Abstract
Photons do not directly interact with magnetic fields. Recent progress in synthetic gauge fields have stimulated investigations in various fields. In this study, we explore the enclosed synthetic magnetic flux in a parity-time ($\mathcal{PT}$)-symmetric system of three coupled optical resonators; this flux suppresses the $\mathcal{PT}$ transition and affects the topological structure of $\mathcal{PT}$ transition points. Although the phase rigidities of the coalesced states no longer vanish at exceptional points (EPs), the orders of the EPs (which are affected by the magnetic flux) can be identified. At a three-state coalescence, the intensity of an initial excitation increases according to a power law, and at a two-state coalescence, the intensity can behave as invariant, oscillatory, quadratic increase, and oscillatory quadratic increase. Our findings provide an insight into the interplay between non-Hermiticity and the effective magnetic flux.
Highlights
The size of the PT symmetric region is at a maximum for a magnetic flux of = nπ + π/2 (n ∈ Z)
The phase rigidity no longer vanishes at the exceptional points (EPs) for a magnetic flux of = nπ, (n ∈ Z); the order of the EPs can still be identified from their power exponents in the exact PT -symmetric phase in the vicinity of the EPs
The time evolution at the EPs is quantitatively studied, and the results provide a paradigm for the study of the dynamics at EPs
Summary
Parity-time (PT )-symmetric systems possess intriguing features that derive from their non-Hermiticity and PT symmetry, and such systems were extensively investigated, both theoretically [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22] and experimentally [23,24,25,26,27,28]. Power oscillation was previously demonstrated in active-passive coupled waveguides [24], and unidirectional reflectionless and invisible transmissions were realized in PT -symmetric periodical structures [26]. The realized PT -symmetric coupled waveguides and resonators were described using concise and simple two-site models, PT symmetry breaking [23], power oscillation [24], and unidirectional reflectionless transmission [26] were all discovered in these linear systems. To determine the dynamic features of the coupled resonators at the PT transition points, we examine the time evolution of different initial excitations. The intensity of an initial excitation has four typical behaviours: (i) invariant, (ii) oscillatory, (iii) quadratic increase, and (iv) oscillatory quadratic increase These are the typical dynamics of the intensity in a PT -symmetric system at EPs with the eigenstates partially coalesced.
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