Effective triangular ladders with staggered flux from spin-orbit coupling in 1D optical lattices
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THE EUROPEAN PHYSICAL JOURNAL D
Regular Article
Effective triangular ladders with staggered flux from spin-orbit coupling in 1D optical lattices? Josep Cabedo1 , Joan Claramunt2,3 , Jordi Mompart1 , Ver`onica Ahufinger1 , and Alessio Celi1,a 1 2 3
Departament de F´ısica, Universitat Aut` onoma de Barcelona, Bellaterra E-08193, Spain Departament de Matem` atiques, Universitat Aut` onoma de Barcelona, Bellaterra E-08193, Spain Departamento de Matem´ atica, Universidade Federal de Santa Catarina, Florian´ opolis SC 88040-900, Brazil Received 2 March 2020 / Received in final form 14 April 2020 Published online 16 June 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 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.
1 Introduction Spin-orbit coupled Bose and Fermi gases both in the bulk or loaded in optical lattices are a flexible playground for studying many-body physics and quantum phase transitions in a controlled manner. By entangling internal and external degrees of freedom the spin-orbit coupling (SOC) produced by Raman beams [1,2] leads already at the single-particle or at the mean-field levels to spatiallydependent dressed states with modified dispersion relation and spatially dependent interactions [3]. Such behavior can be interpreted in terms of a synthetic gauge field [4,5] that can be also density dependent [6]. The successful experimental demonstrations of the last decade of synthetic one-dimensional (1D) and twodimensional (2D) SOC [7–10] have opened interesting perspectives. In the bulk SOC can stabilize exotic phases like the stripe phase [11,12], where translation invariance is spontaneously broken [13], in analogy with supersolids very recently realized in dipolar gases [14–16] (see also [17] for the realization of supersolid-like state in a cavity). Under suitable conditions SOC gives also access to beyond-mean-field dynamics in weakly interacting dilute gases [18] (for experimental demonstrations of beyond?
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