Anomalous Parity-Time Symmetry Transition away from an Exceptional Point

Abstract

Parity-time (PT) symmetric systems have two distinguished phases, e.g., one with real energy eigenvalues and the other with complex conjugate eigenvalues. To enter one phase from the other, it is believed that the system must pass through an exceptional point, which is a non-Hermitian degenerate point with coalesced eigenvalues and eigenvectors. In this letter we reveal an anomalous PT transition that takes place away from an exceptional point in a nonlinear system: as the nonlinearity increases, the original linear system evolves along two distinct PT-symmetric trajectories, each of which can have an exceptional point. However, the two trajectories collide and vanish away from these exceptional points, after which the system is left with a PT-broken phase. We first illustrate this phenomenon using a coupled mode theory and then exemplify it using paraxial wave propagation in a transverse periodic potential.

10 pages, 8 figures

References in corpus (13)

• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Visualization of Branch Points in PT-Symmetric Waveguides
• Spawning rings of exceptional points out of Dirac cones
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Reversing the Pump-Dependence of a Laser at an Exceptional Point
• Asymmetric scattering and non-orthogonal mode patterns in optical micro-spirals
• Experimental observation of the dual behavior of $\mathcal{P}\mathcal{T}$-symmetric scattering
• Nonlinear modal interactions in parity-time ($\mathcal{P}\mathcal{T}$) symmetric lasers
• Exceptional points and lasing self-termination in photonic molecules
• PT-symmetric quantum mechanics
• Stationary states of a PT-symmetric two-mode Bose-Einstein condensate
• Supersymetric laser arrays
• Scattering in $\mathcal{P}\mathcal{T}$ and $\mathcal{R}\mathcal{T}$ Symmetric Multimode Waveguides: Generalized Conservation Laws and Spontaneous Symmetry Breaking beyond One Dimension

Cited by in corpus (4)

• Perspective on topological states of non-Hermitian lattices
• Parity-Time Symmetry in Non-Hermitian Complex Optical Media
• Optical fluxes in coupled $\mathcal{P}\mathcal{T}$-symmetric photonic structures
• Identification of the metric for diagonalizable (anti-)pseudo-Hermitian Hamilton operators represented by two-dimensional matrices