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arXiv:2103.16843 · Physical Review A

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

Koki Manabe, Yoji Ohashi

Published Jun 23, 2021• 10 citations
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Abstract

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.

DOI
10.1103/physreva.103.063317

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We theoretically investigate the thermodynamic stability of a normal-state Bose-Fermi mixture, with a tunable Bose-Fermi pairing interaction \ensuremath−UBF<0\ensuremath{-}{U}_{\mathrm{BF}}<0\ensuremath−UBF​<0 associated with a heteronuclear Feshbach resonance, as well as a weak repulsive Bose-Bose interaction UBB\ensuremath≥0{U}_{\mathrm{BB}}\ensuremath{\ge}0UBB​\ensuremath≥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−UBF\ensuremath{-}{U}_{\mathrm{BF}}\ensuremath−UBF​, 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−UBF\ensuremath{-}{U}_{\mathrm{BF}}\ensuremath−UBF​ 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.
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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 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 the mechanical instability toward density collapse and the transition temperature of Bose-Einstein condensation (BEC) in the weakly coupled boson-fermion many-body mixture of single-component boson and fermion gases, in the case of the repulsive boson-boson and attractive boson-fermion interactions; no fermion-fermion interaction is assumed to be originated from the Pauli exclusion because of the diluteness of the mixture. The mechanical instability occurs in the bosonic gas where the induced boson-boson attraction mediated by the fermion polarization overcomes the boson-boson repulsive interaction at low temperatures. We calculate the onset temperature of the mechanical instability and the BEC transition temperature for the interaction strength and the boson-fermion number ratio. We also discuss the relation between the mechanical instability and the BEC transition using a diagrammatic method.
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