Evanescent Wave Approximation for Non-Hermitian Hamiltonians

TL;DR

This paper introduces an evanescent wave approximation for non-Hermitian Hamiltonians, enabling effective descriptions of decaying systems and predicting quantum Zeno dynamics at high decay rates.

Contribution

It extends the rotating wave approximation to non-Hermitian systems, providing a new method to analyze decay processes and quantum Zeno effects.

Findings

Effective Hamiltonian derivation for decaying systems

Prediction of quantum Zeno dynamics at high decay rates

Removal of certain coupling terms in the effective description

Abstract

The counterpart of the rotating wave approximation for non-Hermitian Hamiltonians is considered, which allows for the derivation of a suitable effective Hamiltonian for systems with some states undergoing decays. In the limit of very high decay rates, on the basis of this effective description we can predict the occurrence of a quantum Zeno dynamics which is interpreted as the removal of some coupling terms and the vanishing of an operatorial pseudo-Lamb shift.