crossover

Wen Wen, Shun-Qing Shen, Guoxiang Huang

We investigate the linear and nonlinear sound propagations in a cigar-shaped superfluid Fermi gas with a large particle number. We first solve analytically the eigenvalue problem of linear collective excitations and provide explicit expressions of all eigenvalues and eigenfunctions, which are valid for all superfluid regimes in the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation (BCS-BEC) crossover. The linear sound speed obtained agrees well with that of a recent experimental measurement. We then consider a weak nonlinear excitation and show that the time evolution of the excitation obeys a Korteweg de Vries equation. Different from the result obtained in quasi-one-dimensional case studied previously, where subsonic dark solitons are obtained via the balance between quantum pressure and nonlinear effect, we demonstrate that bright solitons with supersonic propagating velocity can be generated in the present three-dimensional system through the balance between a waveguidelike dispersion and the interparticle interaction. The supersonic bright solitons obtained display different physical properties in different superfluid regimes and hence can be used to characterize superfluid features of the BCS-BEC crossover.

Physical Review B•Jan 28, 2010•41 citations

Sound modes at the BCS-BEC crossover

H. Heiselberg

First and second sound speeds are calculated for a uniform superfluid gas of Fermi atoms as a function of temperature, density, and interaction strength. The second sound speed is of particular interest as it is a clear signal of a superfluid component and it determines the critical temperature. The sound modes and their dependence on density, scattering length, and temperature are calculated in the BCS, molecular Bose-Einstein condensate (BEC), and unitarity limits and a smooth crossover is extrapolated. It is found that first and second sounds undergo avoided crossing on the BEC side due to mixing. Consequently, they are detectable at crossover both as density and thermal waves in traps.

arXiv:cond-mat/0503101•Physical Review A•Jan 10, 2006•39 citations

Propagation of first and second sound in a two-dimensional Fermi superfluid

Andrea Tononi, Alberto Cappellaro, Giacomo Bighin +1 more

Sound propagation is a macroscopic manifestation of the interplay between the equilibrium thermodynamics and the dynamical transport properties of fluids. Here, for a two-dimensional system of ultracold fermions, we calculate the first and second sound velocities across the whole BCS-BEC crossover, and we analyze the system response to an external perturbation. In the low-temperature regime we reproduce the recent measurements [Phys. Rev. Lett. 124, 240403 (2020)] of the first sound velocity, which, due to the decoupling of density and entropy fluctuations, is the sole mode excited by a density probe. Conversely, a heat perturbation excites only the second sound, which, being sensitive to the superfluid depletion, vanishes in the deep BCS regime and jumps discontinuously to zero at the Berezinskii-Kosterlitz-Thouless superfluid transition. A mixing between the modes occurs only in the finite-temperature BEC regime, where our theory converges to the purely bosonic results.

