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:1205.0234 · Physical Review A

Quantum Bose and Fermi gases with large negative scattering length in the two-body S -matrix approximation

André LeClair, Edgar Marcelino de Carvalho Neto, André Nicolai, I. Roditi

Published Aug 2, 2012• 4 citations
arXivHTMLPDF

Abstract

We study both Bose and Fermi gases at finite temperature and density in an approximation that sums an infinite number of many-body processes that are reducible to two-body scatterings. This is done for arbitrary negative scattering length, which interpolates between the ideal and unitary gas limits. In the unitary limit, we compute the first four virial coefficients within our approximation. The second virial coefficient is exact, and we extend the previously known result for fermions to bosons and also for both bosons and fermions for the upper branch on the other side of unitarity (infinitely large positive scattering length). Assuming bosons can exist in a metastable state before undergoing mechanical collapse, we map out the critical temperatures for strongly coupled Bose-Einstein condensation as a function of scattering length.

DOI
10.1103/physreva.86.023603

Related papers

Virial coefficients for trapped Bose and Fermi gases beyond the unitary limit: An S -matrix approach

Edgar Marcelino de Carvalho Neto, André Nicolai, I. Roditi +1 more

We study the virial expansion for three-dimensional Bose and Fermi gases at finite temperature using an approximation that only considers two-body processes and is valid for high temperatures and low densities. The first virial coefficients are computed and the second is exact. The results are obtained for the full range of values of the scattering length, and the unitary limit is recovered as a particular case. A weak coupling expansion is performed and the free case is also obtained as a proper limit. The influence of an anisotropic harmonic trap is considered using the local density approximation (LDA), analytical results are obtained, and the special case of the isotropic trap is discussed in detail.

arXiv:1407.3770•Physical Review A•Nov 17, 2014•6 citations

S-matrix approach to quantum gases in the unitary limit: II. The three-dimensional case

Pye Ton How, André LeClair

A new analytic treatment of three-dimensional homogeneous Bose and Fermi gases in the unitary limit of negative infinite scattering length is presented, based on the S -matrix approach to statistical mechanics we recently developed. The unitary limit occurs at a fixed point of the renormalization group with dynamical exponent z = 2 where the S -matrix equals − 1. For fermions we find T c / T F ≈0.1. For bosons we present evidence that the gas does not collapse, but rather has a critical point that is a strongly interacting form of Bose–Einstein condensation. This bosonic critical point occurs at n λ T 3 ≈1.3, where n is the density and λ T the thermal wavelength, which is lower than the ideal gas value of ζ(3/2) = 2.61.

arXiv:1004.5390•Journal of Statistical Mechanics Theory and Experiment•Jul 1, 2010•9 citations

Metastability of Bose and Fermi gases on the upper branch

André LeClair, I. Roditi, Joshua William Squires

We study three-dimensional Bose and Fermi gases in the upper branch, a phase defined by the absence of bound states in the repulsive interaction regime, within an approximation that considers only two-body interactions. Employing a formalism based on the $S$ matrix, we derive useful analytic expressions that hold on the upper branch in the weak coupling limit. We determine upper branch phase diagrams for both bosons and fermions with techniques valid for arbitrary positive scattering length.

arXiv:1604.04929•Physical Review A•Dec 8, 2016•0 citations

High-temperature limit of the resonant Fermi gas

Vudtiwat Ngampruetikorn, Meera M. Parish, Jesper Levinsen

We use the virial expansion to investigate the behavior of the two-component, attractive Fermi gas in the high-temperature limit, where the system smoothly evolves from weakly attractive fermions to weakly repulsive bosonic dimers as the short-range attraction is increased. We present a formalism for computing the virial coefficients that employs a diagrammatic approach to the grand potential and allows one to easily include an effective range ${R}^{*}$ in the interaction. In the limit where the thermal wavelength $\ensuremath{\lambda}\ensuremath{\ll}{R}^{*}$, the calculation of the virial coefficients is perturbative even at unitarity and the system resembles a weakly interacting Bose-Fermi mixture for all scattering lengths $a$. By interpolating from the perturbative limits $\ensuremath{\lambda}/|a|\ensuremath{\gg}1$ and ${R}^{*}/\ensuremath{\lambda}\ensuremath{\gg}1$, we estimate the value of the fourth virial coefficient at unitarity for ${R}^{*}=0$ and we find that it is close to the value obtained in recent experiments. We also derive the equations of state for the pressure, density, and entropy, as well as the spectral function at high temperatures.

arXiv:1410.7797•Physical Review A•Jan 8, 2015•30 citations

Achieving a BCS Transition in an Atomic Fermi Gas

Lincoln D. Carr, Gora V. Shlyapnikov, Yvan Castin

We consider a gas of cold fermionic atoms having two spin components with interactions characterized by their s-wave scattering length a. At positive scattering length the atoms form weakly bound bosonic molecules which can be evaporatively cooled to undergo Bose-Einstein condensation, whereas at negative scattering length BCS pairing can take place. It is shown that, by adiabatically tuning the scattering length a from positive to negative values, one may transform the molecular Bose-Einstein condensate into a highly degenerate atomic Fermi gas, with the ratio of temperature to Fermi temperature T/T(F) approximately 10(-2). The corresponding critical final value of k(F)/a/, which leads to the BCS transition, is found to be about one-half, where k(F) is the Fermi momentum.

