Contribution of adiabatic phases to noncyclic evolution

TL;DR

This paper demonstrates that adiabatic phase differences significantly impact interference effects in noncyclic quantum evolutions, emphasizing their importance in accurate physical predictions.

Contribution

It highlights the necessity of considering basis-dependent adiabatic phase differences in noncyclic quantum evolutions for correct interference calculations, supported by a spin-1/2 model analysis.

Findings

Adiabatic phase differences affect interference in noncyclic evolution.

The model shows adiabatic phases reach Berry's phase difference after a cycle.

Proper phase consideration is crucial for accurate quantum interference results.

Abstract

We show that the difference of adiabatic phases, that are basis-dependent, in noncyclic evolution of non-degenerate quantum systems have to be taken into account to give the correct interference result in the calculation of physical quantities in states that are a superposition of instantaneous eigenstates of energy. To verify the contribution of those adiabatic phases in the interference phenomena, we consider the spin-1/2 model coupled to a precessing external magnetic field. In the model, the adiabatic phase increases in time up to reach the difference of the Berry's phases of the model when the external magnetic field completes a period.