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:1707.00428 · Journal of the Physical Society of Japan

Normal-State Properties of a Unitary Bose–Fermi Mixture: A Combined Strong-Coupling Approach with Universal Thermodynamics

Digvijay Kharga, Hiroyuki Tajima, Pieter van Wyk, Daisuke Inotani, Yoji Ohashi

Published Jun 26, 2017• 1 citation
arXivHTMLPDF

Abstract

We theoretically investigate normal-state properties of a unitary Bose-Fermi mixture. Including strong hetero-pairing fluctuations, we evaluate the Bose and Fermi chemical potential, internal energy, pressure, entropy, as well as specific heat at constant volume $C_V$, within the framework of a combined strong-coupling theory with exact thermodynamic identities. We show that hetero-pairing fluctuations at the unitarity cause non-monotonic temperature dependence of $C_V$, being qualitatively different from the monotonic behavior of this quantity in the weak- and strong-coupling limit. On the other hand, such an anomalous behavior is not seen in the other quantities. Our results indicate that the specific heat $C_V$, which has recently become observable in cold atom physics, is a useful quantity for understanding strong-coupling aspects of this quantum system.

DOI
10.7566/jpsj.86.074302

Related papers

Strong-Coupling Properties of ap-Wave Interacting Fermi Gas on the Viewpoint of Specific Heat at Constant Volume

Daisuke Inotani, Pieter van Wyk, Yoji Ohashi

We theoretically investigate the specific heat $C_V$ at constant volume in the normal state of a $p$-wave interacting Fermi gas. Including fluctuations in the $p$-wave Cooper channel within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we clarify how $C_V$ as a function of temperature varies, as one moves from the weak-coupling regime to the strong-coupling limit. In the weak-coupling regime, $C_V$ is shown to be enhanced by $p$-wave pairing fluctuations, near the superfluid phase transition temperature $T_{\rm c}$. Similar enhancement of $C_V(T\simeq T_{\rm c})$ is also obtained in the strong-coupling regime, which, however, reflects that system is close an ideal Bose gas of $p$-wave two-body bound molecules. Using these results, we classify the normal state into (1) the normal Fermi gas regime, (2) the $p$-wave molecular Bose gas regime, and (3) the region between the two, where $p$-wave pairing fluctuations are dominant. Since the current experiments can only access the normal phase of a $p$-wave interacting Fermi gas, our results would be useful for experiments to understand strong-coupling properties of this Fermi system above $T_{\rm c}$.

arXiv:1610.08598•Journal of the Physical Society of Japan•Jan 26, 2017•3 citations

Single-Particle Excitations and Effects of Hetero-Pairing Fluctuations in a Bose–Fermi Mixture with a Feshbach Resonance

Digvijay Kharga, Daisuke Inotani, Ryo Hanai +1 more

We theoretically investigate normal-state properties of a gas mixture of single-component bosons and fermions with a hetero-nuclear Feshbach resonance. Including strong hetero-pairing fluctuations associated with the Feshbach resonance, we calculate single-particle density of states, as well as the spectral weight at various interaction strengths. For this purpose, we employ an improved T-matrix approximation (TMA), where the bare Bose Green's function in the non-selfconsistent TMA self-energy is modified so as to satisfy the Hugenholtz-Pines relation at the Bose-Einstein condensation (BEC) temperature $T_{\rm BEC}$. In the unitary regime at $T_{\rm BEC}$, we show that hetero-pairing fluctuations couple Fermi atomic excitations with Fermi molecular excitations, as well as with Bose atomic excitations. Although a similar coupling phenomenon by pairing fluctuations is known to give a pseudo-gapped density of states in the unitary regime of a two-component Fermi gas, such a dip structure is found to not appear even in the unitary limit of a Bose-Fermi mixture. It only appears in the strong-coupling regime. Instead, a spectral peak along the molecular dispersion appears in the spectral weight.We also clarify how this coupling phenomenon is seen in the Bose channel. Since a hetero-nuclear Feshbach resonance, as well as the formation of Bose-Fermi molecules, have been realized, our results would be useful for the study of strong-coupling properties of this unique quantum gas.

arXiv:1705.02591•Journal of the Physical Society of Japan•Jul 25, 2017•7 citations

Specific heat and effects of strong pairing fluctuations in a superfluid Fermi atom gas in the BCS-BEC crossover region

Pieter van Wyk, Daisuke Inotani, Yoji Ohashi

We theoretically investigate the specific heat at constant volume C V in the BCS(Bardeen-Cooper-Schrieffer)-BEC(Bose-Einstein-condensation)-crossover regime of an ultracold Fermi gas, below the superfluid phase transition temperature T c . Within the strong-coupling framework developed by Nozières and Schmitt-Rink, we show that the temperature dependence of C V drastically changes as one passes through the crossover region, and is sensitive to strong fluctuations in the Cooper channel near the unitarity limit. We also compare our results to a recent experiment on a 6 Li unitary Fermi gas. Since fluctuation effects are a crucial key in the BCS-BEC-crossover phenomenon, our results would be helpful in considering how the fermionic BCS superfluid changes into BEC with increasing the interaction strength, from the viewpoint of specific heat.

