Engineering Photonic Floquet Hamiltonians through Fabry Pérot Resonators

Abstract

In this letter we analyze an optical Fabry-Pérot 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.

18 Pages, 4 Figures

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• Topological Photonics
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• Observation of Laughlin states made of light
• Observation of Cavity Rydberg Polaritons
• Controlling the Floquet state population and observing micromotion in a periodically driven two-body quantum system
• An Autonomous Stabilizer for Incompressible Photon Fluids and Solids
• Hamiltonian Tomography of Photonic Lattices
• Coherent generation of photonic fractional quantum Hall states in a cavity and the search for anyonic quasiparticles
• Photons and polaritons in a time-reversal-broken non-planar resonator
• Asymptotic Floquet states of non-Markovian systems
• Adiabatic flux insertion and growing of Laughlin states of cavity Rydberg polaritons
• Aberrated optical cavities
• Stabilizing the Laughlin state of light: dynamics of hole fractionalization
• 30-Fold Increase in Atom-Cavity Coupling Using a Parabolic Ring Cavity
• A cavity array microscope for parallel single-atom interfacing
• Exotic photonic molecules via Lennard-Jones-like potentials
• Resonant enhancement of three-body loss between strongly interacting photons