We study theoretically the phase diagram of strongly coupled two-dimensional Bose-Fermi mixtures interacting with attractive short-range potentials as a function of the particle densities. We focus on the limit where the size of the bound state between a boson and a fermion is small compared to the average interboson separation and develop a functional-renormalization-group approach that accounts for the bound-state physics arising from the extended Fr\"ohlich Hamiltonian. By including three-body correlations we are able to reproduce the polaron-to-molecule transition in two-dimensional Fermi gases in the extreme limit of vanishing boson density. We predict frequency- and momentum-resolved spectral functions and study the impact of three-body correlations on quasiparticle properties. At finite boson density, we find that when the bound-state energy exceeds the Fermi energy by a critical value, the fermions and bosons can form a fermionic composite with a well-defined Fermi surface. These composites constitute a Fermi sea of dressed Feshbach molecules in the case of ultracold atoms, while in the case of atomically thin semiconductors a trion liquid emerges. As the boson density is increased further, the effective energy gap of the composites decreases, leading to a transition into a strongly correlated phase where polarons are hybridized with molecular degrees of freedom. We highlight the universal connection between two-dimensional semiconductors and ultracold atoms, and we discuss perspectives for further exploring the rich structure of strongly coupled Bose-Fermi mixtures in these complementary systems.
We study theoretically the phase diagram of strongly coupled two-dimensional Bose-Fermi mixtures interacting with attractive short-range potentials as a function of the particle densities. We focus on the limit where the size of the bound state between a boson and a fermion is small compared to the average interboson separation and develop a functional-renormalization-group approach that accounts for the bound-state physics arising from the extended Fr"ohlich Hamiltonian. By including three-body correlations we are able to reproduce the polaron-to-molecule transition in two-dimensional Fermi gases in the extreme limit of vanishing boson density. We predict frequency- and momentum-resolved spectral functions and study the impact of three-body correlations on quasiparticle properties. At finite boson density, we find that when the bound-state energy exceeds the Fermi energy by a critical value, the fermions and bosons can form a fermionic composite with a well-defined Fermi surface. These composites constitute a Fermi sea of dressed Feshbach molecules in the case of ultracold atoms, while in the case of atomically thin semiconductors a trion liquid emerges. As the boson density is increased further, the effective energy gap of the composites decreases, leading to a transition into a strongly correlated phase where polarons are hybridized with molecular degrees of freedom. We highlight the universal connection between two-dimensional semiconductors and ultracold atoms, and we discuss perspectives for further exploring the rich structure of strongly coupled Bose-Fermi mixtures in these complementary systems.
We study the ground-state properties of one-dimensional mixtures of bosonic and fermionic atoms resonantly coupled to fermionic Feshbach molecules. When the particle densities of fermionic atoms and Feshbach molecules differ, the system undergoes various depletion transitions between binary and ternary mixtures as a function of the detuning parameter. However, when the particle densities of fermionic atoms and Feshbach molecules are identical, the molecular conversion and disassociation processes induce a gap in a sector of low-energy excitations, and the remaining system can be described by a two-component Tomonaga-Luttinger liquid. Using a bosonization scheme, we derive the effective low-energy Hamiltonian for the system, which has a similar form as that of the two-chain problem of coupled Tomonaga-Luttinger liquids. With the help of improved perturbative renormalization group analysis of the latter problem, we determine the ground-state phase diagram and find that it contains a phase dominated by composite superfluid or pairing correlations between the open and closed resonant channels.
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.
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 reveal a quantum coherent state characterized by composite bosonic trions, wherein paired fermions further bind with bosons, in one-dimensional Bose-Fermi mixtures.This phase emerges in two separate models, both featuring onsite boson-fermion attraction that induces negative binding energy for the composite trions. The first is the pair-hopping model, in which spinless fermions undergo pair hopping to form preformed pairs. The second is the extended Bose-Fermi Hubbard model, describing dipolar bosons and fermions with density-density interactions. Notably, the formation of composite trions is independent of the specific pairing interactions of fermions. Extensive density matrix renormalization group calculations demonstrate the quasi-condensation of the composite trions, evidenced by algebraically decaying correlations of trions, gapped single-particle excitations, and suppressed fermion pair correlations. Our findings provide valuable insights into the three-body pairing mechanism in mixed-particle systems.
We consider a mixture of bosons and spin-polarized fermions in two dimensions at zero temperature with a tunable Bose-Fermi attraction. By adopting a diagrammatic T T -matrix approach, we analyze the behavior of several thermodynamic quantities for the two species as a function of the density ratio and coupling strength, including the chemical potentials, the momentum distribution functions, the boson condensate density, and the Tan’s contact parameter. By increasing the Bose-Fermi attraction, we find that the condensate is progressively depleted and Bose-Fermi pairs form, with a small fraction of condensed bosons surviving even for strong Bose-Fermi attraction. This small condensate proves sufficient to hybridize molecular and atomic states, producing quasi-particles with unusual Fermi liquid features. A nearly universal behavior of the condensate fraction, the bosonic momentum distribution, and Tan’s contact parameter with respect to the density ratio is also found.
In this thesis, we investigate ultracold Bose-Fermi mixtures in both two and three dimensions using a non-perturbative approach based on the Lowest Order Constrained Variational (LOCV) method. This variational technique, originally developed in the context of nuclear matter, is applied here to dilute quantum gases at zero temperature, allowing for an accurate treatment of two-body correlations beyond perturbative limits. We begin by analysing Bose-Fermi mixtures near a broad Fano-Feshbach resonance, which enables precise tuning of the interspecies interaction strength. Particular attention is devoted to the low-dimensional case, where quantum fluctuations are enhanced and experimental realizations have become increasingly accessible. While the three-dimensional problem serves as a useful benchmark, the two-dimensional Bose-Fermi mixture presents unique challenges. Notably, no prior non-perturbative studies exist on its mechanical stability. A central goal of this work is to determine the conditions under which the 2D Bose-Fermi mixture remains mechanically stable as the boson-fermion attraction is increased. Our results demonstrate that the LOCV approach captures the relevant physics from weak to moderate coupling, offering a complementary perspective to perturbative methods or alternative non-perturbative approaches such as the T-matrix formalism. In this coupling range, we identify the critical strength of boson-boson repulsion necessary to prevent phase separation or collapse, thereby providing the first theoretical variational prediction of a stability phase diagram in this two dimensional regime. Overall, this work fills a gap in the literature and provides a useful reference point for future theoretical and experimental studies of strongly interacting Bose-Fermi systems in reduced dimensionality.