The nonmodular topological phase and phase singularities

TL;DR

This paper introduces a nonmodular topological phase in quantum interference experiments with particles having internal states, providing new insights into phase behavior and an effective Hamiltonian interpretation.

Contribution

It generalizes the noncyclic geometric phase to a nonmodular topological phase and offers a simple proof of the geodesic rule with new insights into phase components.

Findings

Derived a nonmodular topological phase definition.

Provided a proof of the geodesic rule for phase closure.

Presented an effective Hamiltonian interpretation of phase shifts.

Abstract

Generalizing an earlier definition of the noncyclic geometric phase (R.Bhandari, Phys.Lett.A, 157, 221 (1991)), a nonmodular topological phase is defined with reference to a generic time-dependent two-slit interference experiment involving particles with N internal states in which the internal state of both the beams undergoes unitary evolution. A simple proof of the shorter geodesic rule for closure of the open path is presented and several useful new insights into the behaviour of the dynamical and geometrical components of the phase shift presented. An effective hamiltonian interpretation of the observable phase shifts is also presented.