Coherent control of tunneling in driven tight-binding chains: Perturbative analysis

Abstract

Coherent control of quantum tunneling in an ac-driven tight-binding chain made of a finite number of positional sites, such as electronic tunneling in finite superlattices of quantum wells or in linear chains of quantum dots driven by a sinusoidal electric field, is analytically investigated in the large-frequency regime by a multiple-scale asymptotic analysis of the underlying equations, which is exact up to the normalized time scale $\ensuremath{\sim}1/{ϵ}^{3}$, where $ϵ=\ensuremath{\Delta}/\ensuremath{\omega}$ is the ratio between the hopping amplitude $\ensuremath{\Delta}$ of adjacent sites and the modulation frequency $\ensuremath{\omega}$. The results of the analysis are applied to tunneling control in linear chains with $N=2$, 3, 4, 5, and 6 potential wells. For a double-well system $(N=2)$, the usual condition for coherent destruction of tunneling (CDT) of a driven two-level system, with a third-order correction term, is retrieved. For an array comprising $N=3$, 5, or 6 sites, crossing and anticrossing in the quasienergy spectrum near a collapse point, which result in selective CDT, are found according to the numerical (nonperturbative) results previously presented by Villas-B\^oas et al. for driven quantum-dot arrays [Phys. Rev. B 70, 041302 (2003)]. The behavior of quasienergy crossings and avoided crossings for the multiple-well array found in the framework of the third-order perturbative theory is shown to be consistent with the predictions based on generalized symmetries of the Floquet states.