Scheme for measuring topological transitions in a continuous variable system

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.

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Cited by in corpus (4)

• Quantum Geometric Tensor and Critical Metrology in the Anisotropic Dicke Model
• Critical quantum geometric tensors of parametrically-driven nonlinear resonators
• Quantum metric and metrology with parametrically-driven Tavis-Cummings models
• Topological Transitions in a Kerr Nonlinear Oscillator