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:1704.01032 · Physical Review A

Strong-coupling corrections to ground-state properties of a superfluid Fermi gas

Hiroyuki Tajima, Pieter van Wyk, Ryo Hanai, Daichi Kagamihara, Daisuke Inotani, Munekazu Horikoshi, Yoji Ohashi

Published Apr 19, 2017• 35 citations
arXivHTMLPDF

Abstract

We theoretically present an economical and convenient way to study ground-state properties of a strongly interacting superfluid Fermi gas. Our strategy is that complicated strong-coupling calculations are used only to evaluate quantum fluctuation corrections to the chemical potential $\ensuremath{\mu}$. Then, without any further strong-coupling calculations, we calculate the compressibility, sound velocity, internal energy, pressure, and Tan's contact, from the calculated $\ensuremath{\mu}$ without loss of accuracy, by using exact thermodynamic identities. Using a recent precise measurement of $\ensuremath{\mu}$ in a superfluid $^{6}\mathrm{Li}$ Fermi gas, we show that an extended $T$-matrix approximation (ETMA) is suitable for our purpose, especially in the BCS-unitary regime, where our results indicate that many-body corrections are dominated by superfluid fluctuations. Since precise determinations of physical quantities are not always easy in cold Fermi gas physics, our approach would greatly reduce experimental and theoretical efforts toward the understanding of ground-state properties of this strongly interacting Fermi system.

DOI
10.1103/physreva.95.043625

Related papers

Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas

Mark Ku, Ariel Sommer, Lawrence W. Cheuk +1 more

Fermi gases, collections of fermions such as neutrons and electrons, are found throughout nature, from solids to neutron stars. Interacting Fermi gases can form a superfluid or, for charged fermions, a superconductor. We have observed the superfluid phase transition in a strongly interacting Fermi gas by high-precision measurements of the local compressibility, density, and pressure. Our data completely determine the universal thermodynamics of these gases without any fit or external thermometer. The onset of superfluidity is observed in the compressibility, the chemical potential, the entropy, and the heat capacity, which displays a characteristic lambda-like feature at the critical temperature T(c)/T(F) = 0.167(13). The ground-state energy is 3/5ξN E(F) with ξ = 0.376(4). Our measurements provide a benchmark for many-body theories of strongly interacting fermions.

arXiv:1110.3309•Science•Jan 13, 2012•711 citations

Strong-coupling corrections to spin susceptibility in the BCS-BEC-crossover regime of a superfluid Fermi gas

Hiroyuki Tajima, Ryo Hanai, Yoji Ohashi

We theoretically investigate the uniform spin susceptibility $\ensuremath{\chi}$ in the superfluid phase of an ultracold Fermi gas in the region of the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC) crossover. In our previous paper [H. Tajima et al., Phys. Rev. A 89, 033617 (2014)], including pairing fluctuations within an extended $T$-matrix approximation (ETMA), we showed that strong pairing fluctuations cause the so-called spin-gap phenomenon, where $\ensuremath{\chi}$ is anomalously suppressed even in the normal state near the superfluid phase transition temperature ${T}_{\mathrm{c}}$. In this paper, we extend this work to the superfluid phase below ${T}_{\mathrm{c}}$, to clarify how this many-body phenomenon is affected by the superfluid order. From the comparison of the ETMA $\ensuremath{\chi}$ with the Yosida function describing the spin susceptibility in a weak-coupling BCS superfluid, we identify the region where pairing fluctuations crucially affect this magnetic quantity below ${T}_{\mathrm{c}}$ in the phase diagram with respect to the strength of a pairing interaction and the temperature. This spin-gap regime is found to be consistent with the previous pseudogap regime determined from the pseudogapped density of states. We also compare our results with a recent experiment on a $^{6}\mathrm{Li}$ Fermi gas. Since the spin susceptibility is sensitive to the formation of spin-singlet preformed pairs, our results would be useful for the study of pseudogap physics in an ultracold Fermi gas on the viewpoint of the spin degrees of freedom.

arXiv:1510.04401•Physical Review A•Jan 12, 2016•20 citations

Beyond Gaussian pair fluctuation theory for strongly interacting Fermi gases II: the broken-symmetry phase

