The physics of one-dimensional interacting bosonic systems is reviewed. Beginning with results from exactly solvable models and computational approaches, the concept of bosonic Tomonaga-Luttinger liquids relevant for one-dimensional Bose fluids is introduced, and compared with Bose-Einstein condensates existing in dimensions higher than one. The effects of various perturbations on the Tomonaga-Luttinger liquid state are discussed as well as extensions to multicomponent and out of equilibrium situations. Finally, the experimental systems that can be described in terms of models of interacting bosons in one dimension are discussed.

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One dimensional bosons: From condensed matter systems to ultracold gases

This article reviews theoretical and experimental developments for one-dimensional Fermi gases. Specifically, the experimentally realized two-component delta-function interacting Fermi gas-the Gaudin-Yang model-and its generalizations to multicomponent Fermi systems with larger spin symmetries is discussed. The exact results obtained for Bethe ansatz integrable models of this kind enable the study of the nature and microscopic origin of a wide range of quantum many-body phenomena driven by spin population imbalance, dynamical interactions, and magnetic fields. This physics includes Bardeen-Cooper-Schrieffer-like pairing, Tomonaga-Luttinger liquids, spin-charge separation, Fulde-Ferrel-Larkin-Ovchinnikov-like pair correlations, quantum criticality and scaling, polarons, and the few-body physics of the trimer state (trions). The fascinating interplay between exactly solved models and experimental developments in one dimension promises to yield further insight into the exciting and fundamental physics of interacting Fermi systems.

Fermi gases in one dimension: From Bethe ansatz to experiments

We present a density-functional theory for the one-dimensional harmonically trapped Bose-Fermi mixture with repulsive contact interactions. The ground-state density distribution of each component is obtained by solving the Kohn-Sham equations numerically based on the local density approximation and the exact solution for the homogeneous system given by Bethe ansatz method. It is shown that for sufficiently strong interaction, a considerable amount of fermions are repelled out of the central region of the trap, exhibiting partial phase separation of Bose and Fermi components. Oscillations emerge in the Bose density curves, reflecting the strong correlation with fermions. For infinitely strong interaction, the ground-state energy of the mixture and the total density are consistent with the scenario that all atoms in the mixture are fully fermionized.

Density-functional theory for one-dimensional harmonically trapped Bose-Fermi mixture

We derive an analytic expression for the zero temperature Fourier transform of the density-density correlation function of a multicomponent Luttinger liquid with different velocities. By employing Schwinger identity and a generalized Feynman identity exact integral expressions are derived, and approximate analytical forms are given for frequencies close to each component singularity. We find power-like singularities and compute the corresponding exponents. Numerical results are shown for the case of three components.

Response functions in multicomponent Luttinger liquids

Exploratory simulations of Bose-Fermi mixtures on the three-dimensional optical lattice at finite temperature are performed by adopting the lattice quantum chromodynamics technique. We analyze the bosonic superfluid transition and its dependence on the strength of the boson-fermion coupling. The particle densities and the pair occupancies are also studied to understand the effect of the boson-fermion coupling to the microscopic properties of the system. The effect of the induced fermion-fermion interaction by the boson density fluctuation is clearly seen.

Quantum Monte Carlo simulation of three-dimensional Bose-Fermi mixtures

Mixing-demixing transition in one-dimensional mixtures of fermions and bosons is numerically investigated by changing various parameters such as number densities of each component, fermion-boson interactions, boson-boson interactions, and hopping energies. In most cases we found clear evidence of the mixing-demixing transitions and identified the roles of each microscopic parameter in the transitions. Several phase diagrams were obtained.

Mixing-demixing transition in one-dimensional boson-fermion mixtures

We numerically investigated Mott transitions and mixing-demixing transitions in one-dimensional boson-fermion mixtures at a commensurate filling. The mixing-demixing transition occurred in a qualitatively similar manner to the incommensurate filling case. We also found the Mott insulator phase appeared in both the mixing and the demixing states as the fermion-boson interaction or the boson-boson interaction increased. Phase diagrams were obtained in the interaction parameter space.

Mott transition in one-dimensional boson-fermion mixtures

We numerically investigated Mott transitions and mixing-demixing transitions in one-dimensional boson-fermion mixtures at a commensurate filling. The mixing-demixing transition occurred in a qualitatively similar manner to incommensurate filling cases. We also found the Mott insulator phase appeared in both the mixing and the demixing states as the fermion-boson interaction or the boson-boson interaction increased. Phase diagrams were obtained in interaction parameter space.

We numerically investigated the collapse of one-dimensional boson–fermion mixtures with fermion–boson attractive interactions. With Monte Carlo simulations, we observed spatial distributions of the...

Collapse in Boson–Fermion Mixtures of Cold Atoms Trapped in One-Dimensional Space

We numerically investigated the mixing-demixing transition of the boson-fermion mixture on a 1D lattice at an incommensurate filling with the fermion density being kept below the boson density. The phase diagram we obtained suggested that the decrease of the number of the fermions drove the system into the demixing phase.

Yousuke Takeuchi

Papers

Mixing-demixing transition in one-dimensional boson-fermion mixtures

Mott transition in one-dimensional boson-fermion mixtures

Mott transition in one-dimensional boson-fermion mixtures

Collapse in Boson–Fermion Mixtures of Cold Atoms Trapped in One-Dimensional Space

Mixing-Demixing Transition in 1D Boson-Fermion Mixture at Low Fermion Densities