Abstract We discuss an equilibrium mean-field properties of mixtures consisting of bosons and spin-polarized fermionic atoms with a point-like interaction in an arbitrary dimension 2 < d < 4 . Particularly, besides the standard weak-coupling limit of the system with slightly depleted Bose condensate and almost ideal Fermi gas, we discuss the (meta)stable phase with dimers composed exactly of one boson and one fermion. The peculiarities of the fermion-dimer and the boson-dimer three-body effective interactions and their impact on the thermodynamic stability of the dilute Bose-Fermi mixtures are elucidated.
Abstract We discuss an equilibrium mean-field properties of mixtures consisting of bosons and spin-polarized fermionic atoms with a point-like interaction in an arbitrary dimension 2 < d < 4 . Particularly, besides the standard weak-coupling limit of the system with slightly depleted Bose condensate and almost ideal Fermi gas, we discuss the (meta)stable phase with dimers composed exactly of one boson and one fermion. The peculiarities of the fermion-dimer and the boson-dimer three-body effective interactions and their impact on the thermodynamic stability of the dilute Bose-Fermi mixtures are elucidated.
In the strong-coupling Bose-Einstein condensation (BEC) region where a Feshbach resonance gives rise to tightly bound dimer molecules, we show that a spin-polarized Fermi superfluid reduces to a simple Bose-Fermi mixture of Bose-condensed dimers and the leftover unpaired fermions. Using a many-body functional integral formalism, the Gaussian fluctuations give rise to an induced dimer-dimer interaction mediated by the unpaired fermions, with the dimer-fermion vertex being given by the (mean-field) Born approximation. Treating the pairing fluctuations to quartic order, we show how the action for a spin-polarized Fermi superfluid reduces to one for a Bose-Fermi mixture. This Bose-Fermi action includes an expression for the effective dimer-unpaired fermion interaction in a spin-polarized Fermi superfluid beyond the Born approximation, in the BEC limit. In the low-density limit, we show how this dimer-fermion interaction gives the s-wave scattering length aBF=1.18aF (aF is the s-wave fermion scattering length), a result first derived by Skorniakov and Ter-Martirosian in 1957 for three interacting fermions.
We consider a dilute homogeneous mixture of bosons and spin-polarized fermions at zero temperature. We first construct the formal scheme for carrying out systematic perturbation theory in terms of single particle Green's functions. We especially focus on the description of the boson-fermion interaction. To do so we need to introduce the renormalized boson-fermion T matrix, which we determine to second order in the boson-fermion s-wave scattering length. We also discuss how to incorporate the usual boson-boson T matrix in mean field approximation to obtain the total ground-state properties of the system. The next-order term beyond mean field stems from the boson-fermion interaction and is proportional to aBFkF. The total ground-state energy density to this order is the sum of the kinetic energy of the free fermions, the boson-boson mean-field interaction, the usual mean-field contribution to the boson-fermion interaction energy, and the first boson-fermion correction beyond mean field. We also compute the bosonic and the fermionic chemical potentials, the compressibilities, and the modification to the induced fermion-fermion interaction. We discuss the behavior of the total ground-state energy and the importance of the correction beyond mean field for various parameter regimes, in particular considering mixtures of 6Li and 7Li and of 3He and 4He. Moreover, we determine the modification of the induced fermion-fermion interaction due to the effects beyond mean field. We show that there is no effect on the depletion of the Bose condensate to first order in the boson-fermion scattering length aBF.
Motivated by a recent experiment by the Ecole Normale Sup\'erieure de Lyon (ENS) group on the mixture of Bose and Fermi superfluids [I. Ferrier-Barbut et al., Science 345, 1035 (2014)], we investigate the effective scattering between a bosonic atom and a molecule (dimer) of fermion atoms. It is found that the mean-field prediction of the atom-dimer scattering length (aad), as simply given by the boson-fermion scattering length (abf), generically fails. Instead, aad crucially depends on the ratio between abf and aff (the fermion-fermion scattering length), and in addition it log-periodically depends on the three-body parameter. We identify the universal parameters in characterizing aad for a wide range of aff in the molecular side of the fermion-fermion Feshbach resonance, and further demonstrate that the atom-dimer many-body system can become unstable against either phase separation or collapse as tuning aff. Our results have some implications for the ENS experiment.
We investigate the properties of a dilute boson-fermion mixture at zero temperature. The ground-state energy of the system is calculated to second order in the Bose-Fermi coupling constant. The Green's function formalism is applied to obtain results for the effect of Bose-Fermi interactions on the spectrum of phonon excitations, the momentum distribution, the condensate fraction, and the superfluid density of the bosonic component. A quantitative discussion of these effects is presented in the case of mixtures with attractive interspecies interaction.
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.
Motivated by a recent experiment by ENS group on the mixture of Bose and Fermi superfluids (arxiv:1404.2548), we investigate the effective scattering between a bosonic atom and a molecule(dimer) of fermion atoms. It is found that the mean-field prediction of the atom-dimer scattering length (aad), as simply given by the boson-fermion scattering length (abf), generically fails. Instead, aad crucially depends on the ratio between abf and aff (the fermion-fermion scattering length), and in addition log-periodically depends on the three-body parameter. We identify the universal parameters in characterizing aad for a wide range of aff in the molecular side of the fermion-fermion Feshbach resonance, and further demonstrate that the atom-dimer many-body system can become unstable against either phase separation or collapse as tuning aff. Our results have practical implications to the atom loss and collective mode measurement in ENS experiment.