Brendan C. Mulkerin, Xing-Can Yao, Yoji Ohashi +2 more

We theoretically study the thermodynamic properties of a strongly interacting Fermi gas at the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC), by applying a recently outlined strong-coupling theory that includes pair fluctuations beyond the commonly-used many-body $$T$$ -matrix or ladder approximation at the Gaussian level. The beyond Gaussian pair fluctuation (GPF) theory always respects the exact thermodynamic relations and recovers the Bogoliubov theory of molecules in the BEC limit with a nearly correct molecule-molecule scattering length. We show that the beyond-GPF theory predicts quantitatively accurate ground-state properties at the BEC-BCS crossover, in good agreement with the recent measurement by Horikoshi et al. in Phys. Rev. X 7, 041004 (2017). In the unitary limit with infinitely large $$s$$ -wave scattering length, the beyond-GPF theory predicts a reliable universal energy equation of state up to 0.6 $$T_c$$ , where $$T_c$$ is the superfluid transition temperature at unitarity. The theory predicts a Bertsch parameter $$\xi \simeq 0.365$$ at zero temperature, in good agreement with the latest quantum Monte Carlo result $$\xi = 0.367(7)$$ and the latest experimental measurement $$\xi = 0.367(9)$$ . We attribute the excellent and wide applicability of the beyond-GPF theory in the broken-symmetry phase at sufficiently low temperatures to the empirically useful partial re-summation of Feynman diagrams following a dimensional $$\epsilon$$ -expansion analysis near four dimensions ( $$d=4-\epsilon$$ ), which gives rise to accurate predictions at the second order $$\mathcal{O}(\epsilon^2)$$ . Our work indicates the possibility of further improving the strong-coupling theory of strongly interacting fermions based on the systematic inclusion of large-loop Feynman diagrams at higher orders $$\mathcal{O}(\epsilon^n)$$ with $$n\ge 3$$ .

arXiv:2201.04798•AAPPS bulletin•Aug 25, 2026•2 citations

Isothermal compressibility and effects of multibody molecular interactions in a strongly interacting ultracold Fermi gas

Daichi Kagamihara, Ryohei Sato, Koki Manabe +2 more

We theoretically investigate the isothermal compressibility ${\ensuremath{\kappa}}_{T}$ in the normal state of an ultracold Fermi gas. Including pairing fluctuations, as well as preformed-pair formations, within the framework of the self-consistent $T$-matrix approximation, we evaluate the temperature dependence of this thermodynamic quantity over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. While ${\ensuremath{\kappa}}_{T}$ in the weak-coupling BCS regime is dominated by Fermi atoms near the Fermi surface, correlations between tightly bound Cooper-pair molecules are found to play crucial roles in the strong-coupling BEC regime. In the latter region, besides a two-body molecular interaction, a three-body one is shown to sizably affect ${\ensuremath{\kappa}}_{T}$ near the superfluid phase-transition temperature. Our results indicate that the strong-coupling BEC regime of an ultracold Fermi gas would provide a unique opportunity to study multibody correlations between Cooper-pair molecules.

arXiv:2206.02406•Physical Review A•Sep 7, 2022•3 citations

Spin susceptibility and fluctuation corrections in the BCS-BEC crossover regime of an ultracold Fermi gas

Takashi Kashimura, Ryota Watanabe, Yoji Ohashi

We investigate magnetic properties and effects of pairing fluctuations in the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation (BCS-BEC) crossover regime of an ultracold Fermi gas. Recently, Liu and Hu [Europhys. Lett. 75, 364 (2006)], and Parish et al. [Nat. Phys. 3, 124 (2007)], pointed out that the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink (NSR), which has been extensively used to successfully clarify various physical properties of cold Fermi gases, unphysically gives negative spin susceptibility in the BCS-BEC crossover region. The same problem also exists in the ordinary non-self-consistent $T$-matrix approximation. In this paper, we clarify that this serious problem comes from incomplete treatment in term of pseudogap phenomena originating from strong pairing fluctuations, as well as effects of spin fluctuations on the spin susceptibility. Including these two key issues, we construct an extended $T$-matrix theory which can overcome this problem. The resulting positive spin susceptibility agrees well with the recent experiment on a ${}^{6}$Li Fermi gas done by Sanner et al. [Phys. Rev. Lett. 106, 010402 (2011)]. We also apply our theory to a polarized Fermi gas to examine the superfluid phase transition temperature ${T}_{\mathrm{c}}$, as a function of the polarization rate. Since the spin susceptibility is an important physical quantity, especially in singlet Fermi superfluids, our results would be useful in considering how singlet pairs appear above and below ${T}_{\mathrm{c}}$ in the BCS-BEC crossover regime of cold Fermi gases.

