Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices

TL;DR

This paper extends quasiclassical analysis to non-Hermitian lattices, showing that classical phase space dynamics can qualitatively and quantitatively describe quantum Bloch oscillations in these systems.

Contribution

It develops a generalized non-Hermitian phase space approach and applies it to demonstrate classical descriptions of quantum dynamics in non-Hermitian tight-binding lattices.

Findings

Classical phase space dynamics can describe wave packet norm evolution.

Quantum features are qualitatively captured by the classical model.

The approach applies to PT-symmetric systems with real and imaginary couplings.

Abstract

Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the quasiclassical approach is extended to non-Hermitian lattices, which are of increasing interest. The analysis is based on a generalised non-Hermitian phase space dynamics developed recently. Applications to a single-band tight-binding system demonstrate that many features of the quantum dynamics can be understood from this classical description qualitatively and even quantitatively. Two non-Hermitian and $PT$-symmetric examples are studied, a Hatano-Nelson lattice with real coupling constants and a system with purely imaginary couplings, both for initially localised states in space or in momentum. It is shown that the time-evolution of the norm of the wave packet and the expectation values of position and momentum can be described in a classical picture.