Exact solution of a non-stationary cavity with one intermode interaction

TL;DR

This paper provides an exact analytical solution for a non-stationary one-dimensional cavity with intermode interactions, revealing detailed photon generation dynamics due to the dynamical Casimir effect.

Contribution

It introduces an algebraic method to exactly solve the time-dependent Schrödinger equation for a cavity with one intermode interaction, advancing understanding of photon creation in such systems.

Findings

Exact time evolution operator derived as a product of eleven exponentials

Explicit expressions for average photon numbers in each mode

Analysis of statistical properties of the evolved vacuum state

Abstract

A non-stationary one-dimensional cavity can be described by the time-dependent and multi-mode effective Hamiltonian of the so-called dynamical Casimir effect. Due to the non-adiabatic boundary conditions imposed in one of the cavity mirrors, this effect predicts the generation of real photons out of vacuum fluctuations of the electromagnetic field. Such photon generation strongly depends on the number of modes in the cavity and their intermode couplings. Here, by using an algebraic approach, we show that for any set of functions parameterizing the effective Hamiltonian, the corresponding time-dependent Schr\"odinger equation admits an exact solution when the cavity has one intermode interaction. With the exact time evolution operator, written as a product of eleven exponentials, we obtain the average photon number in each mode, a few relevant observables and some statistical properties for the evolved vacuum state.