arXiv:1209.1976•Physical Review A•Oct 22, 2012•52 citations

Strongly interacting Fermi gases

Waseem Bakr, Lawrence W. Cheuk, Mark Ku +6 more

Strongly interacting gases of ultracold fermions have become an amazingly rich test-bed for many-body theories of fermionic matter. Here we present our recent experiments on these systems. Firstly, we discuss high-precision measurements on the thermodynamics of a strongly interacting Fermi gas across the superfluid transition. The onset of superfluidity is directly observed in the compressibility, the chemical potential, the entropy, and the heat capacity. Our measurements provide benchmarks for current many-body theories on strongly interacting fermions. Secondly, we have studied the evolution of fermion pairing from three to two dimensions in these gases, relating to the physics of layered superconductors. In the presence of p-wave interactions, Fermi gases are predicted to display toplogical superfluidity carrying Majorana edge states. Two possible avenues in this direction are discussed, our creation and direct observation of spin-orbit coupling in Fermi gases and the creation of fermionic molecules of 23Na 40K that will feature strong dipolar interactions in their absolute ground state.

EPJ Web of Conferences•Jan 1, 2013•3 citations
We theoretically present an economical and convenient way to study ground-state properties of a strongly interacting superfluid Fermi gas. Our strategy is that complicated strong-coupling calculations are used only to evaluate quantum fluctuation corrections to the chemical potential \ensuremathμ\ensuremath{\mu}\ensuremathμ. Then, without any further strong-coupling calculations, we calculate the compressibility, sound velocity, internal energy, pressure, and Tan's contact, from the calculated \ensuremathμ\ensuremath{\mu}\ensuremathμ without loss of accuracy, by using exact thermodynamic identities. Using a recent precise measurement of \ensuremathμ\ensuremath{\mu}\ensuremathμ in a superfluid 6Li^{6}\mathrm{Li}6Li Fermi gas, we show that an extended TTT-matrix approximation (ETMA) is suitable for our purpose, especially in the BCS-unitary regime, where our results indicate that many-body corrections are dominated by superfluid fluctuations. Since precise determinations of physical quantities are not always easy in cold Fermi gas physics, our approach would greatly reduce experimental and theoretical efforts toward the understanding of ground-state properties of this strongly interacting Fermi system.
Fermi gases, collections of fermions such as neutrons and electrons, are found throughout nature, from solids to neutron stars. Interacting Fermi gases can form a superfluid or, for charged fermions, a superconductor. We have observed the superfluid phase transition in a strongly interacting Fermi gas by high-precision measurements of the local compressibility, density, and pressure. Our data completely determine the universal thermodynamics of these gases without any fit or external thermometer. The onset of superfluidity is observed in the compressibility, the chemical potential, the entropy, and the heat capacity, which displays a characteristic lambda-like feature at the critical temperature T(c)/T(F) = 0.167(13). The ground-state energy is 3/5ξN E(F) with ξ = 0.376(4). Our measurements provide a benchmark for many-body theories of strongly interacting fermions.
We theoretically investigate the uniform spin susceptibility $\ensuremath{\chi}$ in the superfluid phase of an ultracold Fermi gas in the region of the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC) crossover. In our previous paper [H. Tajima et al., Phys. Rev. A 89, 033617 (2014)], including pairing fluctuations within an extended TTT-matrix approximation (ETMA), we showed that strong pairing fluctuations cause the so-called spin-gap phenomenon, where $\ensuremath{\chi}$ is anomalously suppressed even in the normal state near the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​. In this paper, we extend this work to the superfluid phase below Tc{T}_{\mathrm{c}}Tc​, to clarify how this many-body phenomenon is affected by the superfluid order. From the comparison of the ETMA $\ensuremath{\chi}$ with the Yosida function describing the spin susceptibility in a weak-coupling BCS superfluid, we identify the region where pairing fluctuations crucially affect this magnetic quantity below Tc{T}_{\mathrm{c}}Tc​ in the phase diagram with respect to the strength of a pairing interaction and the temperature. This spin-gap regime is found to be consistent with the previous pseudogap regime determined from the pseudogapped density of states. We also compare our results with a recent experiment on a 6Li^{6}\mathrm{Li}6Li Fermi gas. Since the spin susceptibility is sensitive to the formation of spin-singlet preformed pairs, our results would be useful for the study of pseudogap physics in an ultracold Fermi gas on the viewpoint of the spin degrees of freedom.
