Engineering Photon-mediated Long-Range Spin Interactions in Mott Insulators

TL;DR

This paper explores how cavity quantum electromagnetic fields can induce and control long-range spin interactions in Mott insulators, revealing new mechanisms and pathways for quantum engineering.

Contribution

It introduces two novel pathways for long-range spin interactions mediated by cavity photons, including vacuum and laser-driven schemes, with detailed theoretical derivations.

Findings

Vacuum-mediated interactions can surpass local Heisenberg interactions in small resonators.

Laser-driven cavities enable tunable long-range interactions via Floquet engineering.

A fourth-order electronic model is necessary for accurate long-range interaction derivation.

Abstract

We investigate the potential to induce long-range spin interactions in a Mott insulator via the quantum electromagnetic field of a cavity. The coupling between light and spins is inherently non-linear, and occurs via multi-photon processes like Raman scattering and two-photon absorption/emission with electronically excited intermediate states. Based on this, two pathways are elucidated: (i) In the absence of external driving, long-range interactions are mediated by the exchange of at least two virtual cavity photons. We show that these vacuum-mediated interactions can surpass local Heisenberg interactions in mesoscopic setups such as sufficiently small split-ring resonators. (ii) In a laser-driven cavity, interactions can be tailored through a hybrid scheme involving both external laser photons and cavity photons. This offers a versatile pathway for Floquet engineering of long-range interactions in macroscopic systems. In general, the derivation of these interactions requires careful consideration: Notably, we demonstrate that a simple phenomenological approach, based on a spin-photon Hamiltonian that captures Raman and two-photon processes with effective matrix elements, can be used only if the cavity is resonantly driven. Outside of these narrow resonant regimes as well as for the undriven case, a fourth-order series expansion within the underlying electronic model is necessary, which we perform to obtain long-range four-spin interactions in the half-filled Hubbard model.