Phase controllable dynamical localization: a generalization of the Dunlap-Kenkre result

TL;DR

This paper generalizes the Dunlap-Kenkre result on dynamical localization by analytically deriving conditions involving off-diagonal and diagonal drives with different frequencies and phase relationships, broadening the understanding of localization phenomena.

Contribution

It provides a comprehensive analytical framework for achieving dynamical localization with combined off-diagonal and diagonal drives at different frequencies and phase conditions, extending prior results.

Findings

Dynamical localization occurs when specific Bessel function zeros are met.

Phase relationships determine localization conditions for different frequency ratios.

The results include new conditions involving phase and frequency ratios for localization.

Abstract

Dunlap-Kenkre result states that Dynamical Localization (DL) of a field driven quantum particle in a discrete periodic lattice happens when the ratio of the field magnitude to the field frequency (say, $\eta$) of the diagonal sinusoidal drive is a root of the ordinary Bessel function of order 0. This has been experimentally verified. A generalization of the Dunlap-Kenkre result is presented here. We analytically show that if we have an off-diagonal driving field (with modulation $\delta$) and diagonal driving field with different frequencies (say $\omega_1$ and $\omega_2$ respectively) and a definite phase relationship $\phi$ between them, one can obtain DL if (1) $\eta$ is a zero of the Bessel function of order 0 and $\phi$ is an odd multiple of $\pi/2$ for equal and $\frac{\omega_1}{\omega_2}= odd integer$ driving frequencies, (2) $\eta$ is a zero of the Bessel function of order 0 and $\phi$ is an integer multiple of $\pi$ including zero for $\frac{\omega_1}{\omega_2}= even integer \equiv m$, and (3) $\phi = -\arcsin(\frac{J_0(\eta)}{\delta J_m(\eta)})$ and $\eta$ is not a zero of the Bessel function of the even order $m$.