We consider a homogeneous mixture of bosons and polarized fermions. We find that long-range and attractive fermion-mediated interactions between bosons have dramatic effects on the properties of the bosons. We construct the phase diagram spanned by boson-fermion mass ratio and boson-fermion scattering parameter. It consists of a stable region of mixing and unstable region toward phase separation. In the stable mixing phase, the collective long-wavelength excitations can either be well behaved with infinite lifetime or be finite in lifetime suffered from the Landau damping. We examine the effects of the induced interaction on the properties of weakly interacting bosons. It turns out that the induced interaction not only enhances the repulsion between the bosons against collapse but also enhances the stability of the superfluid state by suppressing quantum depletion.
We consider a homogeneous mixture of bosons and polarized fermions. We find that long-range and attractive fermion-mediated interactions between bosons have dramatic effects on the properties of the bosons. We construct the phase diagram spanned by boson-fermion mass ratio and boson-fermion scattering parameter. It consists of a stable region of mixing and unstable region toward phase separation. In the stable mixing phase, the collective long-wavelength excitations can either be well behaved with infinite lifetime or be finite in lifetime suffered from the Landau damping. We examine the effects of the induced interaction on the properties of weakly interacting bosons. It turns out that the induced interaction not only enhances the repulsion between the bosons against collapse but also enhances the stability of the superfluid state by suppressing quantum depletion.
We investigate the homogeneous superfluid mixtures of a Bardeen-Cooper-Schrieffer (BCS) superfluid originating from pairing two-species fermionic atoms and superfluidity stemming from condensation of bosonic atoms. By integrating out the freedoms associated with the BCS superfluid, we derive the fermion-mediated interactions between bosons, which is attractive and can be tuned from long range in the BCS region to short range in the region of Bose-Einstein condensation of molecular dimers. By analyzing the Bogoliubov spectrum and the damping rate of bosonic superfluid, we map out the phase diagram spanned by the boson-fermion mass ratio and the boson-fermion coupling strength, which consists of a phase separation region and two phase-mixing regions with and without Landau damping. The three different phases can coexist at a tricritical point, which moves toward a low boson-fermion mass ratio and a high boson-fermion scattering length as the fermion-fermion interaction strength is tuned up on the BCS side.
We develop a functional integral formulation for binary Bose-Einstein condensates coupled to polarized fermions.We find that spin-dependent fermion-mediated interactions have dramatic effects on the properties of the binary condensates.The quasiparticle spectrum features two branches.The upper branch, which is of density nature, gets modified by the induced interactions, while the lower branch, which is of spin nature, is left intact.The ground-state phase diagram consists of stable region of miscible phases and unstable region toward phase separation.In the stable region, it is further classified by the damping of excitations of the upper branch.We show that it is possible to find region of well-defined, long-lived quasiparticle excitations by tuning relevant parameters, such as boson-fermion mass ratio, boson-fermion number density ratio, and interspecies interactions between bosons as well.We explore the effects of quantum fluctuation due to the effective potential on the binary condensates.It turns out that both the density structure factor and spin density structure factor fulfill the Feynman relation, except that the latter is immune to the fermion-mediated interactions.
The ground-state phase diagram of mixtures of spin polarized fermions and bosons in a 1D periodic lattice is discussed in the limit of large fermion hopping and half filling of the fermions. Numerical simulations performed with the density matrix renormalization group (DMRG) show in addition to bosonic Mott insulating (MI), superfluid (SF), and charge density-wave phases (CDW) a yet unreported phase with spatial separation of MI and CDW regions. We derive an effective bosonic theory which allows for a complete understanding and quantitative prediction of the bosonic phase diagram. In particular the origin of CDW phase and the MI-CDW phase separation is revealed as an effective fermion-mediated long-range interaction between bosons with alternating sign.
We describe recent theoretical and experimental developments on mediated interactions in mixtures of bosonic and fermionic atoms. We discuss how particle-hole excitations of a Fermi sea can induce long-range interactions between heavy impurities or atoms in a Bose-Einstein condensate. Conversely, phonon excitations of a Bose-Einstein condensate induce interactions between fermionic atoms. These mediated interactions exhibit different short-range and long-range scaling regimes with distance and, if strong enough, can induce fermion superfluidity. We discuss the prospects for observing new phenomena that could arise from mediated interactions. Experimentally, we outline recent studies of the 133Cs-6Li Bose-Fermi mixture, a platform well-suited for investigating fermion-mediated interactions. A Cs Bose-Einstein condensate immersed in a degenerate Li Fermi gas is prepared with tunable interspecies interactions. In the weak-coupling regime, precision measurements of condensate properties reveal fermion-mediated attractions between bosons, matching theoretical predictions. In the strong-coupling regime, we observe suppression and revival of sound modes and novel many-body resonances. Altogether, we aim to highlight both instances where experiment and theory agree well, and promising prospects to engineer long-range interactions in atomic quantum gases.
We investigate the collective excitations of a low-temperature dilute gas mixture that consists of a Bose-Einstein condensate (BEC) and a Fermi gas that is a normal (i.e., nonsuperfluid) Fermi liquid. We find that the BEC-mediated fermion-fermion interactions, as a consequence of retardation, can become repulsive and support a zero-sound mode that is essentially undamped. In addition, we find a damped zero-sound mode that can be described as a BEC sound mode modified by fermion-mediated boson-boson interactions, and we derive its decay rate caused by Landau damping. We study the mode structure of these excitations and find avoided-crossing behavior as well as a termination point. The collective-mode dynamics also reveals that phase separation sets in when the fermion-mediated boson-boson interaction destroys the stability of the homogeneous BEC. We estimate the time and length scales of the onset of the phase separation, and we discuss the feasibility of experimentally probing these consequences of mediated interactions.
The phase diagrams of low density Fermi-Fermi mixtures with equal or unequal masses and equal or unequal populations are described at zero and finite temperatures in the strong attraction limit. In this limit, the Fermi-Fermi mixture can be described by a weakly interacting Bose-Fermi mixture, where the bosons correspond to Feshbach molecules and the fermions correspond to excess atoms. First, we discuss the three and four fermion scattering processes, and use the exact boson-fermion and boson-boson scattering lengths to generate the phase diagrams in terms of the underlying fermion-fermion scattering length. In three dimensions, in addition to the normal and uniform superfluid phases, we find two stable nonuniform states corresponding to (i) phase separation between pure unpaired (excess) and pure paired fermions (molecular bosons); and (ii) phase separation between pure excess fermions and a mixture of excess fermions and molecular bosons. Lastly, we also discuss the effects of the trapping potential in the density profiles of condensed and noncondensed molecular bosons, and excess fermions at zero and finite temperatures, and discuss possible implications of our findings to experiments involving mixtures of ultracold fermions.