Spinor Dynamics of Quantum Accelerator Modes near Higher Order Resonances

TL;DR

This paper develops a spinor formalism to analyze quantum accelerator modes near higher order resonances in kicked cold atoms, revealing how stable periodic orbits relate to observable quantum phenomena.

Contribution

It introduces a novel spinor approach and a Born-Oppenheimer type ansatz to decouple variables, enabling classical map analysis of quantum accelerator modes at arbitrary resonance orders.

Findings

Decoupling of spin and orbital variables via a new ansatz.

Identification of stable periodic orbits linked to quantum accelerator modes.

Potential for experimental observation of these modes.

Abstract

Quantum Accelerator Modes were discovered in experiments with Kicked Cold Atoms in the presence of gravity. They were shown to be tightly related to resonances of the Quantum Kicked Rotor. In this paper a spinor formalism is developed for the analysis of Modes associatedwith resonances of arbitrary order q>1. Decoupling of spin variables from orbital ones is achieved by means of an ansatz of the Born-Oppenheimer type, that generates q independent band dynamics. Each of these is described, in classical terms, by a map, and the stable periodic orbits of this map give rise to quantum accelerator modes, which are potentially observable in experiments. The arithmetic organization of such periodic orbits is briefly discussed.