Phases of d-orbital bosons in optical lattices

TL;DR

This paper investigates the phases of bosonic atoms in d orbitals of an optical lattice, revealing vortex lattice superfluidity, symmetry breaking, and complex magnetic interactions through theoretical modeling.

Contribution

It presents a theoretical analysis of d-band bosons in optical lattices, including phase boundaries, vortex lattice formation, and effective spin models, building on recent experimental advancements.

Findings

Identification of vortex/anti-vortex pairs in superfluid phase

Spontaneous breaking of time-reversal and Z2 symmetries

Proposal of effective spin-1/2 models with complex interactions

Abstract

We explore the properties of bosonic atoms loaded into the d bands of an isotropic square optical lattice. Following the recent experimental success reported in [Y. Zhai et al., Phys. Rev. A 87, 063638 (2013)], in which populating d bands with a 99% fidelity was demonstrated, we present a theoretical study of the possible phases that can appear in this system. Using the Gutzwiller ansatz for the three d band orbitals we map the boundaries of the Mott insulating phases. For not too large occupation, two of the orbitals are predominantly occupied, while the third, of a slightly higher energy, remains almost unpopulated. In this regime, in the superfluid phase we find the formation of a vortex lattice, where the vortices come in vortex/anti-vortex pairs with two pairs locked to every site. Due to the orientation of the vortices time-reversal symmetry is spontaneously broken. This state also breaks a discrete Z2-symmetry. We further derive an effective spin-1/2 model that describe the relevant physics of the lowest Mott-phase with unit filling. We argue that the corresponding two dimensional phase diagram should be rich with several different phases. We also explain how to generate antisymmetric spin interactions that can give rise to novel effects like spin canting.