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arXiv:cond-mat/0507513 · Physical Review Letters

Spin Waves in a One-Dimensional Spinor Bose Gas

Jean-Noël Fuchs, Dimitri M. Gangardt, Tassilo Keilmann, Gora V. Shlyapnikov

Published Oct 4, 2005• 105 citations
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Abstract

We study a one-dimensional (iso)spin 1/2 Bose gas with repulsive delta-function interaction by the Bethe Ansatz method and discuss the excitations above the polarized ground state. In addition to phonons the system features spin waves with a quadratic dispersion. We compute analytically and numerically the effective mass of the spin wave and show that the spin transport is greatly suppressed in the strong coupling regime, where the isospin-density (or "spin charge") separation is maximal. Using a hydrodynamic approach, we study spin excitations in a harmonically trapped system and discuss prospects for future studies of two-component ultracold atomic gases.

DOI
10.1103/physrevlett.95.150402

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We study a one-dimensional (iso)spin 1/2 Bose gas with repulsive delta-function interaction by the Bethe Ansatz method and discuss the excitations above the polarized ground state. In addition to phonons the system features spin waves with a quadratic dispersion. We compute analytically and numerically the effective mass of the spin wave and show that the spin transport is greatly suppressed in the strong coupling regime, where the isospin-density (or "spin charge") separation is maximal. Using a hydrodynamic approach, we study spin excitations in a harmonically trapped system and discuss prospects for future studies of two-component ultracold atomic gases.
The exact solutions of a one-dimensional mixture of spinor bosons and spinor fermions with δ-function interactions are studied. Some new sets of Bethe ansatz equations are obtained by using the graded nest quantum inverse scattering method. Many interesting features appear in the system. For example, the wave function has the SU(2|2) supersymmetry. It is also found that the ground state of the system is partial polarized, where the fermions form a spin singlet state and the bosons are totally polarized. From the solution of Bethe ansatz equations, it is shown that all the momentum, spin and isospin rapidities at the ground state are real if the interactions between the particles are repulsive; while the fermions form two-particle bounded states and the bosons form one large bound state, which means the bosons condensed at the zero momentum point, if the interactions are attractive. The charge, spin and isospin excitations are discussed in detail. The thermodynamic Bethe ansatz equations are also derived and their solutions at some special cases are obtained analytically.
We investigate the propagation of spin waves in two-component mixtures of one-dimensional Bose gases interacting through repulsive contact potentials. By using quantum Monte Carlo methods we calculate static ground-state properties, such as the spin susceptibility and the spin structure factor, as a function of the coupling strengths and we determine the critical parameters for phase separation. In homogeneous mixtures, results of the velocity of spin waves and of its softening close to the critical point of phase separation are obtained by means of hydrodynamic theory and a sum-rule approach. We quantify the nondissipative drag effect, resulting from the Andreev-Bashkin current-current interaction between the two components of the gas, and we show that in the regime of strong coupling it causes a significant suppression of the spin-wave velocity.
We study the interplay of quantum statistics, strong interactions, and finite temperatures in the two-component (spinor) Bose gas with repulsive delta-function interactions in one dimension. Using the Thermodynamic Bethe Ansatz, we obtain the equation of state, population densities, and local density correlation numerically as a function of all physical parameters (interaction, temperature, and chemical potentials), quantifying the full crossover between low-temperature ferromagnetic and high-temperature unpolarized regimes. In contrast to the single component, Lieb-Liniger gas, nonmonotonic behavior of the local density correlation as a function of temperature is observed.
We propose the density-functional theory for one-dimensional harmonically trapped spin-1 bosons in the ground state with repulsive density-density interaction and antiferromagnetic spin-exchange interaction. The density distributions of spin-singlet-paired bosons and polarized bosons with different total polarization for various interaction parameters are obtained by solving the Kohn-Sham equations, which are derived based on the local density approximation and the Bethe ansatz exact results for a homogeneous system. Nonmonotonicity of the central densities is attributed to the competition between the density interaction and spin-exchange. The results reveal the phase separation of the paired and polarized bosons, the density profiles of which respectively approach the Tonks-Girardeau gases of Bose-Bose pairs and scalar bosons in the case of strong interaction. We give the radius-polarization phase diagram at strong interaction and find the critical polarization, which paves the way to directly observe the exotic singlet pairing in spinor gas experimentally.
We consider a gas of fermions with parabolic dispersion and N spin components (or spin S, N=2S+1) with SU(N) symmetry in one dimension interacting via a delta -function potential. The model is integrable and its solution has been obtained by Sutherland in terms of N nested Bethe ansatze. The ground-state Bethe ansatz integral equations are solved numerically for both repulsive and attractive interactions to obtain the energy, the chemical potential, and the magnetic susceptibility as a function of the band filling and the interaction strength. For the repulsive interaction the Fermi gas has the properties of a Luttinger liquid. In the attractive case, on the other hand, the fermions in the ground-state form bound states of up to N fermions of different spin components. The spectrum of elemental charge and spin excitations is derived for the repulsive and attractive situations. The spectrum is discussed in the limits of vanishing interaction strength and very strong coupling. For the repulsive interaction the low-lying charge excitations can be characterized by the Fermi momentum and the Fermi velocity. The range of the spin-wave excitations is correlated with the Fermi momentum of the charges. The spin wave velocity is inversely proportional to the magnetic susceptibility. The spin-wave excitations become soft in the infinite-repulsive-coupling limit. In the attractive case in zero field all excitation branches except that of bound states of N fermions have an energy gap. It requires a finite energy to break these bound states and hence there is no response to a field smaller than a critical field. The low-T specific heat is proportional to the temperature.
The ground and excited states of a one-dimensional (1D) spin-1/2 Fermi gas (SFG) with both attractive zero-range odd-wave interactions and repulsive zero-range even-wave interactions are mapped exactly to a 1D Lieb-Liniger-Heisenberg (LLH) model with delta-function repulsions depending on isotropic Heisenberg spin-spin interactions, such that the complete SFG and LLH energy spectra are identical. The ground state in the ferromagnetic phase is given exactly by the Lieb-Liniger (LL) Bethe ansatz, and that in the antiferromagnetic phase by a variational method combining Bethe ansatz solutions of the LL and 1D Heisenberg models. There are excitation branches corresponding to LL type I and II phonons and spin waves, the latter behaving quadratically for small wave numbers in the ferromagnetic phase and linearly in the antiferromagnetic phase.