Dynamical regimes of a quantum swap gate beyond the Fermi Golden Rule

TL;DR

This paper explores how the memory effects of a quantum environment influence the behavior of a swap gate, revealing various dynamical regimes and transitions beyond traditional approximations.

Contribution

It introduces an exactly solvable model that uncovers multiple dynamical regimes and transitions by analyzing the density of states beyond the Fermi Golden Rule.

Findings

Identification of five dynamical regimes: overdamped, oscillatory, diffusion, anomalous diffusion, localized

Discovery of exceptional points and virtual states affecting the swap gate dynamics

Stable oscillation frequencies determined by environment band width in certain regimes

Abstract

We discuss how the bath's memory affects the dynamics of a swap gate. We present an exactly solvable model that shows various dynamical transitions when treated beyond the Fermi Golden Rule. By moving continuously a single parameter, the unperturbed Rabi frequency, we sweep through different analytic properties of the density of states: I) collapsed resonances that split at an exceptional point in II) two resolved resonances ; III) out-of-band resonances; IV) virtual states; and V) pure point spectrum. We associate them with distinctive dynamical regimes: overdamped, damped oscillations, environment controlled quantum diffusion, anomalous diffusion and localized dynamics respectively. The frequency of the swap gate depends differently on the unperturbed Rabi frequency. In region I) there is no oscillation at all, while in the regions III) and IV) the oscillation frequency is particularly stable because it is determined by environment's band width. The anomalous diffusion could be used as a signature for the presence of the elusive virtual states.