Jamming anomaly in $\mathcal{P}\mathcal{T}$-symmetric systems

Abstract

The Schrödinger equation with a $\mathcal{P}\mathcal{T}$-symmetric potential is used to model an optical structure consisting of an element with gain coupled to an element with loss. At low gain-loss amplitudes $\gamma$, raising the amplitude results in the energy flux from the active to the leaky element being boosted. We study the anomalous behaviour occurring for larger $\gamma$, where the increase of the amplitude produces a drop of the flux across the gain-loss interface. We show that this jamming anomaly is either a precursor of the exceptional point, where two real eigenvalues coalesce and acquire imaginary parts, or precedes the eigenvalue's immersion in the continuous spectrum.

20 pages, 4 figures; to appear in New Journal of Physics in the focus issue "Parity-Time Symmetry in Optics and Photonics"

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Cited by in corpus (12)

• $\mathcal{P}\mathcal{T}$-symmetric circuit-QED
• Exceptional points and photonic catastrophe
• Spinor solitons and their $\mathcal{P}\mathcal{T}$-symmetric offspring
• Stationary through-flows in a Bose-Einstein condensate with a PT-symmetric impurity
• Dynamical signature of moire pattern in non-Hermitian ladder
• PT-symmetric quantum oscillator in an optical cavity
• Nonlinear currents in a ring-shaped waveguide with balanced gain and dissipation
• Optical fluxes in coupled $\mathcal{P}\mathcal{T}$-symmetric photonic structures
• Bifurcations of thresholds in essential spectra of elliptic operators under localized non-Hermitian perturbations
• Hybrid patterns and solitonic frequency combs in non-Hermitian Kerr Cavities
• Nonlinear behaviors of parity-time-symmetric lasers
• PT-symmetric and antisymmetric nonlinear states in a split potential box