`Muhammad Ali effect' and incoherent destruction of Wannier-Stark localization in a stochastic field

TL;DR

This paper derives an exact probability propagator for a tight-binding lattice under stochastic electric fields, revealing how noise and static fields influence Bloch oscillations and Wannier-Stark localization, including a novel 'Muhammad Ali effect' that causes incoherent destruction of localization.

Contribution

It provides an exact analytical expression for the propagator in a stochastic field, elucidates the impact of noise on localization and oscillations, and introduces the 'Muhammad Ali effect' as a new phenomenon.

Findings

Rapid noise averaging leads to delocalization.

Static field tuning can destroy Wannier-Stark localization.

Bias in stochastic probabilities induces Bloch oscillations.

Abstract

We calculate an exact expression for the probability propagator for a noisy electric field driven tight-binding lattice. The noise considered is a two-level jump process or a telegraph process (TP) which jumps randomly between two values $\pm\mu$. In the absence of a static field and in the limit of zero jump rate of the noisy field we find that the dynamics yield Bloch oscillations with frequency $\mu$, while with an additional static field $\epsilon$ we find oscillatory motion with a superposition of frequencies $(\epsilon \pm \mu)$. On the other hand, when the jump rate is `rapid', and in the absence of a static field, the stochastic field averages to zero if the two states of the TP are equally probable `a-priori'. In that case, we see a delocalization effect. The intimate relationship between the rapid relaxation case and the zero field case is a manifestation of what we call the `Muhammad Ali effect'. It is interesting to note that even for zero static field and rapid relaxation, Bloch oscillations ensue if there is a bias $\delta p$ in the probabilities of the two levels. Remarkably, the Wannier-Stark localization caused by an additional static field is destroyed if the latter is tuned to be exactly equal and opposite to the average stochastic field $\mu\delta p$. This is an example of \emph{incoherent} destruction of Wannier-Stark localization.