Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices

TL;DR

This paper reports the experimental realization of the Hofstadter Hamiltonian using ultracold atoms in optical lattices, enabling simulation of magnetic fields and quantum spin Hall effects in a controllable quantum system.

Contribution

The authors demonstrate a novel method to generate large, tunable artificial magnetic fields with ultracold atoms, implementing the Hofstadter model and quantum spin Hall effect in optical lattices.

Findings

Successful creation of homogeneous artificial magnetic fields

Observation of cyclotron orbits indicating flux distribution

Realization of time-reversal symmetric Hamiltonian for quantum spin Hall effect

Abstract

We demonstrate the experimental implementation of an optical lattice that allows for the generation of large homogeneous and tunable artificial magnetic fields with ultracold atoms. Using laser-assisted tunneling in a tilted optical potential we engineer spatially dependent complex tunneling amplitudes. Thereby atoms hopping in the lattice accumulate a phase shift equivalent to the Aharonov-Bohm phase of charged particles in a magnetic field. We determine the local distribution of fluxes through the observation of cyclotron orbits of the atoms on lattice plaquettes, showing that the system is described by the Hofstadter model. Furthermore, we show that for two atomic spin states with opposite magnetic moments, our system naturally realizes the time-reversal symmetric Hamiltonian underlying the quantum spin Hall effect, i.e., two different spin components experience opposite directions of the magnetic field.