Regular Article

Effective triangular ladders with staggered flux from spin-orbit coupling in 1D optical lattices^★

¹ Departament de Física, Universitat Autònoma de Barcelona, Bellaterra E-08193, Spain
² Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra E-08193, Spain
³ Departamento de Matemática, Universidade Federal de Santa Catarina, Florianópolis SC 88040-900, Brazil

^a e-mail: alessio.celi@uab.cat

Received: 2 March 2020
Received in final form: 14 April 2020
Published online: 16 June 2020

Abstract

Light-induced spin-orbit coupling is a flexible tool to study quantum magnetism with ultracold atoms. In this work we show that spin-orbit coupled Bose gases in a one-dimensional optical lattice can be mapped into a two-leg triangular ladder with staggered flux following a lowest-band truncation of the Hamiltonian. The effective flux and the ratio of the tunneling strengths can be independently adjusted to a wide range of values. We identify a certain regime of parameters where a hard-core boson approximation holds and the system realizes a frustrated triangular spin ladder with tunable flux. We study the properties of the effective spin Hamiltonian using the density-matrix renormalization-group method and determine the phase diagram at half-filling. It displays two phases: a uniform superfluid and a bond-ordered insulator. The latter can be stabilized only for low Raman detuning. Finally, we provide experimentally feasible trajectories across the parameter space of the SOC system that cross the predicted phase transition.