Enabling Adiabatic Passages Between Disjoint Regions in Parameter Space through Topological Transitions

TL;DR

This paper investigates how topological transitions in parameter space can enable adiabatic passages between disconnected regions, using coupled qubits and Berry curvature analysis, with implications for quantum control and measurement.

Contribution

It introduces a method to exploit topological transitions in parameter space to bypass degeneracies, supported by analysis of Berry curvature and a proposed measurement technique.

Findings

Topological transitions can be used to connect disjoint regions in parameter space.

Symmetry-breaking induces sharp topological changes in charge distributions.

A simple measurement method for Berry curvature is proposed.

Abstract

We explore topological transitions in parameter space in order to enable adiabatic passages between regions adiabatically disconnected within a given parameter manifold. To this end, we study the Hamiltonian of two coupled qubits interacting with external magnetic fields, and make use of the analogy between the Berry curvature and magnetic fields in parameter space, with spectrum degeneracies associated to magnetic charges. Symmetry-breaking terms induce sharp topological transitions on these charge distributions, and we show how one can exploit this effect to bypass crossing degeneracies. We also investigate the curl of the Berry curvature, an interesting but as of yet not fully explored object, which together with its divergence uniquely defines this field. Finally, we suggest a simple method for measuring the Berry curvature, thereby showing how one can experimentally verify our results.