Low-frequency anomalies in dynamic localization

Abstract

Quantum mechanical spreading of a particle hopping on tight binding lattices can be suppressed by the application of an external ac force, leading to periodic wave packet reconstruction. Such a phenomenon, referred to as dynamic localization (DL), occurs for certain ‘magic’ values of the ratio Γ = F0/ω between the amplitude F0 and frequency ω of the ac force. It is generally believed that in the low-frequency limit (ω → 0) DL can be achieved for an infinitesimally small value of the force F0, i.e. at finite values of Γ. Such normal behavior is found in homogeneous lattices as well as in inhomogeneous lattices of the Glauber–Fock (GF) type. Here we introduce a tight-binding lattice model with inhomogeneous hopping rates, referred to as a pseudo-GF lattice, which shows DL but fails to reproduce the normal low-frequency behavior of homogeneous and GF lattices. In pseudo-GF lattices, DL can be exactly realized; however, at the DL condition the force amplitude F0 remains finite as ω → 0. Such an anomalous behavior is explained in terms of a symmetry-breaking transition of an associated two-level non-Hermitian Hamiltonian that effectively describes the dynamics of the Hermitian lattice model.