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

International Journal of Modern Physics B

QUANTUM MONTE CARLO STUDY OF THE GROUND-STATE PROPERTIES OF A FERMI GAS IN THE BCS-BEC CROSSOVER

S. Giorgini, G. E. Astrakharchik, Jordi Boronat, J. Casulleras

Published Dec 15, 2006• 0 citations
Publisher

Abstract

The ground-state properties of a two-component Fermi gas with attractive short-range interactions are calculated using the fixed-node diffusion Monte Carlo method. The interaction strength is varied over a wide range by tuning the value a of the s-wave scattering length of the two-body potential. We calculate the energy per particle, the one- and two-body density matrix as a function of the interaction strength. Results for the momentum distribution of the atoms, as obtained from the Fourier transform of the one-body density matrix, are reported as a function of the interaction strength. Off-diagonal long-range order in the system is investigated through the asymptotic behavior of the two-body density matrix. The condensate fraction of pairs is calculated in the unitary limit and on both sides of the BCS-BEC crossover.

DOI
10.1142/s0217979206036259

Related papers

Equation of State of a Fermi Gas in the BEC-BCS Crossover: A Quantum Monte Carlo Study

G. E. Astrakharchik, Jordi Boronat, J. Casulleras +1 more

We calculate the equation of state of a two-component Fermi gas with attractive short-range interspecies interactions using the fixed-node diffusion Monte Carlo method. The interaction strength is varied over a wide range by tuning the value a of the s-wave scattering length of the two-body potential. For a>0 and a smaller than the inverse Fermi wave vector our results show a molecular regime with repulsive interactions well described by the dimer-dimer scattering length a(m)=0.6a. The pair correlation functions of parallel and opposite spins are also discussed as a function of the interaction strength.

arXiv:cond-mat/0406113•Physical Review Letters•Nov 10, 2004•524 citations

Momentum Distribution and Condensate Fraction of a Fermion Gas in the BCS-BEC Crossover

G. E. Astrakharchik, Jordi Boronat, J. Casulleras +1 more

By using the diffusion Monte Carlo method we calculate the one- and two-body density matrix of an interacting Fermi gas at T = 0 in the BCS to Bose-Einstein condensate (BEC) crossover. Results for the momentum distribution of the atoms, as obtained from the Fourier transform of the one-body density matrix, are reported as a function of the interaction strength. Off-diagonal long-range order in the system is investigated through the asymptotic behavior of the two-body density matrix. The condensate fraction of pairs is calculated in the unitary limit and on both sides of the BCS-BEC crossover.

arXiv:cond-mat/0507483•Physical Review Letters•Dec 1, 2005•116 citations

Atomic Fermi gas in the unitary limit by quantum Monte Carlo methods: Effects of the interaction range

Xin Li, Jindřich Kolorenč, Luboš Mitáš

We calculate the ground-state properties of an unpolarized two-component Fermi gas with the aid of the diffusion quantum Monte Carlo (DMC) methods. Using an extrapolation to the zero effective range of the attractive two-particle interaction, we find $E/{E}_{\mathrm{free}}$ in the unitary limit to be 0.212(2), 0.407(2), 0.409(3), and 0.398(3) for 4, 14, 38, and 66 atoms, respectively. Our calculations indicate that the dependence of the total energy on the effective range of the interaction ${R}_{\mathrm{eff}}$ is sizable and the extrapolation to ${R}_{\mathrm{eff}}=0$ is therefore important for reaching the true unitary limit. To test the quality of nodal surfaces and to estimate the impact of the fixed-node approximation, we perform released-node DMC calculations for 4 and 14 atoms. Analysis of the released-node and the fixed-node results suggests that the main sources of the fixed-node errors are long-range correlations, which are difficult to sample in the released-node approaches due to the fast growth of the bosonic noise. Besides energies, we evaluate the two-body density matrix and the condensate fraction. We find that the condensate fraction for the 66-atom system converges to 0.56(1) after the extrapolation to the zero interaction range.

