Two geometric phases can dramatically differ from each other even if their evolution paths are sufficiently close in a pointwise manner

TL;DR

This paper reveals that tiny initial deviations in quantum states can cause large differences in geometric phases, even when the evolution paths are nearly identical, challenging the traditional understanding of geometric phase dependence.

Contribution

It demonstrates that infinitesimal initial state deviations can lead to significant differences in geometric phases during adiabatic evolution, highlighting a new sensitivity in quantum phase behavior.

Findings

Small initial deviations cause large phase differences

Geometric phases can differ greatly despite similar paths

Challenges traditional assumptions about phase path dependence

Abstract

One milestone in quantum physics is Berry's seminal work [Proc.~R.~Soc.~Lond.~A \textbf{392}, 45 (1984)], in which a quantal phase factor known as geometric phase was discovered to solely depend on the evolution path in state space. Here, we unveil that even an infinitesimal deviation of the initial state from the eigenstate of the initial Hamiltonian can yield a significant change of the geometric phase accompanying an adiabatic evolution. This leads to the surprising observation that two geometric phases can dramatically differ from each other even if their evolution paths are sufficiently close in a pointwise manner.