Scattering Experiments with Microwave Billiards at an Exceptional Point under Broken Time Reversal Invariance

Abstract

Scattering experiments with microwave cavities were performed and the effects of broken time-reversal invariance (TRI), induced by means of a magnetized ferrite placed inside the cavity, on an isolated doublet of nearly degenerate resonances were investigated. All elements of the effective Hamiltonian of this two-level system were extracted. As a function of two experimental parameters, the doublet and also the associated eigenvectors could be tuned to coalesce at a so-called exceptional point (EP). The behavior of the eigenvalues and eigenvectors when encircling the EP in parameter space was studied, including the geometric amplitude that builds up in the case of broken TRI. A one-dimensional subspace of parameters was found where the differences of the eigenvalues are either real or purely imaginary. There, the Hamiltonians were found PT-invariant under the combined operation of parity (P) and time reversal (T) in a generalized sense. The EP is the point of transition between both regions. There a spontaneous breaking of PT occurs.

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• $\mathcal{P}\mathcal{T}$-symmetric wave guide system with evidence of a third-order exceptional point
• State Flip at Exceptional Points in Atomic Spectra
• Rydberg systems in parallel electric and magnetic fields: an improved method for finding exceptional points
• Characteristic dynamics near two coalescing eigenvalues incorporating continuum threshold effects
• Unconventional next nearest neighbor resonance coupling and states flipping mechanism in degenerate optical microcavities
• Topological edge states in the Su-Schrieffer-Heeger model subject to balanced particle gain and loss
• The Shannon entropy and avoided crossings in closed and open quantum billiards
• Analysis of Dirac exceptional points and their isospectral Hermitian counterparts
• Simple models of three coupled $\mathcal{P}\mathcal{T}$-symmetric wave guides allowing for third-order exceptional points
• Quality enhancement with simultaneous suppression in excess noise of longer-lived states in non-uniformly pumped optical microcavities
• Indicators of wavefunction (de)localization in the avoided crossing in a quadrupole cavity
• Population transfer at exceptional points in spectra of the hydrogen atom in parallel electric and magnetic fields
• Stern-Gerlach splitters for lattice quasispin
• Superuniversal Statistics of Complex Time-Delays in Non-Hermitian Scattering Systems
• Linear and nonlinear stability of periodic orbits in annular billiards
• Purity oscillations in coupled Bose-Einstein condensates
• Superuniversal Statistics with Topological Origins for non-Hermitian Scattering Singularities
• Exceptional points in the elliptical three-disk scatterer using semiclassical periodic orbit quantization
• Characteristic influence of exceptional points in quantum dynamics