Localization without recurrence and pseudo-Bloch oscillations in optics

TL;DR

This paper demonstrates that dynamical localization can occur in optical systems with Hamiltonians having continuous spectra, showing localization without recurrence through pseudo-Bloch oscillations in a self-imaging resonator.

Contribution

It introduces a novel optical Hamiltonian with continuous spectrum exhibiting localization without recurrence, supported by a proposed experimental realization.

Findings

Localization observed in continuous spectrum Hamiltonian

Recurrence effects are absent despite localization

Pseudo-Bloch oscillations explain the localization mechanism

Abstract

Dynamical localization, i.e. the absence of secular spreading of a quantum or classical wave packet, is usually associated to Hamiltonians with purely point spectrum, i.e. with a normalizable and complete set of eigenstates, which show quasi-periodic dynamics (recurrence). Here we show rather counter-intuitively that dynamical localization can be observed in Hamiltonians with absolutely continuous spectrum, where recurrence effects are forbidden. An optical realization of such an Hamiltonian is proposed based on beam propagation in a self-imaging optical resonator with a phase grating. Localization without recurrence in this system is explained in terms of pseudo-Bloch optical oscillations.