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:1011.4893 · Physical Review A

Low-temperature thermodynamics of the unitary Fermi gas: Superfluid fraction, first sound, and second sound

Luca Salasnich

Published Dec 15, 2010• 23 citations
arXivHTMLPDF

Abstract

We investigate the low-temperature thermodynamics of the unitary Fermi gas by introducing a model based on the zero-temperature spectra of both bosonic collective modes and fermonic single-particle excitations. We calculate the Helmholtz free energy and from it we obtain the entropy, the internal energy, and the chemical potential as a function of the temperature. By using these quantities and the Landau's expression for the superfluid density we determine analytically the superfluid fraction, the critical temperature, the first sound velocity, and the second sound velocity. We compare our analytical results with other theoretical predictions and experimental data of ultracold atoms and dilute neutron matter.

DOI
10.1103/physreva.82.063619

Related papers

Unitary Fermi superfluid near the critical temperature: Thermodynamics and sound modes from elementary excitations

Giacomo Bighin, Alberto Cappellaro, Luca Salasnich

In superfluid ${}^{4}$He the first sound refers to the propagation of a density wave while the second sound is related to the propagation of a temperature or entropy wave. The authors show that in superfluid Fermi gases this simplified picture is not always valid. Moreover, they calculate the first and second sound velocities, and the superfluid fraction near the critical point in unitary Fermi gases, and find good agreement with recent experimental results.

arXiv:2206.03924•Physical Review A•Jun 30, 2022•3 citations

Measurement of Universal Thermodynamic Functions for a Unitary Fermi Gas

Munekazu Horikoshi, Shuta Nakajima, Masahito Ueda +1 more

Thermodynamic properties of matter generally depend on the details of interactions between its constituent parts. However, in a unitary Fermi gas where the scattering length diverges, thermodynamics is determined through universal functions that depend only on the particle density and temperature. By using only the general form of the equation of state and the equation of force balance, we measured the local internal energy of the trapped gas as a function of these parameters. Other universal functions, such as those corresponding to the Helmholtz free energy, chemical potential, and entropy, were calculated through general thermodynamic relations. The critical parameters were also determined at the superfluid transition temperature. These results apply to all strongly interacting fermionic systems, including neutron stars and nuclear matter.

APS•Mar 1, 2010•0 citations

Measurement of Universal Thermodynamic Functions for a Unitary Fermi Gas

Munekazu Horikoshi, Shuta Nakajima, Masahito Ueda +1 more

Thermodynamic properties of matter generally depend on the details of interactions between its constituent parts. However, in a unitary Fermi gas where the scattering length diverges, thermodynamics is determined through universal functions that depend only on the particle density and temperature. By using only the general form of the equation of state and the equation of force balance, we measured the local internal energy of the trapped gas as a function of these parameters. Other universal functions, such as those corresponding to the Helmholtz free energy, chemical potential, and entropy, were calculated through general thermodynamic relations. The critical parameters were also determined at the superfluid transition temperature. These results apply to all strongly interacting fermionic systems, including neutron stars and nuclear matter.

Science•Jan 21, 2010•213 citations

Second sound and the superfluid fraction in a resonantly interacting Fermi gas

Leonid A. Sidorenkov, Meng Khoon Tey, Rudolf Grimm +3 more

Superfluidity is a macroscopic quantum phenomenon, which shows up below a critical temperature and leads to a peculiar behavior of matter, with frictionless flow, the formation of quantized vortices, and the quenching of the moment of inertia being intriguing examples. A remarkable explanation for many phenomena exhibited by a superfluid at finite temperature can be given in terms of a two-fluid mixture comprised of a normal component that behaves like a usual fluid and a superfluid component with zero viscosity and zero entropy. Important examples of superfluid systems are liquid helium and neutron stars. More recently, ultracold atomic gases have emerged as new superfluid systems with unprecedented possibilities to control interactions and external confinement. Here we report the first observation of `second sound' in an ultracold Fermi gas with resonant interactions. Second sound is a striking manifestation of the two-component nature of a superfluid and corresponds to an entropy wave, where the superfluid and the non-superfluid components oscillate in opposite phase, different from ordinary sound (`first sound'), where they oscillate in phase. The speed of second sound depends explicitly on the value of the superfluid fraction, a quantity sensitive to the spectrum of elementary excitations. Our measurements allow us to extract the temperature dependence of the superfluid fraction, which in strongly interacting quantum gases has been an inaccessible quantity so far.

arXiv:1302.2871•Bulletin of the American Physical Society•Feb 12, 2013•1 citation

First and Second Sound Modes in a Uniform Fermi Gas

Huang Bei-Bing, Shaolong Wan

First and second sound modes in a uniform fermionic atom gas with Feshbach resonance are investigated in the frame of a two-fluid model at finite temperature. All thermodynamic quantities are calculated for a given thermodynamic potential. The analytical results for thermodynamic quantities and sound velocities in BCS and BEC limits are obtained. The numerical results show that there exists a continuous interpolation for sound velocities of the first and second sound modes at fixed T/T c between BCS and BEC limits. The existence of the second sound mode indicates the existence of superfluidity.

