Landau-Zener-St\"{u}ckelberg Interferometry in $\mathcal{PT}$-symmetric Non-Hermitian models

TL;DR

This paper explores non-Hermitian generalizations of Landau-Zener and St"uckelberg interferometry, deriving transition probabilities, analyzing geometric phases, and proposing experimental simulations in photonic systems.

Contribution

It provides analytic formulas for non-Hermitian LZS transition probabilities and demonstrates their robustness and applicability to photonic experiments.

Findings

Analytic expressions for non-Hermitian LZ transition probabilities.

Identification of four types of non-Hermitian LZS interferometry.

Proposal for simulating non-Hermitian dynamics using photonic waveguides.

Abstract

We systematically investigate the non-Hermitian generalisations of the Landau-Zener (LZ) transition and the Landau-Zener-St\"{u}ckelberg (LZS) interferometry. The LZ transition probabilities, or band populations, are calculated for a generic non-Hermitian model and their asymptotic behaviour analysed. We then focus on non-Hermitian systems with a real adiabatic parameter and study the LZS interferometry formed out of two identical avoided level crossings. Four distinctive cases of interferometry are identified and the analytic formulae for the transition probabilities are calculated for each case. The differences and similarities between the non-Hermitian case and its Hermitian counterpart are emphasised. In particular, the geometrical phase originated from the sign change of the mass term at the two level crossings is still present in the non-Hermitian system, indicating its robustness against the non-Hermiticity. We further apply our non-Hermitian LZS theory to describing the Bloch oscillation in one-dimensional parity-time $(\mathcal{PT})$ reversal symmetric non-Hermitian Su-Schrieffer-Heeger model and propose an experimental scheme to simulate such dynamics using photonic waveguide arrays. The Landau-Zener transition, as well as the LZS interferometry, can be visualised through the beam intensity profile and the transition probabilitiess measured by the centre of mass of the profile.