Fidelity of the near resonant quantum kicked rotor

TL;DR

This paper derives a perturbative analytical expression for the fidelity decay in the near-resonant quantum kicked rotor, validated by numerical simulations, enhancing understanding of quantum resonance effects.

Contribution

It introduces a pendulum approximation-based analytical method to describe fidelity in the near-resonant quantum kicked rotor, extending prior numerical studies.

Findings

Analytical fidelity expression matches numerical results near resonance.

The approximation accurately describes rotational orbits in phase space.

Range of validity for the analytical approach is established.

Abstract

We present a perturbative result for the temporal evolution of the fidelity of the quantum kicked rotor, i.e. the overlap of the same initial state evolved with two slightly different kicking strengths, for kicking periods close to a principal quantum resonance. Based on a pendulum approximation we describe the fidelity for rotational orbits in the pseudo-classical phase space of a corresponding classical map. Our results are compared to numerical simulations indicating the range of applicability of our analytical approximation.