Non-adiabatic transitions through exceptional points in the band structure of a PT-symmetric lattice

Abstract

Exceptional points, at which two or more eigenfunctions of a Hamiltonian coalesce, occur in non-Hermitian systems and lead to surprising physical effects. In particular, the behaviour of a system under parameter variation can differ significantly from the familiar Hermitian case in the presence of exceptional points. Here we analytically derive the probability of a non-adiabatic transition in a two-level system driven through two consecutive exceptional points at finite speed. The system is Hermitian far away from the exceptional points. In the adiabatic limit an equal redistribution between the states coalescing in the exceptional point is observed, which can be interpreted as a loss of information when passing through the exceptional point. For finite parameter variation this gets modified. We demonstrate how the transition through the exceptional points can be experimentally addressed in a PT-symmetric lattice using Bloch oscillations.

arXiv commentslightly revised and extended version, 7 pages, 6 figures

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• Nonlinear Non-Hermitian Landau-Zener-Stückelberg-Majorana interferometry
• Crossing exceptional points in non-Hermitian quantum systems
• Quantum Metric Unveils Defect Freezing in Non-Hermitian Systems
• Observables in non-Hermitian systems: A methodological comparison
• Adiabatic-impulse approximation in non-Hermitian Landau-Zener Model
• Nonadiabatic transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric two-level systems
• Nonadiabatic dissociation of molecular Bose-Einstein condensates: competition between chemical reactions
• Bloch oscillations in a Bose-Hubbard chain with single-particle losses
• Non-adiabatic transitions in parabolic and super-parabolic $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian systems
• Landau-Zener transitions through a pair of higher order exceptional points
• Topological Switching via Exceptional Point Pairs in an Optical Microcavity Laser