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arXiv:1105.5700 · Physical Review B

Paired superfluidity and fractionalized vortices in systems of spin-orbit coupled bosons

Chao‐Ming Jian, Hui Zhai

Published Aug 18, 2011• 77 citations
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Abstract

In this Rapid Communication we study finite-temperature properties of spin-$1/2$ interacting bosons with spin-orbit coupling in two dimensions. When the ground state has stripe order, we show that thermal fluctuations will first melt the stripe order and lead to a superfluid of boson pairs if the spin-orbit coupling is isotropic or nearly isotropic. Such a phase supports fractionalized quantum vortices. The Kosterlitz-Thouless transition from superfluid to normal state is driven by proliferation of half vortices. When the ground state is a plane-wave state, the transition to normal state is driven by conventional Kosterlitz-Thouless transition. However, the critical temperature will drop to zero for isotropic spin-orbit coupling.

DOI
10.1103/physrevb.84.060508

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In this Rapid Communication we study finite-temperature properties of spin-1/21/21/2 interacting bosons with spin-orbit coupling in two dimensions. When the ground state has stripe order, we show that thermal fluctuations will first melt the stripe order and lead to a superfluid of boson pairs if the spin-orbit coupling is isotropic or nearly isotropic. Such a phase supports fractionalized quantum vortices. The Kosterlitz-Thouless transition from superfluid to normal state is driven by proliferation of half vortices. When the ground state is a plane-wave state, the transition to normal state is driven by conventional Kosterlitz-Thouless transition. However, the critical temperature will drop to zero for isotropic spin-orbit coupling.
We determine the finite-temperature phase diagram of two-dimensional bosons with two hyperfine (pseudospin) states coupled via a Rashba-Dresselhaus spin-orbit interaction using classical field Monte Carlo calculations. For anisotropic spin-orbit coupling, we find a transition to a Berezinskii-Kosterlitz-Thouless superfluid phase with quasi-long-range order. We show that the spin order of the quasicondensate is driven by the anisotropy of the interparticle interaction, favoring either a homogeneous plane-wave state or stripe phase with broken translational symmetry. Both phases show characteristic behavior in the algebraically decaying spin-density correlation function. For a fully isotropic interparticle interaction, our calculations indicate a fractionalized quasicondensate where the mean-field degeneracy of the plane-wave and stripe phase remains robust against critical fluctuations. In the case of fully isotropic spin-orbit coupling, the circular degeneracy of the single-particle ground state destroys the algebraic ordered phase in the thermodynamic limit, but a crossover remains for finite-size systems.
Experiments on ultracold atoms have started to explore lattice effects and thermal fluctuations for two-component bosons with spin-orbit coupling (SOC). Motivated by this, we derive and study a tJ model for lattice bosons with equal Rashba-Dresselhaus SOC and strong Hubbard repulsion in a uniform Zeeman magnetic field. Using the Gutzwiller ansatz, we find strongly correlated ground states with stripe superfluid (SF) order. We formulate a finite temperature generalization of the Gutzwiller method, and show that thermal fluctuations in the doped Mott insulator drive a two-step melting of the stripe SF, revealing a wide regime of a stripe normal fluid.
Spin-orbit coupling in Bose gases is known to lead to an Ising-symmetry-broken phase where the bosons condense at one of two nonzero momenta. In two dimensions, the finite momentum of the order parameter allows vortex-antivortex pairs that are typically bound in the superfluid phase to freely separate along Ising domain walls. This non-trivial interaction between the superfluid and the Ising order suggests that the critical fluctuations near an Ising transition could drive a Berezinskii-Kosterlitz-Thouless transition of the superfluid. We present numerical evidence of this phenomenon using a Monte Carlo simulation that shows the disappearance of superfluid stiffness near an Ising transition. Additionally, we find numerical evidence that the Ising phase transition becomes first order and we justify this claim with a variational approximation.
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Spin-orbit coupling is predicted to have a dramatic effect on thermal properties of a two-component atomic Bose gas. We show that in three spatial dimensions it lowers the critical temperature of condensation and enhances thermal depletion of the condensate fraction. In two dimensions we show that spin-orbit coupling destroys superfluidity at any finite temperature, modifying dramatically the cerebrated Berezinskii-Kosterlitz-Thouless scenario. We explain this by the increase of the number of low-energy states induced by spin-orbit coupling, enhancing the role of quantum fluctuations.