Mass imbalance effect in resonant Bose-Fermi mixtures

Abstract

We consider a homogeneous Bose-Fermi mixture, with the boson-fermion interaction tuned by a Fano-Feshbach\ud resonance, in the presence of mass and density imbalance between the two species. By using many-body\ud diagrammatic methods, we first study the finite-temperature phase diagram for the specific case of the mass-imbalanced\ud mixture 87Rb-40K for different values of the density imbalance. We then analyze the quantum\ud phase transition associated with the disappearance at zero temperature of the boson condensate above a critical\ud boson-fermion coupling. We find a pronounced dependence of the critical coupling on the mass ratio and a weak\ud dependence on the density imbalance. For a vanishingly small boson density, we derive, within our approximation,\ud the asymptotic expressions for the critical coupling in the limits of small and large mass ratios. These expressions\ud are relevant also for the polaron-molecule transition in a Fermi mixture at small and large mass ratios. The analysis\ud of the momentum distribution functions at sufficiently large density imbalances shows an interesting effect in the\ud bosonic momentum distribution due to the simultaneous presence of composite fermions and unpaired fermions

Energy of strongly attractive Bose-Fermi mixtures

“…where V is the volume occupied by the system, E FG = 3 5 E F is the energy per particle of the non-interacting Fermi gas, N F is the number of fermions and the bosonic chemical potential µ B is determined by solving numerically the T-matrix equations [3]. In principle, the energy could be obtained also from the (bosonic or fermionic) singleparticle Green's function (cf., e.g.…”

“…In general the bosonic and fermionic chemical potentials µ B and µ F need to be determined by solving numerically the T-matrix equations (see [3]) for given values of the densities and of the boson-fermion scattering length. Analytic expressions can be derived in the molecular limit by expanding the T-matrix equations in inverse powers of the bosonic chemical potential [8].…”

“…This complete suppression of condensation occurs even at zero temperature, and is associated with pairing of bosons with fermions into composite fermions. This kind of evolution has been studied already by us with a T-matrix diagrammatic formalism [15,3,6,8] and with the Fixed-Node Diffusion Monte Carlo method [5].…”

“…Bose-Fermi mixtures with a tunable boson-fermion attraction have been object of active theoretical and experimental investigation over the last few years (see [1,2,3,4,5,6,7,8] and [9,10,11,12,13,14] for recent theoretical and experimental works, respectively). Previous theoretical studies of these systems have shown that for a sufficiently strong attraction between fermions and bosons, the boson condensation is completely suppressed in mixtures where the boson density n B does not exceed the fermion density n F .…”

Induced interactions in a superfluid Bose-Fermi mixture

“…In cold atom gases, BoseFermi mixtures have been realised experimentally for sympathetic cooling [6][7][8], molecule formation [9][10][11][12], and for studying few-body physics [13]. The theoretical studies have focused on mixtures where the Fermi gas is in the normal state [14][15][16][17][18][19][20][21][22][23]. Recently, an experimental breakthrough was reported with the realisation of a mixture of superfluid 7 Li and 6 Li gases [24].…”