Chinese Physics Letters•Jul 1, 2009•1 citation

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
We investigate the low-temperature thermodynamics of the unitary Fermi gas by introducing a model based on the zero-temperature spectra of both bosonic collective modes and fermonic single-particle excitations. We calculate the Helmholtz free energy and from it we obtain the entropy, the internal energy, and the chemical potential as a function of the temperature. By using these quantities and the Landau's expression for the superfluid density we determine analytically the superfluid fraction, the critical temperature, the first sound velocity, and the second sound velocity. We compare our analytical results with other theoretical predictions and experimental data of ultracold atoms and dilute neutron matter.
In superfluid 4{}^{4}4He the first sound refers to the propagation of a density wave while the second sound is related to the propagation of a temperature or entropy wave. The authors show that in superfluid Fermi gases this simplified picture is not always valid. Moreover, they calculate the first and second sound velocities, and the superfluid fraction near the critical point in unitary Fermi gases, and find good agreement with recent experimental results.
Thermodynamic properties of matter generally depend on the details of interactions between its constituent parts. However, in a unitary Fermi gas where the scattering length diverges, thermodynamics is determined through universal functions that depend only on the particle density and temperature. By using only the general form of the equation of state and the equation of force balance, we measured the local internal energy of the trapped gas as a function of these parameters. Other universal functions, such as those corresponding to the Helmholtz free energy, chemical potential, and entropy, were calculated through general thermodynamic relations. The critical parameters were also determined at the superfluid transition temperature. These results apply to all strongly interacting fermionic systems, including neutron stars and nuclear matter.
Thermodynamic properties of matter generally depend on the details of interactions between its constituent parts. However, in a unitary Fermi gas where the scattering length diverges, thermodynamics is determined through universal functions that depend only on the particle density and temperature. By using only the general form of the equation of state and the equation of force balance, we measured the local internal energy of the trapped gas as a function of these parameters. Other universal functions, such as those corresponding to the Helmholtz free energy, chemical potential, and entropy, were calculated through general thermodynamic relations. The critical parameters were also determined at the superfluid transition temperature. These results apply to all strongly interacting fermionic systems, including neutron stars and nuclear matter.
Superfluidity is a macroscopic quantum phenomenon, which shows up below a critical temperature and leads to a peculiar behavior of matter, with frictionless flow, the formation of quantized vortices, and the quenching of the moment of inertia being intriguing examples. A remarkable explanation for many phenomena exhibited by a superfluid at finite temperature can be given in terms of a two-fluid mixture comprised of a normal component that behaves like a usual fluid and a superfluid component with zero viscosity and zero entropy. Important examples of superfluid systems are liquid helium and neutron stars. More recently, ultracold atomic gases have emerged as new superfluid systems with unprecedented possibilities to control interactions and external confinement. Here we report the first observation of `second sound' in an ultracold Fermi gas with resonant interactions. Second sound is a striking manifestation of the two-component nature of a superfluid and corresponds to an entropy wave, where the superfluid and the non-superfluid components oscillate in opposite phase, different from ordinary sound (`first sound'), where they oscillate in phase. The speed of second sound depends explicitly on the value of the superfluid fraction, a quantity sensitive to the spectrum of elementary excitations. Our measurements allow us to extract the temperature dependence of the superfluid fraction, which in strongly interacting quantum gases has been an inaccessible quantity so far.
First and second sound modes in a uniform fermionic atom gas with Feshbach resonance are investigated in the frame of a two-fluid model at finite temperature. All thermodynamic quantities are calculated for a given thermodynamic potential. The analytical results for thermodynamic quantities and sound velocities in BCS and BEC limits are obtained. The numerical results show that there exists a continuous interpolation for sound velocities of the first and second sound modes at fixed T/T c between BCS and BEC limits. The existence of the second sound mode indicates the existence of superfluidity.
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.