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

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 similar to 1/epsilon(3), where epsilon = Delta/omega is the ratio between the hopping amplitude Delta of adjacent sites and the modulation frequency 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-Boas 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.