The Quantum Geometric Phase between Orthogonal States

Abstract

We show that the geometric phase between any two states, including orthogonal states, can be computed and measured using the notion of projective measurement, and we show that a topological number can be extracted in the geometric phase change in an infinitesimal loop near an orthogonal state. Also, the Pancharatnam phase change during the passage through an orthogonal state is shown to be either $\pi$ or zero (mod $2\pi$). All the off-diagonal geometric phases can be obtained from the projective geometric phase calculated with our generalized connection.

References in corpus (6)

• Off-Diagonal Geometric Phases
• Observation of off-diagonal geometric phase in polarized neutron interferometer experiments
• Off-diagonal generalization of the mixed state geometric phase
• Geometric Phase, Bundle Classification, and Group Representation
• Observable Dirac-type singularities in Berry's phase and the monopole
• The quantum mechanical geometric phase of a particle in a resonant vibrating cavity

Cited by in corpus (5)

• Singularity of Berry Connections Inhibits the Accuracy of Adiabatic Approximation
• Geometric phase in Stückelberg interferometry
• Geometric and Majorana phases in neutrino oscillations
• Geometric phases in neutrino mixing
• Weak value picture on quantum observables: gauge-invariant vector potentials