Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices

TL;DR

This paper demonstrates the experimental realization of the Harper Hamiltonian in optical lattices using laser-assisted tunneling, enabling exploration of quantum Hall physics and Hofstadter's butterfly in neutral atoms.

Contribution

It introduces a novel method to simulate the Harper Hamiltonian with neutral atoms, bridging condensed matter phenomena and cold atom systems.

Findings

Successful implementation of laser-assisted tunneling in optical lattices.

Observation of atomic expansion indicative of band structure.

Potential to observe quantum Hall effects and chiral edge states.

Abstract

We experimentally implement the Harper Hamiltonian for neutral particles in optical lattices using laser-assisted tunneling and a potential energy gradient provided by gravity or magnetic field gradients. This Hamiltonian describes the motion of charged particles in strong magnetic fields. Laser-assisted tunneling processes are characterized by studying the expansion of the atoms in the lattice. The band structure of this Hamiltonian should display Hofstadter's butterfly. For fermions, this scheme should realize the quantum Hall effect and chiral edge states.