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.
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.
We develop a diagrammatic perturbation treatment to calculate the zero-temperature equation of state of the dilute gas mixture of a single spin component Bose-Einstein condensate (BEC) and a normal Fermi gas of indistinguishable (single spin) fermion particles. We find that the mean-field description breaks down near the mechanical instability related to the phase separation phenomenon. Our analysis shows that the instability is caused by the competition of the usual short-range and fermion-mediated boson-boson interactions, which result in a boson compressibility that diverges. In the low BEC-density limit, we show that the diagrammatic analysis simplifies, we sum part of the higher-order diagrams, and we discuss the effects of other higher-order contributions.
We investigate the mechanical stability of Bose-Fermi mixtures at zero temperature in the presence of a tunable Feshbach resonance, which induces a competition between boson condensation and boson-fermion pairing when the boson density is smaller than the fermion density. Using a many-body diagrammatic approach validated by fixed-node Quantum Monte Carlo calculations and supported by recent experimental observations, we determine the minimal amount of boson-boson repulsion required to guarantee the stability of the mixture across the entire range of boson-fermion interactions from weak to strong coupling. Our stability phase diagrams indicate that mixtures with boson-to-fermion mass ratios near two, such as the ^{87} 87 Rb- ^{40} 40 K system, exhibit optimal stability conditions. Moreover, by applying our results to a recent experiment with a ^{23} 23 Na- ^{40} 40 K mixture, we find that the boson-boson repulsion was insufficient to ensure stability, suggesting that the experimental timescale was short enough to avoid mechanical collapse. On the other hand, we also show that even in the absence of boson-boson repulsion, Bose-Fermi mixtures become intrinsically stable beyond a certain coupling strength, preceding the quantum phase transition associated with the vanishing of the bosonic condensate. We thus propose an experimental protocol for observing this quantum phase transition in a mechanically stable configuration.
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 Tclp (leading to density collapse). When UBB=0,Tclp is always higher than the Bose-Einstein condensation (BEC) temperature Tc. When UBB>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.
We calculate the spectrum of low-lying collective excitations in a gaseous cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas over a range of the boson-fermion coupling strength extending from strongly repulsive to strongly attractive. Increasing boson-fermion repulsions drives the system towards spatial separation of its components (``demixing''), whereas boson-fermion attractions drives it towards implosion (``collapse''). The dynamics of the system is treated in the experimentally relevant collisionless regime by means of a random-phase approximation, and the behavior of a mesoscopic cloud under isotropic harmonic confinement is contrasted with that of a macroscopic mixture at given average particle densities. In the latter case the locations of both the demixing and the collapse phase transitions are sharply defined by the same stability condition, which is determined by the softening of an eigenmode of either fermionic or bosonic origin. In contrast, the transitions to either demixing or collapse in a mesoscopic cloud at fixed confinement and particle numbers are spread out over a range of boson-fermion coupling strength, and some initial decrease of the frequencies of a set of collective modes is followed by hardening, as evidenced by blue shifts of most eigenmodes. The spectral hardening can serve as a signal of the impending transition and is most evident when the number of bosons in the cloud is relatively large. We propose physical interpretations for these dynamical behaviors with the help of suitably defined partial compressibilities for the gaseous cloud under confinement.
We investigate the ground state properties of the gaseous mixture of a single species of bosons and fermions at zero temperature, where bosons are major in population over fermions, and form the Bose-Einstein condensate (BEC). The boson-boson and boson-fermion interactions are assumed to be weakly repulsive and attractive, respectively, while the fermion-fermion interaction is absent due to the Pauli exclusion for the low energy s-wave scattering. We treat fermions as a gas of polarons dressed with Bogoliubov phonons, which is an elementary excitation of the BEC, and evaluate the ground state properties with the method developed by Lemmens, Devreese, and Brosens (LDB) originally for the electron polaron gas, and also with a general extension of the Lee-Low-Pines theory for many-body systems (eLLP), which incorporates the phonon drag effects as in the original LLP theory. The formulation of eLLP is developed and discussed in the present paper. The binding (interaction) energy of the polaron gas is calculated in these methods and shown to be finite (negative) for the dilute gas of heavy fermions with attractive boson-fermion interactions, though the suppression by the many-body effects exists.
We investigate an ultracold Bose-Fermi mixture with a Feshbach resonance between two hyperfine states of fermions. Using a functional integral method, we calculate collective modes associated with fermion pairs and bosons in the superfluid phase. We derive a stability condition of the mixtures that is valid in the entire region of the BCS-BEC crossover. This stability condition, which smoothly connects the well-known results obtained in both the BCS and Bose-Einstein Condensate (BEC) limits, shows that sufficiently strong fermion-boson (FB) interactions destabilize the mixtures. In order to investigate the consequence of this instability, we study the ground-state energy of both the uniformly mixed and the phase-separated states. We find that FB repulsion induces a phase separation, whereas FB attraction should cause a collapse of the mixture. The possibilities for the experimental observation of such instabilities are also discussed.