Excitation of a moving oscillator

TL;DR

This paper analyzes how a moving harmonic oscillator's state transitions depend on its motion, showing that excitation probabilities oscillate with frequency and can be observed in atomic traps.

Contribution

It provides a general formula for transition amplitudes based on the Fourier transform of the trap's acceleration, applicable to arbitrary motions.

Findings

Transition probabilities depend on the Fourier transform of acceleration.

No net excitation occurs with constant acceleration over a period.

Excitation effects are observable in current atomic trap experiments.

Abstract

We calculate transition amplitudes and probabilities between the coherent and Fock states of a quantum harmonic oscillator with a moving center for an arbitrary law of motion. These quantities are determined by the Fourier transform of the moving center acceleration. In the case of a constant acceleration, the probabilities oscillate with the oscillator frequency, so that no excitation occurs after every period. Examples of oscillating and rotating motion of the harmonic trap center are considered too. Estimations show that the effect of excitation of vibration states due to the motion of the harmonic trap center can be observed in available atomic traps.