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arXiv:1907.12257 · Physical Review A

Single-particle properties of a strongly interacting Bose-Fermi mixture with mass and population imbalance

Koki Manabe, Daisuke Inotani, Yoji Ohashi

Published Dec 5, 2019• 9 citations
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Abstract

We theoretically investigate strong-coupling properties of a Bose-Fermi mixture. In the mass- and population-balanced case, two of the authors have shown that a strong heteropairing interaction in this mixture brings about coupling phenomena between Fermi atomic excitations and Bose atomic and composite molecular excitations, that appear as an anomalous multiple peak structure in the single-particle spectral weight (SW) [Kharga, Inotani, Hanai, and Ohashi, J. Phys. Soc. Jpn. 86, 084301 (2017)]. In this paper, we show that, although these many-body phenomena are sensitive to mass and population imbalances between the Bose and Fermi components, SW still exhibits the multiple peak structure in moderately mass-imbalanced $^{87}\mathrm{Rb}\text{\ensuremath{-}}^{40}\mathrm{K}$ and $^{23}\mathrm{Na}\text{\ensuremath{-}}^{40}\mathrm{K}$ mixtures. We also point out that the photoemission spectrum is a useful quantity to observe this spectral anomaly. Since a real trapped Bose-Fermi mixture is usually accompanied by mass and (local) population imbalances, our results would contribute to the study of a strongly interacting Bose-Fermi mixture, under realistic imbalanced conditions.

DOI
10.1103/physreva.100.063609

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We theoretically investigate strong-coupling properties of a Bose-Fermi mixture. In the mass- and population-balanced case, two of the authors have shown that a strong heteropairing interaction in this mixture brings about coupling phenomena between Fermi atomic excitations and Bose atomic and composite molecular excitations, that appear as an anomalous multiple peak structure in the single-particle spectral weight (SW) [Kharga, Inotani, Hanai, and Ohashi, J. Phys. Soc. Jpn. 86, 084301 (2017)]. In this paper, we show that, although these many-body phenomena are sensitive to mass and population imbalances between the Bose and Fermi components, SW still exhibits the multiple peak structure in moderately mass-imbalanced 87Rb\ensuremath-40K^{87}\mathrm{Rb}\text{\ensuremath{-}}^{40}\mathrm{K}87Rb\ensuremath-40K and 23Na\ensuremath-40K^{23}\mathrm{Na}\text{\ensuremath{-}}^{40}\mathrm{K}23Na\ensuremath-40K mixtures. We also point out that the photoemission spectrum is a useful quantity to observe this spectral anomaly. Since a real trapped Bose-Fermi mixture is usually accompanied by mass and (local) population imbalances, our results would contribute to the study of a strongly interacting Bose-Fermi mixture, under realistic imbalanced conditions.
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.
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We calculate the single-particle spectral functions and quasiparticle dispersions for a Bose-Fermi mixture when the boson-fermion attraction is sufficiently strong to suppress completely the condensation of bosons at zero temperature. Within a T-matrix diagrammatic approach, we vary the boson-fermion attraction from the critical value where the boson condensate first disappears to the strongly attractive (molecular) regime and study the effect of both mass and density imbalance on the spectral weights and dispersions. An interesting spectrum of particle-hole excitations mixing two different Fermi surfaces is found. These unconventional excitations could be produced and explored experimentally with radio-frequency spectroscopy.
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We theoretically investigate the thermodynamic stability of a normal-state Bose-Fermi mixture, with a tunable Bose-Fermi pairing interaction $\ensuremath{-}{U}_{\mathrm{BF}}<0$ 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.
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