Scheme for measuring topological transitions in a continuous variable system

TL;DR

This paper introduces a scheme to measure topological properties in a Kerr-nonlinear resonator using Berry curvature and Chern number, revealing topological transitions through nonadiabatic responses in a continuous variable system.

Contribution

It presents a novel method to detect topological transitions in a continuous variable quantum system via nonadiabatic responses and parameter manifold adjustments.

Findings

Topological transitions can be detected through degeneracy crossings in the parameter manifold.

Berry curvature and Chern number serve as indicators of topological properties.

The scheme enables exploration of geometry and topology in mesoscale continuous variable systems.

Abstract

We propose a scheme for measuring topological properties in a two-photon-driven Kerr-nonlinear resonator (KNR) subjected to a single-photon modulation. The topological properties are revealed through the observation of the Berry curvature and hence the first Chern number, as a nonadiabatic response of the physical observable to the change rate of the control parameter of the modulated drive. The parameter manifold, constructed from the system's Hamiltonian that determines its dynamics constrained in the state space spanned by the even and odd cat states as two basis states, is adjusted so that the degeneracy crossing the manifold indicates a topological transition. The scheme, with such continuous variable states in mesoscpic systems, provides a new perspective for exploration of the geometry and the related topology with complex systems.