Engineering Photonic Floquet Hamiltonians through Fabry P\'erot Resonators

TL;DR

This paper demonstrates how optical Fabry-Pérot resonators can simulate complex Hamiltonians, revealing synthetic magnetic fields and relativistic effects, thus enabling exploration of quantum fluids and spacetime physics with light.

Contribution

It introduces a Floquet formalism for analyzing resonator-induced Hamiltonians, showing how twist and aberrations create synthetic gauge fields and relativistic dynamics in optical systems.

Findings

Resonator twist induces synthetic magnetic fields.

Mirror aberrations lead to relativistic and anharmonic effects.

The formalism enables simulation of quantum fluids in gauge fields.

Abstract

In this letter we analyze an optical Fabry-P\'erot resonator as a time-periodic driving of the (2D) optical field repeatedly traversing the resonator, uncovering that resonator twist produces a synthetic magnetic field applied to the light within the resonator, while mirror aberrations produce relativistic dynamics, anharmonic trapping, and spacetime curvature. We develop a Floquet formalism to compute the effective Hamiltonian for the 2D field, generalizing the idea that the intra-cavity optical field corresponds to an ensemble of non-interacting, massive, harmonically trapped particles. This work illuminates the extraordinary potential of optical resonators for exploring the physics of quantum fluids in gauge fields and exotic space-times.