Quantum adiabatic evolution with energy-degeneracy levels

TL;DR

This paper develops a classical-like phase-space formalism to analyze tiny deviations from the Wilczek-Zee theorem during quantum adiabatic evolution on degenerate energy levels, revealing deviations perpendicular to the degeneracy subspace.

Contribution

It introduces a novel phase-space formalism for quantum adiabatic evolution with degeneracy, showing deviations are always perpendicular to the degeneracy subspace, differing from previous methods.

Findings

Deviation is always perpendicular to the degeneracy subspace.

Formalism applied to a tripod scheme Hamiltonian with degenerate dark states.

Provides new insights into quantum adiabatic evolution with degeneracy.

Abstract

A classical-kind phase-space formalism is developed to address the tiny intrinsic dynamical deviation from what is predicted by Wilczek-Zee theorem during quantum adiabatic evolution on degeneracy levels. In this formalism, the Hilbert space and the aggregate of degenerate eigenstates become the classical-kind phase-space and a high-dimensional subspace in the phase-space, respectively. Compared with the previous same study by a different method, the current result is qualitatively different in that the first-order deviation derived here is always perpendicular to the degeneracy subspace. A tripod scheme Hamiltonian with two degenerate dark states is employed to illustrate the adiabatic deviation with degeneracy levels.