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arXiv:cond-mat/0303550 · Physical Review Letters

Instabilities in Binary Mixtures of One-Dimensional Quantum Degenerate Gases

Miguel A. Cazalilla, A. F. Ho

Published Oct 8, 2003• 169 citations
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Abstract

We show that one-dimensional binary mixtures of bosons or of a boson and a spin-polarized fermion are Luttinger liquids with the following instabilities: (i) For different particle densities, strong attraction between the mixture components leads to collapse, while strong repulsion leads to demixing, and (ii) For a low-density mixture of two gases of impenetrable bosons (or a spin-polarized fermion and an impenetrable boson) of equal densities, the system develops a gap and exhibits enhanced pairing fluctuations when there is attraction between the components. In the boson-fermion mixture, the pairing fluctuations occur at finite momentum. Our conclusions apply to mixtures both on the continuum and on optical lattices away from integer or fractional commensurability.

DOI
10.1103/physrevlett.91.150403

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We show that one-dimensional binary mixtures of bosons or of a boson and a spin-polarized fermion are Luttinger liquids with the following instabilities: (i) For different particle densities, strong attraction between the mixture components leads to collapse, while strong repulsion leads to demixing, and (ii) For a low-density mixture of two gases of impenetrable bosons (or a spin-polarized fermion and an impenetrable boson) of equal densities, the system develops a gap and exhibits enhanced pairing fluctuations when there is attraction between the components. In the boson-fermion mixture, the pairing fluctuations occur at finite momentum. Our conclusions apply to mixtures both on the continuum and on optical lattices away from integer or fractional commensurability.
We study numerically and analytically the phases of a mixture of ultracold bosons and spin-polarized fermions in a one-dimensional lattice. In particular, along a symmetry plane in the parameter space, we obtain the exact boundary of the boson-demixing transition from the Bethe ansatz solution of the standard Hubbard model. For a region of parameter space, we prove the existence of boson-fermion mixed phase at all densities. This phase is a two-component Luttinger liquid for weak couplings or for incommensurate total density, otherwise it has a charge gap but retains a gapless mode of mixture composition fluctuations. We show that the static density correlations in these two regimes are markedly different.
We study numerically and analytically the phases of a mixture of ultracold bosons and spin-polarized fermions in a one-dimensional lattice. In particular, along a symmetry plane in the parameter space, we obtain the exact boundary of the boson-demixing transition from the Bethe ansatz solution of the standard Hubbard model. For a region of parameter space, we prove the existence of boson-fermion mixed phase at all densities. This phase is a two-component Luttinger liquid for weak couplings or for incommensurate total density, otherwise it has a charge gap but retains a gapless mode of mixture composition fluctuations. We show that the static density correlations in these two regimes are markedly different.
We combine model mapping, exact spectral bounds, and a quantum Monte Carlo method to study the ground state phases of a mixture of ultracold bosons and spin-polarized fermions in a one-dimensional optical lattice. The exact boundary of the boson-demixing transition is obtained from the Bethe Ansatz solution of the standard Hubbard model. We prove that along a symmetry plane in the parameter space, the boson-fermion mixed phase is stable at all densities. This phase is a two-component Luttinger liquid for weak couplings or for incommensurate total density, otherwise it has a charge gap but retains a gapless mode of mixture composition fluctuations. The static density correlations are studied in these two limits and shown to have markedly different features.
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 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 consider a mixture of single-component bosonic and fermionic atoms in an array of coupled one-dimensional "tubes." For an attractive Bose-Fermi interaction, we show that the system exhibits phase separation instead of the usual collapse. Moreover, above a critical intertube hopping, all first-order instabilities disappear in both attractive and repulsive mixtures. The possibility of suppressing instabilities in this system suggests a route towards the realization of paired phases, including a superfluid of p-wave pairs unique to the coupled-tube system, and quantum critical phenomena.