Time dependence of quantum oscillator excitation by electromagnetic pulses

TL;DR

This paper provides a theoretical analysis of how electromagnetic pulses influence the excitation over time of a quantum harmonic oscillator, linking quantum excitation dynamics to classical oscillator energy.

Contribution

It derives a general formula for quantum excitation as a function of time based on the classical oscillator energy, applicable for arbitrary pulse amplitudes.

Findings

The excitation dynamics are fully determined by the classical oscillator energy.

Explicit expressions for total and state-specific excitation probabilities are obtained.

The excitation spectra are analyzed in detail.

Abstract

The paper is devoted to the theoretical investigation of time dependences of quantum oscillator excitation by electromagnetic pulses for arbitrary values of field amplitude in the pulse. We consider the harmonic oscillator without relaxation and excitation between stationary states. The general formula for excitation of quantum states as function of time is derived in terms of instant energy of associated classical oscillator in the field of electromagnetic pulse. Thus, it is established that time dependence of quantum oscillator excitation is completely determined by the energy of the associated classical oscillator at given moment of time. Using derived expression time dependence of quantum oscillator excitation is investigated in details including total excitation from ground state, excitation from excited states, total excitation probability and corresponding excitation spectra.