Journal of Physics Conference Series•Mar 1, 2018•0 citations

Thermodynamic stability, compressibility matrices, and effects of mediated interactions in a strongly interacting Bose-Fermi mixture

Koki Manabe, Yoji Ohashi

We theoretically investigate the thermodynamic stability of a normal-state Bose-Fermi mixture, with a tunable Bose-Fermi pairing interaction $\ensuremath{-}{U}_{\mathrm{BF}}<0$ associated with a heteronuclear Feshbach resonance, as well as a weak repulsive Bose-Bose interaction ${U}_{\mathrm{BB}}\ensuremath{\ge}0$. Including strong heteropairing fluctuations associated with the former interaction within the self-consistent $T$-matrix approximation, as well as the latter within the mean-field level, we calculate the compressibility matrix, to assess the stability of this system against density fluctuations. In the weak- and the intermediate-coupling regimes with respect to $\ensuremath{-}{U}_{\mathrm{BF}}$, we show that an effective attractive interaction between bosons mediated by density fluctuations in the Fermi component makes the system unstable below a certain temperature ${T}_{\mathrm{clp}}$ (leading to density collapse). When ${U}_{\mathrm{BB}}=0, {T}_{\mathrm{clp}}$ is always higher than the Bose-Einstein condensation (BEC) temperature ${T}_{\mathrm{c}}$. When ${U}_{\mathrm{BB}}>0$, the density collapse is suppressed, and the BEC transition becomes possible. It is also suppressed by the formation of tightly bound Bose-Fermi molecules when the heteropairing interaction $\ensuremath{-}{U}_{\mathrm{BF}}$ is strong; however, since the system may be viewed as a molecular Fermi gas in this case, the BEC transition does not also occur. Since quantum gases involving Bose atoms are known to be sensitive to interparticle correlations, our results would be useful for the study of many-body properties of a Bose-Fermi mixture in a stable manner, without facing the unwanted density collapse.

arXiv:2103.16843•Physical Review A•Jun 23, 2021•10 citations

Universal thermodynamics of a strongly interacting Fermi gas: theory versus experiment

Hui Hu, Xia-Ji Liu, P. D. Drummond

Strongly interacting, dilute Fermi gases exhibit a scale-invariant, universal thermodynamic behavior. This is notoriously difficult to understand theoretically because of the absence of a small interaction parameter. Here, we present a systematic comparison of theoretical predictions from different quantum many-body theories with recent experimental data of Nascimbne et al (2010 Nature 463 1057). Our comparisons have no adjustable parameters, either theoretically or experimentally. All the model approximations seem to fluctuate rather than converge on the experimental data. It turns out that a simple Gaussian pair fluctuation theory gives the best quantitative agreement, except at the critical superfluid transition region. In the normal state, we also calculate the equation of state by using a quantum cluster expansion theory and explore in detail its applicability to low temperatures. Using the accurate experimental result for the thermodynamic function S ( T ), we determine the temperature T of a trapped Fermi gas at unitarity as a function of a non-interacting temperature T i , which can be obtained by an adiabatic sweep to the free gas limit. By analyzing the recent experimental data, we find a characteristic temperature ( T / T F ) 0 =0.19±0.02 or ( T i / T F ) 0 =0.16±0.02 in a harmonic trap, below which there are deviations from normal Fermi-liquid-like behavior that may be attributed to pairing effects. Here, T F is the Fermi temperature for a trapped ideal, non-interacting Fermi gas. Our thorough comparison may shed light on the further theoretical development of strongly interacting fermions.

arXiv:1001.2085•New Journal of Physics•Jun 30, 2010•72 citations

Specific heat and effects of pairing fluctuations in the BCS-BEC-crossover regime of an ultracold Fermi gas

