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:2602.17420 · Physical Review A

Hartree shift and pairing gap in ultracold Fermi gases in the framework of low-momentum interactions

Mi­chael Urban, S. Ramanan

Published May 7, 2026• 1 citation
arXivHTMLPDF

Abstract

In this paper we consider a two-component gas of fermions on the BCS side of the BCS-BEC crossover at zero temperature. We use a momentum dependent interaction that reproduces the s-wave scattering phase shifts of a contact interaction up to a momentum cutoff that is scaled with the Fermi momentum. Using a diagrammatic formulation of Bogoliubov many-body perturbation theory, suitably augmented by self-consistency conditions, we obtain the Hartree shift and the pairing gap to third order. In the weak-coupling regime, our results are not only well-converged but also agree with the well-established Gor'kov-Melik-Barkhudarov corrections for the gap and the Galitskii result for the Hartree shift. Near the unitary regime, our results for the Nambu-Gor'kov self-energy are less converged, but there is still reasonable agreement with experiments as well as with quantum Monte-Carlo results. Perspectives for improvements and applications of this approach to neutron matter are discussed.

DOI
10.1103/w6mp-38jz

Related papers

Low-momentum interactions for ultracold Fermi gases

Mi­chael Urban, S. Ramanan

We consider a two-component Fermi gas with a contact interaction from the BCS regime to the unitary limit. Starting from the idea that many-body effects should not depend on short-distance or high-momentum physics which is encoded in the $s$-wave scattering length, but only on momentum scales of the order of the Fermi momentum, we build effective low-momentum interactions that reproduce the scattering phase shifts of the contact interaction below some momentum cutoff. Inspired by recent successes of this method in nuclear structure theory, we use these interactions to describe the equation of state of the Fermi gas in the framework of Hartree-Fock-Bogliubov theory with perturbative corrections. In the BCS regime, there is a range of cutoffs where we obtain fully converged results. Near unitarity, convergence is not yet reached, but we obtain promising results for the ground-state energies close to the experimental ones. Limitations and possible extensions of the approach are discussed.

arXiv:2104.01901•Physical Review A•Jun 14, 2021•6 citations

Excitation Spectrum and Superfluid Gap of an Ultracold Fermi Gas

Hauke Biss, Lennart Sobirey, Niclas Luick +5 more

Ultracold atomic gases are a powerful tool to experimentally study strongly correlated quantum many-body systems. In particular, ultracold Fermi gases with tunable interactions have allowed to realize the famous BEC-BCS crossover from a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. However, large parts of the excitation spectrum of fermionic superfluids in the BEC-BCS crossover are still unexplored. In this work, we use Bragg spectroscopy to measure the full momentum-resolved low-energy excitation spectrum of strongly interacting ultracold Fermi gases. This enables us to directly observe the smooth transformation from a bosonic to a fermionic superfluid that takes place in the BEC-BCS crossover. We also use our spectra to determine the evolution of the superfluid gap and find excellent agreement with previous experiments and self-consistent T-matrix calculations both in the BEC and crossover regime. However, toward the BCS regime a calculation that includes the effects of particle-hole correlations shows better agreement with our data.

arXiv:2105.09820•Physical Review Letters•Mar 8, 2022•71 citations

Universal enhancement of the pairing gap in a dilute Fermi superfluid

Silas R. Beane, Roland C. Farrell, Cameron P. Shotwell

At zero temperature, a dilute Fermi gas with an attractive contact interaction forms a superfluid with gapped fermionic excitations. We show that the gap at weak coupling can be organized as a trans-series expansion in the interaction strength and the asymptotic Gor'kov-Melik-Barkhudarov gap. Low-energy virtual quasiparticles generate corrections that are linear in the gap with a leading coefficient nearly 25$\times$ larger than the other known coefficients. This substantially increases the gap at intermediate densities, highlighting that systematic corrections are crucial for quantitative predictions.

cond-mat.quant-gasCross-listedarXiv:2610.20434•Oct 15, 2026•0 citations

Modified Fermi sphere, pairing gap, and critical temperature for the BCS-BEC crossover

Stefan Floerchinger, Michael M. Scherer, CHRISTOF WETTERICH

We investigate the phase diagram of two-component fermions in the BCS-BEC (Bose-Einstein condensate) crossover. Using functional renormalization-group equations we calculate the effect of quantum fluctuations on the fermionic self-energy parametrized by a wave-function renormalization, an effective Fermi radius, and the gap. This allows us to follow the modifications of the Fermi surface and the dispersion relation for fermionic excitations throughout the whole crossover region. We also determine the critical temperature of the second-order phase transition to superfluidity. Our results are in agreement with BCS theory including Gorkov's correction for a small negative scattering length $a$ and with an interacting Bose gas for a small positive $a$. At the unitarity point the result for the gap at zero temperature agrees well with quantum Monte Carlo simulations, while the critical temperature differs.

arXiv:0912.4050•Physical Review A•Jun 14, 2010•38 citations

Universal corrections to the superfluid gap in a cold Fermi gas

Silas R. Beane, Zeno Capatti, Roland C. Farrell

A framework for computing the superfluid gap in an effective field theory (EFT) of fermions interacting via momentum-independent contact forces is developed. The leading universal corrections in the EFT are one-loop in-medium effects at the Fermi surface, and reproduce the well-known Gor'kov-Melik-Barkhudarov result. The complete subleading universal corrections are presented here, and include one-loop effects away from the Fermi surface, two-loop in-medium effects, as well as modifications to the fermion propagator. Together, these effects are found to reduce the gap at low densities. Applications to neutron superfluidity in neutron stars are also discussed.

