Non-adiabatic transitions in parabolic and super-parabolic $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian systems

Abstract

Exceptional points, the spectral degeneracy points in the complex parameter space, are fundamental to non-Hermitian quantum systems. The dynamics of non-Hermitian systems in the presence of exceptional points differ significantly from those of Hermitian ones. Here we investigate non-adiabatic transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric systems, in which the exceptional points are driven through at finite speed which are quadratic or cubic functions of time. We identity different transmission dynamics separated by exceptional points, and derive analytical approximate formulas for the non-adiabatic transmission probabilities. We discuss possible experimental realizations with a $\mathcal{P}\mathcal{T}$-symmetric non-Hermitian one-dimensional tight-binding optical waveguide lattice.

References in corpus (9)

• Making Sense of Non-Hermitian Hamiltonians
• Loss-induced suppression and revival of lasing
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Visualization of Branch Points in PT-Symmetric Waveguides
• PT-Symmetric Phonon Laser
• Reversing the Pump-Dependence of a Laser at an Exceptional Point
• Optomechanically-Induced Transparency in partiy-time-symmetric microresonators
• Time evolution of a Vlasov-Poisson plasma with different species and infinite mass in ${\mathbb{R}}^3$
• Oscillating potential well in complex plane and the adiabatic theorem

Cited by in corpus (1)

• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference