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arXiv:0911.3157 · Physical Review A

Spontaneous population imbalance in two-component Bose and Fermi gases

Shintaro Takayoshi, Masahiro Sato, Shunsuke Furukawa

Published May 10, 2010• 19 citations
arXivHTMLPDF

Abstract

We study two-component (or pseudo-spin-$\frac{1}{2}$) Bose or Fermi gases in one dimension, in which particles are convertible between the components. Through bosonization and numerical analyses of a simple lattice model, we demonstrate that, in such gases, a strong intercomponent repulsion induces spontaneous population imbalance between the components, namely, the ferromagnetism of the pseudo spins. The imbalanced phase contains gapless charge excitations characterized as a Tomonaga-Luttinger liquid and gapped spin excitations. We uncover a crucial effect of the intercomponent particle hopping on the transition to the imbalanced phase. In the absence of this hopping, the transition is of first order. At the transition point, the energy spectrum reveals certain degeneracy indicative of an emergent $\text{SU}(2)$ symmetry. With an infinitesimal intercomponent hopping, the transition becomes of Ising type. We determine the phase diagram of the model accurately and test the reliability of the weak-coupling bosonization formalism.

DOI
10.1103/physreva.81.053606

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We study the effect of the synthetic spin-orbit coupling in a two-component Bose-Hubbard model in one dimension by employing the density-matrix renormalization group method. A ferromagnetic long-range order emerges in both Mott-insulator and superfluid phases resulting from the spontaneous breaking of the Z2{Z}_{2}Z2​ symmetry, when the spin-orbit coupling term becomes comparable to the hopping kinetic energy and the intercomponent interaction is smaller than the intracomponent one as well. This effect is expected to be detectable with the present realization of the synthetic spin-orbit coupling in experiments.
We numerically determine the very rich phase diagram of mass-imbalanced binary mixtures of hardcore bosons (or equivalently —fermions, or hardcore Bose/Fermi mixtures) loaded in one-dimensional optical lattices. Focusing on commensurate fillings away from half-filling, we find a strong asymmetry between attractive and repulsive interactions. Attraction is found to always lead to pairing, associated with a spin gap, and to pair crystallization for very strong mass imbalance. In the repulsive case the two atomic components remain instead fully gapless over a large parameter range; only a very strong mass imbalance leads to the opening of a spin gap. The spin-gap phase is the precursor of a crystalline phase occurring for an even stronger mass imbalance. The fundamental asymmetry of the phase diagram is at odds with recent theoretical predictions, and can be tested directly via time-of-flight experiments on trapped cold atoms.
We focus on three-component SU(3) Fermi gases loaded into a square optical lattice, with population imbalance between one component and the others.At strong coupling the system is described by the SU(3) Heisenberg model with an external field that couples to the population imbalance.We discuss the ground state at the mean-field level and then analyze the thermal fluctuations with the semiclassical Monte Carlo method.The interplay of interactions, population imbalance, and thermal fluctuations gives rise to a phase transition linked to the breaking of an emergent Ising symmetry, despite the absence of frustration.This represents another scenario of discrete symmetry breaking in low-dimensional systems with continuous symmetries.Possible implementations with cold alkaline-earth(-like) atoms are discussed.
The ground-state properties of two-component repulsive Fermi gases in two dimensions are investigated by means of fixed-node diffusion Monte Carlo simulations. The energy per particle is determined as a function of the intercomponent interaction strength and of the population imbalance. The regime of universality in terms of the sss-wave scattering length is identified by comparing results for hard-disk and for soft-disk potentials. In the large imbalance regime, the equation of state turns out to be well described by a Landau-Pomeranchuk functional for two-dimensional polarons. To fully characterize this expansion, we determine the polarons' effective mass and their coupling parameter, complementing previous studies on their chemical potential. Furthermore, we extract the magnetic susceptibility from low-imbalance data, finding only small deviations from the mean-field prediction. While the mean-field theory predicts a direct transition from a paramagnetic to a fully ferromagnetic phase, our diffusion Monte Carlo results suggest that the partially ferromagnetic phase is stable in a narrow interval of the interaction parameter. This finding calls for further analyses on the effects due to the fixed-node constraint.
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 phase diagram of population balanced and imbalanced ultracold atomic Fermi gases with a short-range attractive interaction throughout the crossover from BCS to Bose-Einstein condensation (BEC), in a two-dimensional (2D) optical lattice comprised of a 2D array of 1D lines. We find that the mixing of lattice and continuum dimensions, together with population imbalance, has an extraordinary effect on pairing and the superfluidity of atomic Fermi gases. In the balanced case, the superfluid ground state prevails over the majority of the phase space. However, for relatively small lattice hopping integral ttt and large lattice constant ddd, a pair density wave (PDW) emerges unexpectedly at intermediate coupling strength, and the nature of the in-plane and overall pairing changes from particlelike to holelike in the BCS and unitary regimes, associated with an abnormal increase in the Fermi volume with the pairing strength. In the imbalanced case, the stable polarized superfluid phase shrinks to only a small portion of the entire phase space spanned by t,dt, dt,d, imbalance ppp, and interaction strength UUU, mainly in the bosonic regime of low ppp, moderately strong pairing, relatively large ttt, and small ddd. Due to the Pauli exclusion between paired and excessive fermions within the confined momentum space, a PDW phase emerges and the overall pairing evolves from particlelike into holelike, as the pairing strength grows stronger in the BEC regime. In both cases, the ground-state property is largely governed by the Fermi surface topology. These findings are very different from the cases of a pure 3D continuum, a 3D lattice, or a 1D optical lattice.