Harmonically confined n -electron systems coupled to light in a cavity: Time-dependent case

Abstract

An analytically solvable time-dependent coupled light-matter problem is presented. An $n$-electron system is confined by a harmonic-oscillator potential and interacts with photons in a cavity. Both the electrons and the photons can interact with a time-dependent external field. The light-matter coupling is described by the Pauli-Fierz Hamiltonian. By separating the relative and center-of-mass motion, the Hamiltonian of the system can be simplified to a sum of a Hamiltonian of the relative and the center-of-mass motion. The Hamiltonian of the relative motion is time-independent, not coupled to light, and it can be solved by conventional approaches. The Hamiltonian of the center-of-mass motion reduces to that of a time-dependent harmonic oscillator and can be solved analytically. The analytical solution will be used to study excitations, the high-harmonic-generation spectrum, and nonlinear optical properties in a cavity.