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 Zhai et al (2013 Phys. Rev. A 87 063638), 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 -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 anti-symmetric spin interactions that can give rise to novel effects like spin canting.
Highlights
Interest in systems of cold atoms in optical lattices has greatly increased during the last decade [1] partly because of their versatility as simulators of quantum systems
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
The depopulation of the dxy orbital does not derive from such a spurious effect, but instead, it appears together with the self-consistent minimization of the full energy functional, that includes both the interacting and tunneling processes simultaneously. This means, that the combined knowledge of onsite properties with additional considerations accounting for effects of the tunneling—as one usually proceeds for studying the system in the p band, is not enough to determine the physics in the d band
Summary
Using the Gutzwiller ansatz for the three d band author(s) and the title of the work, journal citation orbitals we map the boundaries of the Mott insulating phases. 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 breaks a discrete 2 -symmetry. We further derive an effective spin-1/2 model that describe the relevant physics of the lowest Mott-phase with unit filling. We explain how to generate anti-symmetric spin interactions that can give rise to novel effects like spin canting
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