Abstract
We theoretically study dilute superfluidity of spin-1 bosons with antiferromagnetic interactions and synthetic spin-orbit coupling (SOC) in a one-dimensional lattice. Employing a combination of density matrix renormalization group and quantum field theoretical techniques we demonstrate the appearance of a robust superfluid spin-liquid phase in which the spin-sector of this spinor Bose-Einstein condensate remains quantum disordered even after introducing quadratic Zeeman and helical magnetic fields. Despite remaining disordered, the presence of these symmetry breaking fields lifts the perfect spin-charge separation and thus the nematic correlators obey power-law behavior. We demonstrate that, at strong coupling, the SOC induces a charge density wave state that is not accessible in the presence of linear and quadratic Zeeman fields alone. In addition, the SOC induces oscillations in the spin and nematic expectation values as well as the bosonic Green's function. These non-trivial effects of a SOC are suppressed under the application of a large quadratic Zeeman field. We discuss how our results could be observed in experiments on ultracold gases of $^{23}$Na in an optical lattice.
Highlights
Ultracold gases of spin-1 bosons offer an exciting platform to understand the interplay of superfluidity and magnetism [1,2]
Introducing a quadratic Zeeman field and a transverse magnetic field in this regime we interestingly find that the spin sector remains quantum disordered in a remarkably robust spin-liquid phase
We focus on the spin-1 Bose Hubbard model in the presence of a quadratic Zeeman field and an spin-orbit coupling (SOC)
Summary
Ultracold gases of spin-1 bosons offer an exciting platform to understand the interplay of superfluidity and magnetism [1,2]. With the development of artificial gauge fields in ultracold atoms, it is possible to couple the internal hyperfine spin states to their momentum through an engineered spin-orbit coupling (SOC) [5,6] This has been realized in gases of fermions [7] or bosons [8,9,10,11,12] with an SOC in one and two dimensions [13,14,15,16]. In the presence of a full SOC, the ground state displays superfluidity at zero and nonzero momenta concomitant with the existence of a strong coupling charge density wave oscillating at the bosonic particle density This imprints strong density oscillations in the nematic correlation function and the von Neumann entanglement entropy. The detailed derivation of the field theory is exposed in Appendix A (effective field theory Hamiltonian), Appendix B (contribution of phase slips), and Appendix C (reduction of Luttinger parameter)
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