arXiv:cond-mat/0308306•Physical Review Letters•Apr 15, 2004•112 citations

Bose Gases near Unitarity

Weiran Li, Tin-Lun Ho

We study the properties of strongly interacting Bose gases at the density and temperature regime when the three-body recombination rate is substantially reduced. In this regime, one can have a Bose gas with all particles in scattering states (i.e., the "upper branch") with little loss even at unitarity over the duration of the experiment. We show that because of bosonic enhancement, pair formation is shifted to the atomic side of the original resonance (where scattering length a(s)<0), opposite to the fermionic case. In a trap, a repulsive Bose gas remains mechanically stable when brought across resonance to the atomic side until it reaches a critical scattering length a(s)*<0. For a(s)<a(s)*, the density consists of a core of upper branch bosons surrounded by an outer layer of equilibrium branch. The conditions of low three-body recombination require that the particle number N<1.024(T/ω)(5/2) in a harmonic trap with frequency ω.

arXiv:1201.1958•Physical Review Letters•May 7, 2012•50 citations
We study both Bose and Fermi gases at finite temperature and density in an approximation that sums an infinite number of many-body processes that are reducible to two-body scatterings. This is done for arbitrary negative scattering length, which interpolates between the ideal and unitary gas limits. In the unitary limit, we compute the first four virial coefficients within our approximation. The second virial coefficient is exact, and we extend the previously known result for fermions to bosons and also for both bosons and fermions for the upper branch on the other side of unitarity (infinitely large positive scattering length). Assuming bosons can exist in a metastable state before undergoing mechanical collapse, we map out the critical temperatures for strongly coupled Bose-Einstein condensation as a function of scattering length.
We study the virial expansion for three-dimensional Bose and Fermi gases at finite temperature using an approximation that only considers two-body processes and is valid for high temperatures and low densities. The first virial coefficients are computed and the second is exact. The results are obtained for the full range of values of the scattering length, and the unitary limit is recovered as a particular case. A weak coupling expansion is performed and the free case is also obtained as a proper limit. The influence of an anisotropic harmonic trap is considered using the local density approximation (LDA), analytical results are obtained, and the special case of the isotropic trap is discussed in detail.
A new analytic treatment of three-dimensional homogeneous Bose and Fermi gases in the unitary limit of negative infinite scattering length is presented, based on the S -matrix approach to statistical mechanics we recently developed. The unitary limit occurs at a fixed point of the renormalization group with dynamical exponent z = 2 where the S -matrix equals − 1. For fermions we find T c / T F ≈0.1. For bosons we present evidence that the gas does not collapse, but rather has a critical point that is a strongly interacting form of Bose–Einstein condensation. This bosonic critical point occurs at n λ T 3 ≈1.3, where n is the density and λ T the thermal wavelength, which is lower than the ideal gas value of ζ(3/2) = 2.61.
We study three-dimensional Bose and Fermi gases in the upper branch, a phase defined by the absence of bound states in the repulsive interaction regime, within an approximation that considers only two-body interactions. Employing a formalism based on the SSS matrix, we derive useful analytic expressions that hold on the upper branch in the weak coupling limit. We determine upper branch phase diagrams for both bosons and fermions with techniques valid for arbitrary positive scattering length.
We use the virial expansion to investigate the behavior of the two-component, attractive Fermi gas in the high-temperature limit, where the system smoothly evolves from weakly attractive fermions to weakly repulsive bosonic dimers as the short-range attraction is increased. We present a formalism for computing the virial coefficients that employs a diagrammatic approach to the grand potential and allows one to easily include an effective range R∗{R}^{*}R∗ in the interaction. In the limit where the thermal wavelength $\ensuremath{\lambda}\ensuremath{\ll}{R}^{*}$, the calculation of the virial coefficients is perturbative even at unitarity and the system resembles a weakly interacting Bose-Fermi mixture for all scattering lengths aaa. By interpolating from the perturbative limits $\ensuremath{\lambda}/|a|\ensuremath{\gg}1$ and ${R}^{*}/\ensuremath{\lambda}\ensuremath{\gg}1$, we estimate the value of the fourth virial coefficient at unitarity for R∗=0{R}^{*}=0R∗=0 and we find that it is close to the value obtained in recent experiments. We also derive the equations of state for the pressure, density, and entropy, as well as the spectral function at high temperatures.
We consider a gas of cold fermionic atoms having two spin components with interactions characterized by their s-wave scattering length a. At positive scattering length the atoms form weakly bound bosonic molecules which can be evaporatively cooled to undergo Bose-Einstein condensation, whereas at negative scattering length BCS pairing can take place. It is shown that, by adiabatically tuning the scattering length a from positive to negative values, one may transform the molecular Bose-Einstein condensate into a highly degenerate atomic Fermi gas, with the ratio of temperature to Fermi temperature T/T(F) approximately 10(-2). The corresponding critical final value of k(F)/a/, which leads to the BCS transition, is found to be about one-half, where k(F) is the Fermi momentum.
We study the properties of strongly interacting Bose gases at the density and temperature regime when the three-body recombination rate is substantially reduced. In this regime, one can have a Bose gas with all particles in scattering states (i.e., the "upper branch") with little loss even at unitarity over the duration of the experiment. We show that because of bosonic enhancement, pair formation is shifted to the atomic side of the original resonance (where scattering length a(s)<0), opposite to the fermionic case. In a trap, a repulsive Bose gas remains mechanically stable when brought across resonance to the atomic side until it reaches a critical scattering length a(s)*<0. For a(s)<a(s)*, the density consists of a core of upper branch bosons surrounded by an outer layer of equilibrium branch. The conditions of low three-body recombination require that the particle number N<1.024(T/ω)(5/2) in a harmonic trap with frequency ω.