arXiv:2009.06491•Physical Review A•Jun 14, 2021•11 citations
Second sound is an entropy wave which propagates in the superfluid component of a quantum liquid. Because it is an entropy wave, it probes the thermodynamic properties of the quantum liquid which are determined, e.g., by the interaction strength between the particles of the quantum liquid and their temperature. Here, we study second sound propagation for a large range of interaction strengths within the crossover between a Bose-Einstein condensate (BEC) and the Bardeen-Cooper-Schrieffer (BCS) superfluid. In particular, we investigate the strongly-interacting regime where currently theoretical predictions only exist in terms of an interpolation between the BEC, BCS and unitary regimes. Working with a quantum gas of ultracold fermionic 6^66Li atoms with tunable interactions, we show that the second sound speed varies only slightly in the crossover regime. We gain deeper insights into sound propagation and excitation of second sound by varying the excitation procedure which ranges from a sudden force pulse to a gentle heating pulse at the cloud center. These measurements are accompanied by classical-field simulations which help with the interpretation of the experimental data. Furthermore, we determine the spatial extension of the superfluid phase and estimate the superfluid density. In the future, this may be used to construct the so far unknown equation of state throughout the crossover.
Abstract Second sound is an entropy wave which propagates in the superfluid component of a quantum liquid. Because it is an entropy wave, it probes the thermodynamic properties of the quantum liquid. Here, we study second sound propagation for a large range of interaction strengths within the crossover between a Bose-Einstein condensate (BEC) and the Bardeen-Cooper-Schrieffer (BCS) superfluid, extending previous work at unitarity. In particular, we investigate the strongly-interacting regime where currently theoretical predictions only exist in terms of an interpolation in the crossover. Working with a quantum gas of ultracold fermionic 6Li atoms with tunable interactions, we show that the second sound speed varies only slightly in the crossover regime. By varying the excitation procedure, we gain deeper insight on sound propagation. We compare our measurement results with classical-field simulations, which help with the interpretation of our experiments.
We map out the critical velocity in the crossover from Bose-Einstein condensation to Bardeen-Cooper-Schrieffer superfluidity with ultracold ^{6}Li gases. A small attractive potential is dragged along lines of constant column density. The rate of the induced heating increases steeply above a critical velocity v_{c}. In the same samples, we measure the speed of sound v_{s} by exciting density waves and compare the results to the measured values of v_{c}. We perform numerical simulations in the Bose-Einstein condensation regime and find very good agreement, validating the approach. In the strongly correlated regime our measurements of v_{c} provide a testing ground for theoretical approaches.
The thermodynamic potential is calculated for a uniform superfluid gas of fermi atoms from the mean field BCS equations including corrections from induced interactions, Hartree-Fock energies and quasiparticle selfenergies. The entropy, specific heat and sound modes are calculated as function of temperature, density and interaction strength from the BCS to the unitarity limit and around the BCS-BEC crossover. The second sound speed is of particular interest as it is a clear signal of a superfluid component and it determines the critical temperature.
We investigate the linear and nonlinear sound propagations in a cigar-shaped superfluid Fermi gas with a large particle number. We first solve analytically the eigenvalue problem of linear collective excitations and provide explicit expressions of all eigenvalues and eigenfunctions, which are valid for all superfluid regimes in the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation (BCS-BEC) crossover. The linear sound speed obtained agrees well with that of a recent experimental measurement. We then consider a weak nonlinear excitation and show that the time evolution of the excitation obeys a Korteweg de Vries equation. Different from the result obtained in quasi-one-dimensional case studied previously, where subsonic dark solitons are obtained via the balance between quantum pressure and nonlinear effect, we demonstrate that bright solitons with supersonic propagating velocity can be generated in the present three-dimensional system through the balance between a waveguidelike dispersion and the interparticle interaction. The supersonic bright solitons obtained display different physical properties in different superfluid regimes and hence can be used to characterize superfluid features of the BCS-BEC crossover.
First and second sound speeds are calculated for a uniform superfluid gas of Fermi atoms as a function of temperature, density, and interaction strength. The second sound speed is of particular interest as it is a clear signal of a superfluid component and it determines the critical temperature. The sound modes and their dependence on density, scattering length, and temperature are calculated in the BCS, molecular Bose-Einstein condensate (BEC), and unitarity limits and a smooth crossover is extrapolated. It is found that first and second sounds undergo avoided crossing on the BEC side due to mixing. Consequently, they are detectable at crossover both as density and thermal waves in traps.
Sound propagation is a macroscopic manifestation of the interplay between the equilibrium thermodynamics and the dynamical transport properties of fluids. Here, for a two-dimensional system of ultracold fermions, we calculate the first and second sound velocities across the whole BCS-BEC crossover, and we analyze the system response to an external perturbation. In the low-temperature regime we reproduce the recent measurements [Phys. Rev. Lett. 124, 240403 (2020)] of the first sound velocity, which, due to the decoupling of density and entropy fluctuations, is the sole mode excited by a density probe. Conversely, a heat perturbation excites only the second sound, which, being sensitive to the superfluid depletion, vanishes in the deep BCS regime and jumps discontinuously to zero at the Berezinskii-Kosterlitz-Thouless superfluid transition. A mixing between the modes occurs only in the finite-temperature BEC regime, where our theory converges to the purely bosonic results.