Continued fraction analysis of dressed systems: application to periodically driven optical lattices

TL;DR

This paper compares different theoretical approaches, including continued fraction analysis, to understand how periodic electromagnetic fields influence the energy and tunneling properties of particles in optical lattices, with implications for quantum control.

Contribution

It introduces a continued fraction method to analyze dressed systems in periodically driven optical lattices, highlighting the semiclassical approach as most effective for tunneling renormalization.

Findings

Semiclassical treatment effectively predicts tunneling renormalization.

Continued fraction approach provides detailed system analysis.

Comparison clarifies the validity of different models.

Abstract

Radio-frequency quantum engineering of spins is based on the dressing by a non resonant electromagnetic field. Radio-frequency dressing occurs also for the motion of particles, electrons or ultracold atoms, within a periodic spatial potential. The dressing, producing a renormalisation and also a freeze of the system energy, is described by different approaches, dressed atom, magnetic resonance semiclassical treatment, continued fraction solution of the Schr\"odinger equation. A comparison between those solutions points out that the semiclassical treatment, to be denoted as the $S$-solution, represents the most convenient tool to evaluate the tunneling renormalization of ultracold atoms.