Evolution of magnetic structure driven by synthetic spin-orbit coupling in a two-component Bose-Hubbard model

Abstract

We study the evolution of magnetic structure driven by a synthetic spin-orbit coupling in a one-dimensional two-component Bose-Hubbard model. In addition to the Mott insulator-superfluid transition, we found in Mott insulator phases a transition from a gapped ferromagnetic phase to a gapless chiral phase by increasing the strength of spin-orbit coupling. Further increasing the spin-orbit coupling drives a transition from the gapless chiral phase to a gapped antiferromagnetic phase. These magnetic structures persist in superfluid phases. In particular, in the chiral Mott insulator and chiral superfluid phases, incommensurability is observed in characteristic correlation functions. These unconventional Mott insulator phase and superfluid phase demonstrate the novel effects arising from the competition between the kinetic energy and the spin-orbit coupling.

Topological phases in spin-orbit-coupled dipolar lattice bosons

“…We have four degenerate states for the two neighboring sites, i.e., |I f ,0 f >|0f+1, lf+1 >, |1 -,0 f)|lf+1,0f+ l), and Sf = (bjbj -aja,)/2. With the use of the second-order perturbation theory, the effective Hamiltonian that describes the tunnel and SO couplings is written as [26,27] where X = 2J2/Uab and A -eb -ea. The last terms in Eq.…”

“…Indeed, dipolar interactions in ultracold atom ic gases can give rise to spectacular quantum phenom ena [18] such as spin texture [19] and the Einstein-de Haas effect [20], In addition, a chrom ium gas in an optical lattice [21,22] has recently been realized. Since a chrom ium atom has a relatively large m agnetic dipole m om ent [23], the intersite interactions becom e strong enough [22] to allow experim ental study of quantum m agnetism [24], In this paper, w e consider SO -coupled bosonic atom s in a ID optical lattice, w here the atom s at the different sites couple to each other via m agnetic dipolar interactions [22], In the M ott-insulating regim e, this system can be described by the quantum X Y Z spin m odel w ith D zyaloshinskii-M oriya [25][26][27], w here a tw o-com ponent boson at each site can be viewed as a sp in -1 /2 particle [28]. Indeed, a spin chain is equivalent to a ID spinless ferm ion model upon the perform ance o f the Jordan-W igner transform ation [29], This enables us to study topological phenom ena, such as M ajorana ferm ions, w ith a quantum spin chain [29,30].…”

Thermodynamics of a spin-12XYZ Heisenberg chain with a Dzyaloshinskii-Moriya interaction

“…However, when U ′ ≠ U , the DM interaction cannot be simply eliminated 25 and several phases have been predicted. For U ′ > U , there are a gapped FM phase, a gapped AF phase, and in between a TLL phase with a chiral order [26][27][28] (without ambiguity, we will call it TLL phase below). The transition from the FM (AF) phase to the TLL phase is of first order 27,29 .…”

“…Recently, a synthetic spin-orbit coupling (SOC), or equivalently, gauge field, was successfully realized in experiments and a variety of phases as well as phase transitions were observed [15][16][17][18] . These experiments have spurred great interest in studying the artificial SOC as well as gauge field in ultracold systems [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] . In the deep insulating region, such an SOC can be approximated 21,26 by the Dzyaloshinskii-Moriya (DM) interaction 35,36 .…”

“…The Hamiltonian (2), or equivalently Hamiltonian (1) at unit filling in the strong coupling limit, has been studied by several groups using density-matrix renormalization group (DMRG) method in combination with some analytic methods [25][26][27][28][29] . For U ′ = U , the DM interaction can be eliminated by a site-dependent rotation of the spin operators, resulting in an isotropic Heisenberg chain with FM coupling 20 .…”