Topological Transitions in a Kerr Nonlinear Oscillator

A Kerr nonlinear oscillator (KNO) supports a pair of steady eigenstates, coherent states with opposite phases, that are good for the encoding of continuous variable qubit basis states. Arbitrary control of the KNO confined within the steady state subspace allows extraction of the Berry curvature through the linear response of the physical observable to the quench velocity of the system, providing an effective method for the characterization of topology in the KNO. As an alternative, the control adopting the "shortcut to adiabaticity" to the KNO enables the exploration of the topology through accelerated adiabatic eigenstate evolution to measure all three physical observables. Topological transitions are revealed by the jump of the first Chern number, obtained respectively from the integral of the Berry curvature and of the new polar angle relation, over the whole parameter space. Our strategy paves the way for measuring topological transitions in continuous variable systems.