Interaction-Dependent Photon-Assisted Tunneling in Optical Lattices: A Quantum Simulator of Strongly-Correlated Electrons and Dynamical Gauge Fields

TL;DR

This paper presents a versatile quantum simulation scheme using photon-assisted tunneling in optical lattices, enabling exploration of strongly-correlated electron models, magnetic phenomena, and dynamical gauge fields with cold atoms.

Contribution

It introduces a method to simulate complex many-body models, including Hubbard, t-J, and dynamical gauge field models, with tunable parameters in optical lattice experiments.

Findings

Realization of effective Hubbard Hamiltonian with bond-charge interactions.

Simulation of Nagaoka ferromagnetism at finite Hubbard repulsion.

Implementation of models with controllable tunneling, super-exchange, and gauge fields.

Abstract

We introduce a scheme that combines photon-assisted tunneling by a moving optical lattice with strong Hubbard interactions, and allows for the quantum simulation of paradigmatic quantum many-body models. We show that, in a certain regime, this quantum simulator yields an effective Hubbard Hamiltonian with tunable bond-charge interactions, a model studied in the context of strongly-correlated electrons. In a different regime, we show how to exploit a correlated destruction of tunneling to explore Nagaoka ferromagnetism at finite Hubbard repulsion. By changing the photon-assisted tunneling parameters, we can also obtain a $t$-$J$ model with independently controllable tunneling $t$, super-exchange interaction $J$, and even a Heisenberg-Ising anisotropy. Hence, the full phase diagram of this paradigmatic model becomes accessible to cold-atom experiments, departing from the region $t\gg J$ allowed by standard single-band Hubbard Hamiltonians in the strong-repulsion limit. We finally show that, by generalizing the photon-assisted tunneling scheme, the quantum simulator yields models of dynamical Gauge fields, where atoms of a given electronic state dress the tunneling of the atoms with a different internal state, leading to Peierls phases that mimic a dynamical magnetic field.