Phase dependence of localization in the driven two-level model

TL;DR

This paper investigates how the phase of a high-frequency driving field influences the suppression of tunneling in a two-level quantum system, revealing phase-dependent revival phenomena using analytical and geometric methods.

Contribution

It demonstrates the phase dependence of tunneling suppression and revivals in driven two-level systems, providing a geometric interpretation with squarewave driving that applies to sinusoidal cases.

Findings

Phase of driving affects tunneling suppression and revival patterns.

Squarewave driving allows analytical geometric interpretation.

Results are applicable to sinusoidal driving scenarios.

Abstract

A two-level system subjected to a high-frequency driving field can exhibit an effect termed ``coherent destruction of tunneling'', in which the tunneling of the system is suppressed at certain values of the frequency and strength of the field. This suppression becomes less effective as the frequency of the driving field is reduced, and we show here how the detailed form of its fall-off depends on the phase of the driving, which for certain values can produce small local maxima (or revivals) in the overall decay. By considering a squarewave driving field, which has the advantage of being analytically tractable, we show how this surprising behavior can be interpreted geometrically in terms of orbits on the Bloch sphere. These results are of general applicability to more commonly used fields, such as sinusoidal driving, which display a similar phenomenology.