Kicked rotor quantum resonances in position space

TL;DR

This paper introduces a position-space approach to kicked rotor quantum resonances, drawing an analogy with the optical Talbot effect, providing simple physical insights and analytical expressions for key quantities.

Contribution

It presents a novel position-space perspective on quantum resonances in the kicked rotor, linking it to the Talbot effect and deriving analytical formulas for physical observables.

Findings

Ballistic behavior arises from coherent addition of kicks.

Quantum resonances linked to periodic wavepacket reconstruction.

Analytical expressions for mean momentum and kinetic energy.

Abstract

We present an approach of the kicked rotor quantum resonances in position-space, based on its analogy with the optical Talbot effect. This approach leads to a very simple picture of the physical mechanism underlying the dynamics and to analytical expressions for relevant physical quantities, such as mean momentum or kinetic energy. The ballistic behavior, which is closely associated to quantum resonances, is analyzed and shown to emerge from a coherent adding of successive kicks applied to the rotor thanks to a periodic reconstruction of the spatial wavepacket.