Effects of quantum geometric phase of a particle in an oscillating hard-wall spherical trap

TL;DR

This paper investigates the geometric phase of a quantum particle in a spherical potential well with a moving wall, analyzing both monotonic and oscillatory radius changes, and explores observable effects in acousto-optic systems.

Contribution

It provides new analytical and approximate solutions for the geometric phase in a spherical well with oscillating boundaries and links these phases to measurable transition rates.

Findings

Geometric phase depends on wall motion type

Oscillatory wall motion leads to transition rate modifications

Absorption peaks relate to energy gap and oscillation frequency

Abstract

We obtain the geometric phase for states of a particle in a spherical infinite potential well with a moving wall in two different cases; First, when the radius of the well increases (or decreases) monotonically. Second, when the radius changes oscillatory. In the latter case, we have solved the Schrodinger equation and found its solutions approximately. {We obtain the transition rate for the possible real situation in an acousto-optic case which can reveal the effect of the geometric phase. We show that the absorption or radiation peaks will appear if the energy gap between the incident photon and the modified energy difference of two levels by the geometric phase, is equal to the integer multiple of oscillation frequency.