Loschmidt echo and Berry phase around degeneracies in nonlinear systems

TL;DR

This paper investigates how nonlinearity affects the Loschmidt echo and Berry phase around degeneracies in nonlinear systems, proposing a new witness of nonlinearity and connecting it to quantum fidelity, with potential experimental observations.

Contribution

It introduces a novel witness of nonlinearity in quantum systems and explores its relationship with Loschmidt echo and Berry phase around degeneracies.

Findings

Nonlinearity alters the Berry phase compared to linear systems.

A new witness of nonlinearity is proposed and characterized.

Loschmidt echo is connected to the nonlinearity witness and can be experimentally observed.

Abstract

We study the Loschmidt echo and Berry phase in a nonlinear system transported around a double and triple degeneracy. The nonlinearity of the system makes the Berry phase different from that in linear systems. We propose a witness of nonlinearity for the nonlinear system and show its dependence on the parameters of the system, taking the standard Landau-Zener model as an example. We calculate the Loschmidt echo(LE) or quantum fidelity in the quantum dynamics under perturbations around the degeneracy, and establish a connection between the LE and the witness of nonlinearity. These phases and Loschmidt echo can be observed with current experimental technology in a nonlinear resonator.