Nonlinear Non-Hermitian Landau-Zener-St\"uckelberg-Majorana interferometry

TL;DR

This paper investigates how nonreciprocity and nonlinearity influence Landau-Zener-Stückelberg-Majorana interferometry in a non-Hermitian bosonic system, revealing effects on energy spectra, dynamics, and interference patterns.

Contribution

It introduces a mean-field approach to analyze nonlinear non-Hermitian LZSM interferometry, highlighting the roles of nonreciprocity types and nonlinearity in system behavior and interference phenomena.

Findings

Nonreciprocity significantly affects population transfer and interference patterns.

Symmetries and reciprocity types influence phase transitions and energy spectra.

Interference conditions depend on nonlinearity strength under weak coupling.

Abstract

In this work, we have studied the non-Hermitian nonlinear LZSM interferometry in a non-Hermitian N-body interacting boson system in which the non-Hermicity is from the nonreciprocal tunnelings between the bosons. By using the mean-field approximation and projective Hilbert space, the effect of nonreciprocity and nonlinearity on the energy spectrum, the dynamics, and the formation of the interference fringes have been studied. The different symmetries and the impact of the two different types of reciprocity, i.e. the in-phase tunneling and anti-phase tunneling, on the energy spectrum and the phase transition between the Josephson oscillation and the self-trapping have been investigated. For the LZSM interferometry, the strength of the nonreciprocity is found to take an essential role in the population of the projective state and the strengths of the interference patterns in the projective space. While the conditions of destructive and constructive interference under the weak-coupling approximation still only depend on the strength of nonlinearity. Our result provides an application of the nonlinear non-Hermitian LZSM interferometry in studying the parameters of a non-Hermitian nonlinear two-level system which related to the nonlinearity and the non-Hermicity.