We study by diagrammatic means a Bose-Fermi mixture, with boson-fermion coupling tuned by a Fano- Feshbach resonance. For increasing coupling, the growing boson-fermion pairing correlations progressively reduce the boson condensation temperature and make it eventually vanish at a critical coupling. Such quantum critical point depends very weakly on the population imbalance and, for vanishing boson densities, coincides with that found for the polaron-molecule transition in a strongly imbalanced Fermi gas, thus bridging two quite distinct physical systems

We study a resonant Bose-Fermi mixture at zero temperature by using the fixed-node diffusion Monte Carlo method. We explore the system from weak to strong boson-fermion interaction, for different concentrations of the bosons relative to the fermion component. We focus on the case where the boson density nB is smaller than the fermion density nF , for which a first-order quantum phase transition is found from a state with condensed bosons immersed in a Fermi sea, to a Fermi-Fermi mixture of composite fermions and unpaired fermions. We obtain the equation of state and the phase diagram, and we find that the region of phase separation shrinks to zero for vanishing nB.PACS numbers: 67.85. Pq, 03.75.Ss, 03.75.Hh Let us consider a system of bosons and spinless fermions with a tunable short-range boson-fermion (BF) attraction. For weak attraction, at sufficiently low temperature the bosons condense, while the fermions fill a Fermi sphere, and the BF interaction can be treated with perturbative methods [1,2]. For sufficiently strong attraction, bosons and fermions pair into molecules. In particular, for a fermion density n F larger than the boson density n B , one expects all the bosons to pair with fermions. The boson condensate is then absent in such a regime, and the system should be described as a weakly interacting Fermi-Fermi mixture, one component consisting of molecules, with density n M = n B , and the other component of unpaired fermions, with densityHow does the system evolve at zero temperature between the two above physical regimes? Several scenarios could be imagined in principle: (i) a continuous quantum phase transition, with the condensate fraction vanishing smoothly at a certain critical value of the BF coupling; (ii) a first-order quantum phase transition, with phase separation between a condensed phase and a molecular phase without condensate; (iii) the collapse of the system in the intermediate coupling region, with no stable state connecting the two different regimes.The above question has been the object of increasing attention recently, especially in the field of ultracold trapped gases, where the interaction can be tuned by using Feshbach resonances [3]. In particular, for "broad" resonances, a Bose-Fermi mixture can be accurately described by a minimal set of parameters: the scattering lengths a BB and a BF describing, respectively, the bosonboson (BB) and boson-fermion interaction, the boson and fermion densities n B and n F , and their masses m B and m F (the short-range fermion-fermion interaction being negligible, due to Pauli exclusion).Initial experiments [4,5] with ultracold Bose-Fermi mixtures supported the collapse scenario, with the instability occurring already for moderate BF coupling. However, only a limited region of the parameter space was explored (e.g., a boson number N B considerably greater than the fermion number N F and nonresonant values of the scattering lengths). 12] mixtures, in the latter case observing lifetimes of the order of 100ms, sufficient for the setup of m...

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