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arXiv:1304.0335 · Physical Review A

Composite pairing and superfluidity in a one-dimensional resonant Bose-Fermi mixture

Shimul Akhanjee, Masahisa Tsuchiizu, Akira Furusaki

Published Oct 16, 2013• 0 citations
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Abstract

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.

DOI
10.1103/physreva.88.043620

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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.
We have considered one-dimensional Bose-Fermi mixture with equal densities and unequal masses using numerical density matrix renormalization group. For the mass ratio of K-Rb mixture and attraction between bosons and fermions, we determined the phase diagram. For weak boson-boson interactions, there is a direct transition between two-component Luttinger liquid and collapsed phases as the boson-fermion attraction is increased. For strong enough boson-boson interactions, we find an intermediate ``paired'' phase, which is a single-component Luttinger liquid of composite particles. We investigated correlation functions of such a ``paired'' phase, studied the stability of ``paired'' phase to density imbalance, and discussed various experimental techniques which can be used to detect it.
We study a model of one-dimensional fermionic atoms with a narrow Feshbach resonance that allows them to bind in pairs to form bosonic molecules. We show that at low energy, a coherence develops between the molecule and fermion Luttinger liquids. At the same time, a gap opens in the spin excitation spectrum. The coherence implies that the order parameters for the molecular Bose-Einstein condensation and the atomic BCS pairing become identical. Moreover, both bosonic and fermionic charge density wave correlations decay exponentially, in contrast with a usual Luttinger liquid. We exhibit a Luther-Emery point where the systems can be described in terms of noninteracting pseudofermions. At this point we discuss the threshold behavior of density-density response functions.
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 an atomic Bose gas with an sss-wave Feshbach resonance in one dimension. Most of the parameter region is occupied by a phase in which the superfluid fluctuations of atoms and molecules are the predominant ones, due to the phase fluctuations of atoms and molecules being locked by a Josephson coupling between them. When the density difference between atoms and molecules is close to zero, two additional phases may exist: the two-component Luttinger liquid, which contains two branches of gapless excitations, and the interchannel charge density wave where the relative density fluctuations between atoms and molecules are frozen at low energy.
We describe the properties of a mixture of fermionic and bosonic atoms, as they are tuned across a Feshbach resonance associated with a fermionic molecular state. Provided the number of fermionic atoms exceeds the number of bosonic atoms, we argue that there is a critical detuning at which the Bose-Einstein condensate (BEC) is completely depleted. The phases on either side of this quantum phase transition can also be distinguished by the distinct Luttinger constraints on their Fermi surfaces. In both phases, the total volume enclosed by all Fermi surfaces is constrained by the total number of fermions. However, in the phase without the BEC, which has two Fermi surfaces, there is a second Luttinger constraint: the volume enclosed by one of the Fermi surfaces is constrained by the total number of bosons, so that the volumes enclosed by the two Fermi surfaces are separately conserved. The phase with the BEC may have one or two Fermi surfaces, but only their total volume is conserved. We obtain the phase diagram as a function of atomic parameters and temperature, and describe critical fluctuations in the vicinity of all transitions. We make quantitative predictions valid for the case of a narrow Feshbach resonance, but we expect the qualitative features we describe to be more generally applicable. As an aside, we point out intriguing connections between the BEC depletion transition and the transition to the fractionalized Fermi liquid in Kondo lattice models.
We study a one-dimensional gas of fermionic atoms interacting via an s-wave molecular Feshbach resonance. At low energies the system is characterized by two Josephson-coupled Luttinger liquids, corresponding to paired atomic and molecular superfluids. We show that, in contrast to higher dimensions, the system exhibits a quantum phase transition from a phase in which the two superfluids are locked together to one in which, at low energies, quantum fluctuations suppress the Feshbach resonance (Josephson) coupling, effectively decoupling the molecular and atomic superfluids. Experimental signatures of this quantum transition include the appearance of an out-of-phase gapless mode (in addition to the standard gapless in-phase mode) in the spectrum of the decoupled superfluid phase and a discontinuous change in the molecular momentum distribution function.