Frustrated two-dimensional XY models with cold atoms in optical lattices

K. Sugimoto

Xiaoyu Zhao, X. W. Lei

Pil Maria Saugmann, Jonas Larson

Abstract In the Hamburg cold atom experiment with orbital states in an optical lattice, s- and p-orbital atomic states hybridize between neighboring sites. In this work we show how this alternation of sites hosting s- and p-orbital states gives rise to a plethora of different magnetic phases, quantum and classical. We focus on phases whose properties derive from frustration originating from a competition between nearest and next nearest neighboring exchange interactions. The physics of the Mott insulating phase with unit filling is described by an effective spin-1/2 Hamiltonian showing great similarities with the J 1–J 2 model. Based on the knowledge of the J 1–J 2 model, supported by numerical simulations, we discuss the possibility of a quantum spin liquid phase in the present optical lattice system. In the superfluid regime we consider the parameter regime where the s-orbital states can be adiabatically eliminated to give an effective model for the p-orbital atoms. At the mean-field level we derive a generalized classical XY model, and show that it may support maximum frustration. When quantum fluctuations can be disregarded, the ground state should be a spin glass.

W. Zwerger

William D. Phillips

Subroto Mukerjee

The realization of optical lattices of cold atoms has opened up the possibility of engineering interacting lattice systems of bosons and fermions, stimulating a frenzy of research over the last decade. More recently, experimental techniques have been developed to apply synthetic gauge fields to these optical lattices. As a result, it has become possible to study quantum Hall physics and the effects of frustration in lattices of cold atoms. In this article we describe the combined effect of frustration and interactions on the superfluidity of bosons. By focussing on a frustrated ladder of interacting bosons, we show that the effect of frustration is for ``chiral'' order to develop, which manifests itself as an alternating pattern of circulating supercurrents. Remarkably, this order persists even when superfluidity is lost and the system enters a Mott phase giving rise to a novel chiral Mott insulator. We describe the combined physics of frustration and interactions by studying a fully frustrated one dimensional model of interacting bosons. The model is studied using mean-field theory, a direct quantum simulation and a higher dimensional classical theory in order to offer a full description of the different quantum phases contained in it and transitions between the different phases. In addition, we provide physical descriptions of the chiral Mott insulator as a vortex-anitvortex super solid and indirect excitonic condensate in addition to obtaining a variational wavefunction for it. We also briefly describe the chiral Mott states arising in other microscopic models.