Complex time method for quantum dynamics when an exceptional point is encircled in the parameter space

TL;DR

This paper extends the complex time method to analyze quantum dynamics around exceptional points by using complex contour integration, revealing how encircling such points affects quantum state transitions.

Contribution

It introduces a novel application of the complex time method to study quantum systems near exceptional points, highlighting the role of complex degeneracies in parameter space.

Findings

Transition between Rabi oscillations and rapid adiabatic passage.

Encircling an exceptional point causes distinct quantum dynamical effects.

Complex degeneracies influence quantum state evolution.

Abstract

We revisit the complex time method for the application to quantum dynamics as an exceptional point is encircled in the parameter space of the Hamiltonian. The basic idea of the complex time method is using complex contour integration to perform the first-order adiabatic perturbation integral. In this way, the quantum dynamical problem is transformed to a study of singularities in the complex time plane -- transition points -- which represent complex degeneracies of the adiabatic Hamiltonian as the time-dependent parameters defining the encircling contour are analytically continued to complex plane. As an underlying illustration of the approach we discuss a switch between Rabi oscillations and rapid adiabatic passage which occurs upon the encircling of an exceptional point in a special time-symmetric case.