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.

References in corpus (5)

• Observation of topological transitions in interacting quantum circuits
• Measuring a topological transition in an artificial spin 1/2 system
• Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit
• Quantum simulation of gravitational-like waves in minisuperspace with an artificial qubit
• Tracking quantum state evolution by the Berry curvature with a two-level system

Cited by in corpus (2)

• Quantum Geometric Tensor and Critical Metrology in the Anisotropic Dicke Model
• Topological Transitions in a Kerr Nonlinear Oscillator