Topological phases of shaken quantum Ising lattices

TL;DR

This paper demonstrates how to simulate topological phases of the quantum compass model using shaken quantum Ising lattices, enabling experimental exploration of topological degeneracy with current atomic systems.

Contribution

It introduces a method to realize the quantum compass model via photon-assisted tunneling in quantum Ising systems, facilitating topological phase studies in experimental setups.

Findings

Successful adiabatic preparation of degenerate ground states

Validation through exact diagonalizations for small lattices

Proposals for implementation with ultracold and Rydberg atoms

Abstract

The quantum compass model consists of a two-dimensional square spin lattice where the orientation of the spin-spin interactions depends on the spatial direction of the bonds. It has remarkable symmetry properties and the ground state shows topological degeneracy. The implementation of the quantum compass model in quantum simulation setups like ultracold atoms and trapped ions is far from trivial, since spin interactions in those sytems typically are independent of the spatial direction. Ising spin interactions, on the contrary, can be induced and controlled in atomic setups with state-of-the art experimental techniques. In this work, we show how the quantum compass model on a rectangular lattice can be simulated by the use of the photon-assisted tunneling induced by periodic drivings on a quantum Ising spin model. We describe a procedure to adiabatically prepare one of the doubly-degenerate ground states of this model by adiabatically ramping down a transverse magnetic field, with surprising differences depending on the parity of the lattice size. Exact diagonalizations confirm the validity of this approach for small lattices. Specific implementations of this scheme are presented with ultracold atoms in optical lattices in the Mott insulator regime, as well as with Rydberg atoms.