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arXiv:1202.3348 · Physical Review A

Mass imbalance effect in resonant Bose-Fermi mixtures

Elisa Fratini, P. Pieri

Published Jun 26, 2012• 44 citations
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Abstract

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

DOI
10.1103/physreva.85.063618

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We consider a homogeneous Bose-Fermi mixture, with the boson-fermion interaction tuned by a Fano-Feshbach resonance, in the presence of mass and density imbalance between the two species. By using many-body diagrammatic methods, we first study the finite-temperature phase diagram for the specific case of the mass-imbalanced mixture 87{}^{87}87Rb-40{}^{40}40K for different values of the density imbalance. We then analyze the quantum phase transition associated with the disappearance at zero temperature of the boson condensate above a critical boson-fermion coupling. We find a pronounced dependence of the critical coupling on the mass ratio and a weak dependence on the density imbalance. For a vanishingly small boson density, we derive, within our approximation, the asymptotic expressions for the critical coupling in the limits of small and large mass ratios. These expressions are relevant also for the polaron-molecule transition in a Fermi mixture at small and large mass ratios. The analysis of the momentum distribution functions at sufficiently large density imbalances shows an interesting effect in the bosonic momentum distribution due to the simultaneous presence of composite fermions and unpaired fermions.
We consider a homogeneous Bose-Fermi mixture, with the boson-fermion interaction tuned by a broad Fano-Feshbach resonance, in the presence of mass and density imbalance between the two species. For increasing coupling, the growing boson-fermion pairing correlations progressively reduce the boson condensation temperature and make it eventually vanish at a critical coupling. We find a pronounced dependence of the critical couplingn on the mass ratio and a weak dependence on the density imbalance. For a vanishingly small boson density, we present asymptotic expressions for the critical coupling at small and large mass ratios. The analysis of the momentum distribution functions at sufficiently large density imbalance shows a peculiar feature in the bosonic momentum distribution due to the simultaneous presence of composite fermions and unpaired fermions.
We consider a Bose-Fermi mixture with a broad and tunable Feshbach resonance allowing to change continuously the attraction between bosons and fermions from weak to strong coupling. We set up a diagrammatic formalism which includes both the Bose-Fermi tunable attraction and the Bose-Bose repulsion at zero temperature. Remarkably, we find that for boson density smaller than or equal to the fermion density, the boson condensate fraction does not depend on the density imbalance across most of the resonance. In the limit of vanishing boson concentration, we find very good agreement with previous results for the polaron quasi-particle residue obtained in the context of strongly polarized Fermi-Fermi mixtures [1]. We calculate also the boson and fermion chemical potentials and momentum distribution functions and, when the condensate fraction vanishes, we recover the results of our previous works for the normal phase [2,3]. In addition, we calculate the effective masses and Fermi steps for the unpaired and composite fermions. We find that the Fermi step of the unpaired fermions remains pinned to the value given by the Fermi radius of a free Fermi gas across most of the resonance, in agreement with the Luttinger’s theorem [4], until molecules start to form (g≈1). The formation of molecules is signalled by the appearance of a second pole in the boson-fermion propagator, which marks the access to a regime where bosons, fermions and molecules cohexist, and by the presence of a Fermi step for the composite fermions, which is related to the density of molecules. Finally, we find quite a good agreement between our results for the condensate fraction and Quantum Monte Carlo calculations [5].
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 analyze a two-dimensional Bose-Fermi mixture at zero temperature in the presence of a tunable Bose-Fermi attraction. We adopt a diagrammatic T -matrix approach and study the behavior of several thermodynamic quantities for the two species as functions of density, mass ratio, and coupling strength. These include the chemical potentials, the boson momentum distribution function, the condensate density, and Tan's contact parameter. We analytically demonstrate that the present T -matrix formalism recovers the correct second-order perturbative expansion of the chemical potentials in the weak-coupling regime, and test it numerically. The near-universal behavior of the condensate fraction already found in prior work for the mass-balanced case is confirmed for different masses and becomes even more accurate when the boson mass is large. The mass imbalance emerges as an additional control parameter that qualitatively affects the bosonic momentum distribution. In particular, we found that it can be used to allow for the experimental observation of a peculiar peak in the boson momentum distribution at finite momentum.
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 analyze the phase diagram of uniform superfluidity for two-species fermion mixtures from the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation (BEC) limit as a function of the scattering parameter and population imbalance. We find at zero temperature that the phase diagram of population imbalance versus scattering parameter is asymmetric for unequal masses, having a larger stability region for uniform superfluidity when the lighter fermions are in excess. In addition, we find topological quantum phase transitions associated with the disappearance or appearance of momentum space regions of zero quasiparticle energies. Lastly, near the critical temperature, we derive the Ginzburg-Landau equation and show that it describes a dilute mixture of composite bosons and unpaired fermions in the BEC limit.