Effective Hamiltonian for the radiation in a cavity with a moving mirror and a time-varying dielectric medium

1994/01/01 by C. K. Law · 13 citations
Engineering · Physics and Astronomy · #Mechanical and Optical Resonators #Quantum Electrodynamics and Casimir Effect #Thermal Radiation and Cooling Technologies

paper · doi:10.1103/physreva.49.433

openalex publication_date 1994/01/01 · openalex created_date 2017/10/27 · openalex updated_date 2026/07/28

Abstract

We study the quantized field in a one-dimensional electromagnetic resonant cavity. The cavity contains a linear and lossless dielectric medium with frequency-independent polarizability. The dielectric permittivity is an externally prescribed function of both the space and the time. We also allow one of the cavity's mirrors to move in a given trajectory. Unlike other previous studies on the same system, we formulate an effective Hamiltonian so that the dynamics of the cavity field can be described in the Schr"odinger picture. The effective Hamiltonian is quadratic in structure, therefore two-photon generation from the vacuum state can occur. We also discuss the case of resonant behavior of the system.

Cited by

• Towards quantum superpositions of a mirror: an exact open systems analysis—calculational details
• Theory of circle maps and the problem of one-dimensional optical resonator with a periodically moving wall
• Ponderomotive control of quantum macroscopic coherence
• Properties of squeezed-state excitations
• Vacuum effects in a vibrating cavity: Time refraction, dynamical Casimir effect, and effective Unruh acceleration
• Exact closed-form analytical solutions for vibrating cavities
• Photon generation from vacuum in nondegenerate cavities with regular and random periodic displacements of boundaries
• Entanglement of Resonantly Coupled Field Modes in Cavities with Vibrating Boundaries
• Hamiltonian Approach to the Dynamical Casimir Effect
• The dynamical Casimir effect for two oscillating mirrors in 3D
• Numerical observation of Hawking radiation from acoustic black holes in atomic Bose–Einstein condensates
• Path-integral approach to the dynamic Casimir effect with fluctuating boundaries
• Cavity optomechanics [wikipedia]