arXiv:2407.20168•Physical Review A•Jan 13, 2025•1 citation

Finite-range effect in the two-dimensional density-induced BCS–BEC crossover

Hikaru Sakakibara, Hiroyuki Tajima, Haozhao Liang

Abstract We theoretically investigate the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) crossover in a two-dimensional Fermi gas with the finite-range interaction by using the Hartree–Fock–Bogoliubov theory. Expanding the scattering phase shift in terms of the scattering length and effective range, we discuss the effect of the finite-range interaction on the pairing and thermodynamic properties. By solving the gap equation and the number equation self-consistently, we numerically calculate the effective-range dependence of the pairing gap, chemical potential, and pair size throughout the BCS–BEC crossover. Our results would be useful for further understanding of low-dimensional many-body problems.

arXiv:2306.02127•Progress of Theoretical and Experimental Physics•Jul 27, 2023•1 citation
In this paper we consider a two-component gas of fermions on the BCS side of the BCS-BEC crossover at zero temperature. We use a momentum dependent interaction that reproduces the s-wave scattering phase shifts of a contact interaction up to a momentum cutoff that is scaled with the Fermi momentum. Using a diagrammatic formulation of Bogoliubov many-body perturbation theory, suitably augmented by self-consistency conditions, we obtain the Hartree shift and the pairing gap to third order. In the weak-coupling regime, our results are not only well-converged but also agree with the well-established Gor'kov-Melik-Barkhudarov corrections for the gap and the Galitskii result for the Hartree shift. Near the unitary regime, our results for the Nambu-Gor'kov self-energy are less converged, but there is still reasonable agreement with experiments as well as with quantum Monte-Carlo results. Perspectives for improvements and applications of this approach to neutron matter are discussed.
We consider a two-component Fermi gas with a contact interaction from the BCS regime to the unitary limit. Starting from the idea that many-body effects should not depend on short-distance or high-momentum physics which is encoded in the sss-wave scattering length, but only on momentum scales of the order of the Fermi momentum, we build effective low-momentum interactions that reproduce the scattering phase shifts of the contact interaction below some momentum cutoff. Inspired by recent successes of this method in nuclear structure theory, we use these interactions to describe the equation of state of the Fermi gas in the framework of Hartree-Fock-Bogliubov theory with perturbative corrections. In the BCS regime, there is a range of cutoffs where we obtain fully converged results. Near unitarity, convergence is not yet reached, but we obtain promising results for the ground-state energies close to the experimental ones. Limitations and possible extensions of the approach are discussed.
Ultracold atomic gases are a powerful tool to experimentally study strongly correlated quantum many-body systems. In particular, ultracold Fermi gases with tunable interactions have allowed to realize the famous BEC-BCS crossover from a Bose-Einstein condensate (BEC) of molecules to a Bardeen-Cooper-Schrieffer (BCS) superfluid of weakly bound Cooper pairs. However, large parts of the excitation spectrum of fermionic superfluids in the BEC-BCS crossover are still unexplored. In this work, we use Bragg spectroscopy to measure the full momentum-resolved low-energy excitation spectrum of strongly interacting ultracold Fermi gases. This enables us to directly observe the smooth transformation from a bosonic to a fermionic superfluid that takes place in the BEC-BCS crossover. We also use our spectra to determine the evolution of the superfluid gap and find excellent agreement with previous experiments and self-consistent T-matrix calculations both in the BEC and crossover regime. However, toward the BCS regime a calculation that includes the effects of particle-hole correlations shows better agreement with our data.
At zero temperature, a dilute Fermi gas with an attractive contact interaction forms a superfluid with gapped fermionic excitations. We show that the gap at weak coupling can be organized as a trans-series expansion in the interaction strength and the asymptotic Gor'kov-Melik-Barkhudarov gap. Low-energy virtual quasiparticles generate corrections that are linear in the gap with a leading coefficient nearly 25×\times× larger than the other known coefficients. This substantially increases the gap at intermediate densities, highlighting that systematic corrections are crucial for quantitative predictions.
We investigate the phase diagram of two-component fermions in the BCS-BEC (Bose-Einstein condensate) crossover. Using functional renormalization-group equations we calculate the effect of quantum fluctuations on the fermionic self-energy parametrized by a wave-function renormalization, an effective Fermi radius, and the gap. This allows us to follow the modifications of the Fermi surface and the dispersion relation for fermionic excitations throughout the whole crossover region. We also determine the critical temperature of the second-order phase transition to superfluidity. Our results are in agreement with BCS theory including Gorkov's correction for a small negative scattering length aaa and with an interacting Bose gas for a small positive aaa. At the unitarity point the result for the gap at zero temperature agrees well with quantum Monte Carlo simulations, while the critical temperature differs.
A framework for computing the superfluid gap in an effective field theory (EFT) of fermions interacting via momentum-independent contact forces is developed. The leading universal corrections in the EFT are one-loop in-medium effects at the Fermi surface, and reproduce the well-known Gor'kov-Melik-Barkhudarov result. The complete subleading universal corrections are presented here, and include one-loop effects away from the Fermi surface, two-loop in-medium effects, as well as modifications to the fermion propagator. Together, these effects are found to reduce the gap at low densities. Applications to neutron superfluidity in neutron stars are also discussed.
Abstract We theoretically investigate the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein condensation (BEC) crossover in a two-dimensional Fermi gas with the finite-range interaction by using the Hartree–Fock–Bogoliubov theory. Expanding the scattering phase shift in terms of the scattering length and effective range, we discuss the effect of the finite-range interaction on the pairing and thermodynamic properties. By solving the gap equation and the number equation self-consistently, we numerically calculate the effective-range dependence of the pairing gap, chemical potential, and pair size throughout the BCS–BEC crossover. Our results would be useful for further understanding of low-dimensional many-body problems.