Pieter van Wyk, Hiroyuki Tajima, Ryo Hanai +1 more

We investigate the specific heat at constant volume ${C}_{V}$ in the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC)-crossover regime of an ultracold Fermi gas above the superfluid phase transition temperature ${T}_{\mathrm{c}}$. Within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that this thermodynamic quantity is sensitive to the stability of preformed Cooper pairs. That is, while ${C}_{V}(T\ensuremath{\gtrsim}{T}_{\mathrm{c}})$ in the unitary regime is remarkably enhanced by metastable preformed Cooper pairs or pairing fluctuations, it is well described by that of an ideal Bose gas of long-lived stable molecules in the strong-coupling BEC regime. Using these results, we identify the region where the system may be viewed as an almost ideal Bose gas of stable pairs, as well as the pseudogap regime where the system is dominated by metastable preformed Cooper pairs, in the phase diagram of an ultracold Fermi gas with respect to the strength of a pairing interaction and the temperature. We also show that the calculated specific heat agrees with the recent experiment on a $^{6}\text{Li}$ unitary Fermi gas. Since the formation of preformed Cooper pairs is a crucial key in the BCS-BEC-crossover phenomenon, our results would be helpful in considering how fluctuating preformed Cooper pairs appear in a Fermi gas to eventually become stable as one passes through the BCS-BEC-crossover region.

