$\mathcal{P}\mathcal{T}-$Symmetric Dimers with Time-Periodic Gain/Loss Function

Abstract

$\mathcal{P}T-$symmetric dimers with a time-periodic gain/loss function in a balanced configuration where the amount of gain equals that of loss are investigated analytically and numerically. Two prototypical dimers in the linear regime are investigated: a system of coupled classical oscillators, and a Schrödinger dimer representing the coupling of field amplitudes; each system representing a wide class of physical models. Through a thorough analysis of their stability behaviour, we find that turning on the coupling parameter in the classical dimer system, leads initially to decreased stability but then to re-entrant transitions from the exact to the broken $\mathcal{P}T-$phase and vice versa, as it is increased beyond a critical value. On the other hand, the Schrödinger dimer behaves more like a single oscillator with time-periodic gain/loss. In addition, we are able to identify the conditions under which the behaviour of the two dimer systems coincides and/or reduces to that of a single oscillator.

9 pages, 9 figures, META14 Conference, subm. Special Issue Appl. Phys. A

References in corpus (10)

• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Gain-Driven Discrete Breathers in PT-Symmetric Nonlinear Metamaterials
• Breathers in PT-symmetric optical couplers
• Stable dark solitons in PT-symmetric dual-core waveguides
• Discrete solitons in PT-symmetric lattices
• Actively coupled optical waveguides
• PT-Symmetric Dimer of Coupled Nonlinear Oscillators
• On the integrability of PT-symmetric dimers
• Parity-Time Synthetic Laser

Cited by in corpus (6)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Experimental realization of Floquet PT-symmetric systems
• Photonic Floquet media with a complex time-periodic permittivity
• Floquet Protocols of Adiabatic State-Flips and Re-Allocation of Exceptional Points
• Non-Convergent Perturbation Theory and Misleading Inferences about Parameter Relationships: the Case of Superexchange
• Exceptional Points of Degeneracy Induced by Linear Time-Periodic Variation Hamidreza