Abstract
In this paper 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.
Highlights
In parallel, there is an aggressive effort to explore optical modes coupled to matter as a platform for quantum manybody phenomenology
We formalize a new approach to photonic quantum materials based upon exotic optical resonators; following up on our prior work describing Rydberg-dressed photons in a near-degenerate optical resonator as interacting, massive, harmonically trapped 2D particles in synthetic magnetic fields [35], we provide a more detailed framework for designing the resonators and characterizing the resulting single-particle photonic Hamiltonian dynamics
We show that these corrections provide a route to arbitrary potentials and dispersion relations for resonator photons, along with a path to photonic dynamics on curved spatial manifolds
Summary
A paraxial optical resonator may be characterized by an ABCD [36] matrix M , describing the round trip evolution of all light rays in a given transverse plane of the resonator. The ray described by V ≡ , where x is the (2D) transverse location of the s ray, and s its slope, becomes M V under round-trip propagation This describes a discrete linear transformation in phase space, and suggests that such stroboscopic dynamics (see Figure 2a) are equivalent to periodically sampled continuous evolution under a quadratic time invariant Hamiltonian. To develop a Hamiltonian formalism describing the continuous evolution of the ray within a particular transverse plane we must first convert the slope s into a momentum p which is canonically conjugate to x. This momentum is p = ks, with k ≡ 2π/λ and λ the optical x wavelength.
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