arXiv:1509.07232•Physical Review A•Jan 25, 2016•23 citations
We theoretically investigate normal-state properties of a unitary Bose-Fermi mixture. Including strong hetero-pairing fluctuations, we evaluate the Bose and Fermi chemical potential, internal energy, pressure, entropy, as well as specific heat at constant volume CVC_VCV​, within the framework of a combined strong-coupling theory with exact thermodynamic identities. We show that hetero-pairing fluctuations at the unitarity cause non-monotonic temperature dependence of CVC_VCV​, being qualitatively different from the monotonic behavior of this quantity in the weak- and strong-coupling limit. On the other hand, such an anomalous behavior is not seen in the other quantities. Our results indicate that the specific heat CVC_VCV​, which has recently become observable in cold atom physics, is a useful quantity for understanding strong-coupling aspects of this quantum system.
We theoretically investigate the specific heat CVC_VCV​ at constant volume in the normal state of a ppp-wave interacting Fermi gas. Including fluctuations in the ppp-wave Cooper channel within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we clarify how CVC_VCV​ as a function of temperature varies, as one moves from the weak-coupling regime to the strong-coupling limit. In the weak-coupling regime, CVC_VCV​ is shown to be enhanced by ppp-wave pairing fluctuations, near the superfluid phase transition temperature TcT_{\rm c}Tc​. Similar enhancement of CV(T≃Tc)C_V(T\simeq T_{\rm c})CV​(T≃Tc​) is also obtained in the strong-coupling regime, which, however, reflects that system is close an ideal Bose gas of ppp-wave two-body bound molecules. Using these results, we classify the normal state into (1) the normal Fermi gas regime, (2) the ppp-wave molecular Bose gas regime, and (3) the region between the two, where ppp-wave pairing fluctuations are dominant. Since the current experiments can only access the normal phase of a ppp-wave interacting Fermi gas, our results would be useful for experiments to understand strong-coupling properties of this Fermi system above TcT_{\rm c}Tc​.
We theoretically investigate normal-state properties of a gas mixture of single-component bosons and fermions with a hetero-nuclear Feshbach resonance. Including strong hetero-pairing fluctuations associated with the Feshbach resonance, we calculate single-particle density of states, as well as the spectral weight at various interaction strengths. For this purpose, we employ an improved T-matrix approximation (TMA), where the bare Bose Green's function in the non-selfconsistent TMA self-energy is modified so as to satisfy the Hugenholtz-Pines relation at the Bose-Einstein condensation (BEC) temperature TBECT_{\rm BEC}TBEC​. In the unitary regime at TBECT_{\rm BEC}TBEC​, we show that hetero-pairing fluctuations couple Fermi atomic excitations with Fermi molecular excitations, as well as with Bose atomic excitations. Although a similar coupling phenomenon by pairing fluctuations is known to give a pseudo-gapped density of states in the unitary regime of a two-component Fermi gas, such a dip structure is found to not appear even in the unitary limit of a Bose-Fermi mixture. It only appears in the strong-coupling regime. Instead, a spectral peak along the molecular dispersion appears in the spectral weight.We also clarify how this coupling phenomenon is seen in the Bose channel. Since a hetero-nuclear Feshbach resonance, as well as the formation of Bose-Fermi molecules, have been realized, our results would be useful for the study of strong-coupling properties of this unique quantum gas.
We theoretically investigate the specific heat at constant volume C V in the BCS(Bardeen-Cooper-Schrieffer)-BEC(Bose-Einstein-condensation)-crossover regime of an ultracold Fermi gas, below the superfluid phase transition temperature T c . Within the strong-coupling framework developed by Nozières and Schmitt-Rink, we show that the temperature dependence of C V drastically changes as one passes through the crossover region, and is sensitive to strong fluctuations in the Cooper channel near the unitarity limit. We also compare our results to a recent experiment on a 6 Li unitary Fermi gas. Since fluctuation effects are a crucial key in the BCS-BEC-crossover phenomenon, our results would be helpful in considering how the fermionic BCS superfluid changes into BEC with increasing the interaction strength, from the viewpoint of specific heat.
We theoretically investigate the thermodynamic stability of a normal-state Bose-Fermi mixture, with a tunable Bose-Fermi pairing interaction $\ensuremath{-}{U}_{\mathrm{BF}}<0$ associated with a heteronuclear Feshbach resonance, as well as a weak repulsive Bose-Bose interaction ${U}_{\mathrm{BB}}\ensuremath{\ge}0$. Including strong heteropairing fluctuations associated with the former interaction within the self-consistent TTT-matrix approximation, as well as the latter within the mean-field level, we calculate the compressibility matrix, to assess the stability of this system against density fluctuations. In the weak- and the intermediate-coupling regimes with respect to $\ensuremath{-}{U}_{\mathrm{BF}}$, we show that an effective attractive interaction between bosons mediated by density fluctuations in the Fermi component makes the system unstable below a certain temperature Tclp{T}_{\mathrm{clp}}Tclp​ (leading to density collapse). When UBB=0,Tclp{U}_{\mathrm{BB}}=0, {T}_{\mathrm{clp}}UBB​=0,Tclp​ is always higher than the Bose-Einstein condensation (BEC) temperature Tc{T}_{\mathrm{c}}Tc​. When UBB>0{U}_{\mathrm{BB}}>0UBB​>0, the density collapse is suppressed, and the BEC transition becomes possible. It is also suppressed by the formation of tightly bound Bose-Fermi molecules when the heteropairing interaction $\ensuremath{-}{U}_{\mathrm{BF}}$ is strong; however, since the system may be viewed as a molecular Fermi gas in this case, the BEC transition does not also occur. Since quantum gases involving Bose atoms are known to be sensitive to interparticle correlations, our results would be useful for the study of many-body properties of a Bose-Fermi mixture in a stable manner, without facing the unwanted density collapse.
Strongly interacting, dilute Fermi gases exhibit a scale-invariant, universal thermodynamic behavior. This is notoriously difficult to understand theoretically because of the absence of a small interaction parameter. Here, we present a systematic comparison of theoretical predictions from different quantum many-body theories with recent experimental data of Nascimbne et al (2010 Nature 463 1057). Our comparisons have no adjustable parameters, either theoretically or experimentally. All the model approximations seem to fluctuate rather than converge on the experimental data. It turns out that a simple Gaussian pair fluctuation theory gives the best quantitative agreement, except at the critical superfluid transition region. In the normal state, we also calculate the equation of state by using a quantum cluster expansion theory and explore in detail its applicability to low temperatures. Using the accurate experimental result for the thermodynamic function S ( T ), we determine the temperature T of a trapped Fermi gas at unitarity as a function of a non-interacting temperature T i , which can be obtained by an adiabatic sweep to the free gas limit. By analyzing the recent experimental data, we find a characteristic temperature ( T / T F ) 0 =0.19±0.02 or ( T i / T F ) 0 =0.16±0.02 in a harmonic trap, below which there are deviations from normal Fermi-liquid-like behavior that may be attributed to pairing effects. Here, T F is the Fermi temperature for a trapped ideal, non-interacting Fermi gas. Our thorough comparison may shed light on the further theoretical development of strongly interacting fermions.
We investigate the specific heat at constant volume CV{C}_{V}CV​ in the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC)-crossover regime of an ultracold Fermi gas above the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​. Within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that this thermodynamic quantity is sensitive to the stability of preformed Cooper pairs. That is, while ${C}_{V}(T\ensuremath{\gtrsim}{T}_{\mathrm{c}})$ in the unitary regime is remarkably enhanced by metastable preformed Cooper pairs or pairing fluctuations, it is well described by that of an ideal Bose gas of long-lived stable molecules in the strong-coupling BEC regime. Using these results, we identify the region where the system may be viewed as an almost ideal Bose gas of stable pairs, as well as the pseudogap regime where the system is dominated by metastable preformed Cooper pairs, in the phase diagram of an ultracold Fermi gas with respect to the strength of a pairing interaction and the temperature. We also show that the calculated specific heat agrees with the recent experiment on a 6Li^{6}\text{Li}6Li unitary Fermi gas. Since the formation of preformed Cooper pairs is a crucial key in the BCS-BEC-crossover phenomenon, our results would be helpful in considering how fluctuating preformed Cooper pairs appear in a Fermi gas to eventually become stable as one passes through the BCS-BEC-crossover region.