arXiv:1105.1748•Physical Review A•Aug 8, 2011•20 citations

Quantum Monte Carlo studies of superfluid Fermi gases

Siyuan Chang, Vijay R. Pandharipande, Joseph Carlson +1 more

We report results of quantum Monte Carlo calculations of the ground state of dilute Fermi gases with attractive short-range two-body interactions. The strength of the interaction is varied to study different pairing regimes which are characterized by the product of the $s$-wave scattering length and the Fermi wave vector, $a{k}_{F}$. We report results for the ground-state energy, the pairing gap $\ensuremath{\Delta}$, and the quasiparticle spectrum. In the weak-coupling regime, $1∕a{k}_{F}<\ensuremath{-}1$, we obtain Bardeen-Cooper-Schrieffer (BCS) superfluid and the energy gap $\ensuremath{\Delta}$ is much smaller than the Fermi gas energy ${E}_{\mathrm{FG}}$. When $a>0$, the interaction is strong enough to form bound molecules with energy ${E}_{\mathrm{mol}}$. For $1∕a{k}_{F}\ensuremath{\gtrsim}0.5$, we find that weakly interacting composite bosons are formed in the superfluid gas with $\ensuremath{\Delta}$ and gas energy per particle approaching $\ensuremath{\mid}{E}_{\mathrm{mol}}\ensuremath{\mid}∕2$. In this region, we seem to have Bose-Einstein condensation (BEC) of molecules. The behavior of the energy and the gap in the BCS-to-BEC transition region, $\ensuremath{-}0.5<1∕a{k}_{F}<0.5$, is discussed.

arXiv:physics/0404115•Physical Review A•Oct 5, 2004•221 citations

Diffusion Monte Carlo study of strongly interacting two-dimensional Fermi gases

Alexander Galea, Hillary Dawkins, Stefano Gandolfi +1 more

Ultracold atomic Fermi gases have been a popular topic of research, with attention being paid recently to two-dimensional (2D) gases. In this work, we perform $T=0$ ab initio diffusion Monte Carlo calculations for a strongly interacting two-component Fermi gas confined to two dimensions. We first go over finite-size systems and the connection to the thermodynamic limit. After that, we illustrate pertinent 2D scattering physics and properties of the wave function. We then show energy results for the strong-coupling crossover, in between the Bose-Einstein condensation (BEC) and Bardeen-Cooper-Schrieffer (BCS) regimes. Our energy results for the BEC-BCS crossover are parametrized to produce an equation of state, which is used to determine Tan's contact. We carry out a detailed comparison with other microscopic results. Finally, we calculate the pairing gap for a range of interaction strengths in the strong coupling regime, following from variationally optimized many-body wave functions.

arXiv:1511.05123•Physical Review A•Feb 1, 2016•41 citations

Zero-range Fermi gas along the BCS-BEC crossover

Renato Pessoa, S. A. Vitiello, Kevin E. Schmidt

Properties of the ground state of an unpolarized ultracold Fermi gas along the BCS-BEC crossover are investigated by the variational and diffusion Monte Carlo methods. We apply the Wigner-Bethe-Peierls boundary condition in our calculations to avoid any bias from using an interatomic potential with finite effective range. Properties for several values of the scattering length are studied in the range $\ensuremath{-}8\ensuremath{\le}1/a{k}_{F}\ensuremath{\le}4$, including the unitary limit. The contact parameters as a function of scattering length are obtained by fitting the pair distribution functions for particles with different spins. The energies and contact parameters are in very good agreement with experimental data reported in the literature.