We theoretically study the thermodynamic properties of a strongly interacting Fermi gas at the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC), by applying a recently outlined strong-coupling theory that includes pair fluctuations beyond the commonly-used many-body TTT -matrix or ladder approximation at the Gaussian level. The beyond Gaussian pair fluctuation (GPF) theory always respects the exact thermodynamic relations and recovers the Bogoliubov theory of molecules in the BEC limit with a nearly correct molecule-molecule scattering length. We show that the beyond-GPF theory predicts quantitatively accurate ground-state properties at the BEC-BCS crossover, in good agreement with the recent measurement by Horikoshi et al. in Phys. Rev. X 7, 041004 (2017). In the unitary limit with infinitely large sss -wave scattering length, the beyond-GPF theory predicts a reliable universal energy equation of state up to 0.6 TcT_cTc​ , where TcT_cTc​ is the superfluid transition temperature at unitarity. The theory predicts a Bertsch parameter ξ≃0.365\xi \simeq 0.365ξ≃0.365 at zero temperature, in good agreement with the latest quantum Monte Carlo result ξ=0.367(7)\xi = 0.367(7)ξ=0.367(7) and the latest experimental measurement ξ=0.367(9)\xi = 0.367(9)ξ=0.367(9) . We attribute the excellent and wide applicability of the beyond-GPF theory in the broken-symmetry phase at sufficiently low temperatures to the empirically useful partial re-summation of Feynman diagrams following a dimensional ϵ\epsilonϵ -expansion analysis near four dimensions ( d=4−ϵd=4-\epsilond=4−ϵ ), which gives rise to accurate predictions at the second order O(ϵ2)\mathcal{O}(\epsilon^2)O(ϵ2) . Our work indicates the possibility of further improving the strong-coupling theory of strongly interacting fermions based on the systematic inclusion of large-loop Feynman diagrams at higher orders O(ϵn)\mathcal{O}(\epsilon^n)O(ϵn) with n≥3n\ge 3n≥3 .
We theoretically investigate the isothermal compressibility ${\ensuremath{\kappa}}_{T}$ in the normal state of an ultracold Fermi gas. Including pairing fluctuations, as well as preformed-pair formations, within the framework of the self-consistent TTT-matrix approximation, we evaluate the temperature dependence of this thermodynamic quantity over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. While ${\ensuremath{\kappa}}_{T}$ in the weak-coupling BCS regime is dominated by Fermi atoms near the Fermi surface, correlations between tightly bound Cooper-pair molecules are found to play crucial roles in the strong-coupling BEC regime. In the latter region, besides a two-body molecular interaction, a three-body one is shown to sizably affect ${\ensuremath{\kappa}}_{T}$ near the superfluid phase-transition temperature. Our results indicate that the strong-coupling BEC regime of an ultracold Fermi gas would provide a unique opportunity to study multibody correlations between Cooper-pair molecules.
We investigate magnetic properties and effects of pairing fluctuations in the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation (BCS-BEC) crossover regime of an ultracold Fermi gas. Recently, Liu and Hu [Europhys. Lett. 75, 364 (2006)], and Parish et al. [Nat. Phys. 3, 124 (2007)], pointed out that the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink (NSR), which has been extensively used to successfully clarify various physical properties of cold Fermi gases, unphysically gives negative spin susceptibility in the BCS-BEC crossover region. The same problem also exists in the ordinary non-self-consistent TTT-matrix approximation. In this paper, we clarify that this serious problem comes from incomplete treatment in term of pseudogap phenomena originating from strong pairing fluctuations, as well as effects of spin fluctuations on the spin susceptibility. Including these two key issues, we construct an extended TTT-matrix theory which can overcome this problem. The resulting positive spin susceptibility agrees well with the recent experiment on a 6{}^{6}6Li Fermi gas done by Sanner et al. [Phys. Rev. Lett. 106, 010402 (2011)]. We also apply our theory to a polarized Fermi gas to examine the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​, as a function of the polarization rate. Since the spin susceptibility is an important physical quantity, especially in singlet Fermi superfluids, our results would be useful in considering how singlet pairs appear above and below Tc{T}_{\mathrm{c}}Tc​ in the BCS-BEC crossover regime of cold Fermi gases.
Strongly interacting gases of ultracold fermions have become an amazingly rich test-bed for many-body theories of fermionic matter. Here we present our recent experiments on these systems. Firstly, we discuss high-precision measurements on the thermodynamics of a strongly interacting Fermi gas across the superfluid transition. The onset of superfluidity is directly observed in the compressibility, the chemical potential, the entropy, and the heat capacity. Our measurements provide benchmarks for current many-body theories on strongly interacting fermions. Secondly, we have studied the evolution of fermion pairing from three to two dimensions in these gases, relating to the physics of layered superconductors. In the presence of p-wave interactions, Fermi gases are predicted to display toplogical superfluidity carrying Majorana edge states. Two possible avenues in this direction are discussed, our creation and direct observation of spin-orbit coupling in Fermi gases and the creation of fermionic molecules of 23Na 40K that will feature strong dipolar interactions in their absolute ground state.