Landau-Zener transitions through a pair of higher order exceptional points

Abstract

Non-Hermitian quantum systems with explicit time dependence are of ever-increasing importance. There are only a handful of models that have been analytically studied in this context. Here, a PT-symmetric non-Hermitian $N$-level Landau-Zener type problem with two exceptional points of $N$th order is introduced. The system is Hermitian for asymptotically large times, far away from the exceptional points, and has purely imaginary eigenvalues between the exceptional points. The full Landau-Zener transition probabilities are derived, and found to show a characteristic binomial behaviour. In the adiabatic limit the final populations are given by the ratios of binomial coefficients. It is demonstrated how this behaviour can be understood on the basis of adiabatic analysis, despite the breakdown of adiabaticity that is often associated with non-Hermitian systems.

arXiv comment12 pages, 5 figures

References in corpus (31)

• The physics of exceptional points
• Dynamically encircling exceptional points in a waveguide: asymmetric mode switching from the breakdown of adiabaticity
• Biorthogonal Quantum Mechanics
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Symmetry and Higher-Order Exceptional Points
• Signatures of three coalescing eigenfunctions
• High-order exceptional points in optomechanics
• Geometric phase around exceptional points
• Dynamically encircling exceptional points: in situ control of encircling loops and the role of the starting point
• Symmetry-protected multifold exceptional points and their topological characterization
• Dynamically encircling an exceptional point in a real quantum system
• Observation of Bloch oscillations in complex PT-symmetric photonic lattices
• Landau-Zener transition in a multilevel system. An exact result
• Non-Hermitian shortcut to adiabaticity
• Theory of Coupled Resonator Optical Waveguides (CROW) Exhibiting High Order Exceptional Points of Degeneracy
• Hierarchical construction of higher-order exceptional points
• Breakdown of adiabatic transfer of light in waveguides in the presence of absorption
• Parity-time symmetry in a flat band system
• Integrable time-dependent quantum Hamiltonians
• Impact of loss on the wave dynamics in photonic waveguide lattices
• Counterintuitive transitions in the multistate Landau-Zener problem with linear level crossings
• Integrable time-dependent Hamiltonians, solvable Landau-Zener models and Gaudin magnets
• The Quest for Solvable Multistate Landau-Zener Models
• Higher-order exceptional point and Landau-Zener Bloch oscillations in driven non-Hermitian photonic Lieb lattices
• Quantum integrability in the multistate Landau-Zener problem
• Quantum information dynamics in a high-dimensional parity-time-symmetric system
• Landau-Zener-Stückelberg Interferometry in $\mathcal{P}\mathcal{T}$-symmetric Non-Hermitian models
• Imaginary couplings in non-Hermitian coupled-mode theory: Effects on exceptional points of optical resonators
• Non-adiabatic transitions through exceptional points in the band structure of a PT-symmetric lattice
• Landau-Zener transitions mediated by an environment: population transfer and energy dissipation
• Stable Bloch oscillations and Landau-Zener tunneling in a non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric flat band lattice