Physical Review A•Nov 4, 2019•6 citations
The ground-state properties of a two-component Fermi gas with attractive short-range interactions are calculated using the fixed-node diffusion Monte Carlo method. The interaction strength is varied over a wide range by tuning the value a of the s-wave scattering length of the two-body potential. We calculate the energy per particle, the one- and two-body density matrix as a function of the interaction strength. Results for the momentum distribution of the atoms, as obtained from the Fourier transform of the one-body density matrix, are reported as a function of the interaction strength. Off-diagonal long-range order in the system is investigated through the asymptotic behavior of the two-body density matrix. The condensate fraction of pairs is calculated in the unitary limit and on both sides of the BCS-BEC crossover.
We calculate the equation of state of a two-component Fermi gas with attractive short-range interspecies interactions using the fixed-node diffusion Monte Carlo method. The interaction strength is varied over a wide range by tuning the value a of the s-wave scattering length of the two-body potential. For a>0 and a smaller than the inverse Fermi wave vector our results show a molecular regime with repulsive interactions well described by the dimer-dimer scattering length a(m)=0.6a. The pair correlation functions of parallel and opposite spins are also discussed as a function of the interaction strength.
By using the diffusion Monte Carlo method we calculate the one- and two-body density matrix of an interacting Fermi gas at T = 0 in the BCS to Bose-Einstein condensate (BEC) crossover. Results for the momentum distribution of the atoms, as obtained from the Fourier transform of the one-body density matrix, are reported as a function of the interaction strength. Off-diagonal long-range order in the system is investigated through the asymptotic behavior of the two-body density matrix. The condensate fraction of pairs is calculated in the unitary limit and on both sides of the BCS-BEC crossover.
We calculate the ground-state properties of an unpolarized two-component Fermi gas with the aid of the diffusion quantum Monte Carlo (DMC) methods. Using an extrapolation to the zero effective range of the attractive two-particle interaction, we find E/EfreeE/{E}_{\mathrm{free}}E/Efree​ in the unitary limit to be 0.212(2), 0.407(2), 0.409(3), and 0.398(3) for 4, 14, 38, and 66 atoms, respectively. Our calculations indicate that the dependence of the total energy on the effective range of the interaction Reff{R}_{\mathrm{eff}}Reff​ is sizable and the extrapolation to Reff=0{R}_{\mathrm{eff}}=0Reff​=0 is therefore important for reaching the true unitary limit. To test the quality of nodal surfaces and to estimate the impact of the fixed-node approximation, we perform released-node DMC calculations for 4 and 14 atoms. Analysis of the released-node and the fixed-node results suggests that the main sources of the fixed-node errors are long-range correlations, which are difficult to sample in the released-node approaches due to the fast growth of the bosonic noise. Besides energies, we evaluate the two-body density matrix and the condensate fraction. We find that the condensate fraction for the 66-atom system converges to 0.56(1) after the extrapolation to the zero interaction range.
We report results of quantum Monte Carlo calculations of the ground state of dilute Fermi gases with attractive short-range two-body interactions. The strength of the interaction is varied to study different pairing regimes which are characterized by the product of the sss-wave scattering length and the Fermi wave vector, akFa{k}_{F}akF​. We report results for the ground-state energy, the pairing gap $\ensuremath{\Delta}$, and the quasiparticle spectrum. In the weak-coupling regime, $1∕a{k}_{F}<\ensuremath{-}1$, we obtain Bardeen-Cooper-Schrieffer (BCS) superfluid and the energy gap $\ensuremath{\Delta}$ is much smaller than the Fermi gas energy EFG{E}_{\mathrm{FG}}EFG​. When a>0a>0a>0, the interaction is strong enough to form bound molecules with energy Emol{E}_{\mathrm{mol}}Emol​. For $1∕a{k}_{F}\ensuremath{\gtrsim}0.5$, we find that weakly interacting composite bosons are formed in the superfluid gas with $\ensuremath{\Delta}$ and gas energy per particle approaching $\ensuremath{\mid}{E}_{\mathrm{mol}}\ensuremath{\mid}∕2$. In this region, we seem to have Bose-Einstein condensation (BEC) of molecules. The behavior of the energy and the gap in the BCS-to-BEC transition region, $\ensuremath{-}0.5<1∕a{k}_{F}<0.5$, is discussed.
Ultracold atomic Fermi gases have been a popular topic of research, with attention being paid recently to two-dimensional (2D) gases. In this work, we perform T=0T=0T=0 ab initio diffusion Monte Carlo calculations for a strongly interacting two-component Fermi gas confined to two dimensions. We first go over finite-size systems and the connection to the thermodynamic limit. After that, we illustrate pertinent 2D scattering physics and properties of the wave function. We then show energy results for the strong-coupling crossover, in between the Bose-Einstein condensation (BEC) and Bardeen-Cooper-Schrieffer (BCS) regimes. Our energy results for the BEC-BCS crossover are parametrized to produce an equation of state, which is used to determine Tan's contact. We carry out a detailed comparison with other microscopic results. Finally, we calculate the pairing gap for a range of interaction strengths in the strong coupling regime, following from variationally optimized many-body wave functions.
Properties of the ground state of an unpolarized ultracold Fermi gas along the BCS-BEC crossover are investigated by the variational and diffusion Monte Carlo methods. We apply the Wigner-Bethe-Peierls boundary condition in our calculations to avoid any bias from using an interatomic potential with finite effective range. Properties for several values of the scattering length are studied in the range $\ensuremath{-}8\ensuremath{\le}1/a{k}_{F}\ensuremath{\le}4$, including the unitary limit. The contact parameters as a function of scattering length are obtained by fitting the pair distribution functions for particles with different spins. The energies and contact parameters are in very good agreement with experimental data reported in the literature.