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arXiv:1403.3491 · Physical Review A

Mott-superfluid transition for spin-orbit-coupled bosons in one-dimensional optical lattices

Zhihao Xu, William S. Cole, Shizhong Zhang

Published May 22, 2014• 40 citations
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Abstract

We study the effects of spin-orbit coupling on the Mott-superfluid transition of bosons in a one-dimensional optical lattice. We determine the strong-coupling magnetic phase diagram by a combination of exact analytic and numerical means. Smooth evolution of the magnetic structure into the superfluid phases is investigated with the density matrix renormalization group technique. Other magnetic phases are seen and phase transitions between them within the superfluid regime are discussed. Possible experimental detection is discussed.

DOI
10.1103/physreva.89.051604

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In this review, we discuss the physics of spin-orbit coupled quantum gases in optical lattices. After reviewing some relevant experimental techniques, we introduce the basic theoretical model and discuss some of its generic features. In particular, we concentrate on the interplay between spin-orbit coupling and strong interactions and show how it leads to various exotic quantum phases in both the Mott insulating and superfluid regimes. Phase transitions between the Mott and superfluid states are also discussed.
Mott insulator to superfluid phase transitions and unconventional superfluid phases in spin-orbit coupled Bose-Einstein condensate in one dimensional, square and hexagonal optical lattices are investigated using decoupling approximation and variational Gutzwiller wave function. We considered a system with two components. In the first part, we used decoupling approximation along side perturbation to chart the phase diagrams of the system in the absence of spin-orbit coupling. Our results show that the occupation number of the species, interspecies interaction and the ratio of the hopping matrix of the species dictate the critical point and the separation of the insulating phases. Applying decoupling approximation to spin-orbit coupled Bose-Einstein condensate in one dimensional optical we find that spin-orbit coupling reduces the phase boundary of Mott insulator-superfluid transition and also modifies the critical point in a way that the critical point reduces as the coupling strength increases. In the second part, we applied the variational Gutzwiller wave function to spin-orbit coupled Bose-Einstein condensate in square and hexagonal lattice. Our results show that the geometry of the optical lattice plays a role in the transition. We find that the mean-field Mott insulator-superfluid phase transition boundary of hexagonal lattice is smaller than that of square lattice for the same system. Finally, we showed that the Gutzwiller variational approach gives us access to the twisted superfluid phase realized in the system. The nonuniformity of the superfluid phase is different for the two lattices.
We investigate magnetic properties in the superfluid and Mott-insulating states of two-component bosons with spin-orbit (SO) coupling in two-dimensional square optical lattices. The spin-independent hopping integral ttt and SO coupled one $\ensuremath{\lambda}$ are fitted from band-structure calculations in the continuum, which exhibit oscillations with increasing SO coupling strength. The magnetic superexchange model is derived in the Mott-insulating state with one particle per site, characterized by the Dzyaloshinsky-Moriya interaction. In the limit of $|\ensuremath{\lambda}|\ensuremath{\ll}|t|$, we find a spin spiral Mott state whose pitch value is the same as that in the incommensurate superfluid state, while in the opposite limit $|t|\ensuremath{\ll}|\ensuremath{\lambda}|$, the ground state exhibits a $2\ifmmode\times\else\texttimes\fi{}2$ in-plane spin pattern.
We study the Bose-Hubbard model using the finite size density matrix renormalization group method. We obtain a complete phase diagram for a system in the presence of a harmonic trap and compare it with that of the homogeneous system. The superfluid to the Mott-insulator phase transition is investigated using different experimental signatures of these phases in quantities such as momentum distribution, visibility, condensate fraction, and the total number of bosons at a particular density. The relationships between the various experimental signatures and the phase diagram are highlighted.