Abstract
We investigate a parity-time ($\mathcal{PT}$)-symmetric system that consists of two symmetrically coupled asymmetric dimers. The enclosed magnetic flux controls the $\mathcal{PT}$ phase transition. The system can reenter the exact $\mathcal{PT}$-symmetric phase from a broken $\mathcal{PT}$-symmetric phase with large non-Hermiticity. Two-state coalescence may have one or two defective eigenstates. The topology of exceptional points is reflected by the phase rigidity scaling exponents. The topology changes when exceptional points coincide. The geometric phases accumulate when encircling the exceptional points and vary as the magnetic flux. The magnetic flux is favorable for the realization of high-order exceptional points. A triple point of different quantum phases has an order of 4. The perturbation around the four-state coalescence leads to a fourth-root mode frequency splitting; the sensing sensitivity is significantly enhanced.
Highlights
Parity-time (PT )-symmetric non-Hermitian Hamiltonians can possess real spectra; this discovery stimulated a burst of research interest in the extension of quantum mechanics [1,2,3,4,5,6,7,8,9,10]
The nonreciprocal coupling induces effective magnetic flux, which provides an extra degree of freedom, which helps with control of the PT phase transition
The effective magnetic flux is favorable for the realization of high-order exceptional points (EPs)
Summary
Parity-time (PT )-symmetric non-Hermitian Hamiltonians can possess real spectra; this discovery stimulated a burst of research interest in the extension of quantum mechanics [1,2,3,4,5,6,7,8,9,10]. The. PT phase transition threshold exists in a PT -symmetric sinusoidal potential, but any higher degree of non-Hermiticity leads to PT -symmetry breaking [25]. We demonstrate that the energy-level structure, the quantum phases, and the topology of EPs are affected by the magnetic flux, the coupling, and the degree of nonHermiticity. We investigate the influence of nonreciprocal couplings that induce effective magnetic flux on the spectrum, quantum phases, and topology of EPs. Notably, the magnetic flux as an additional degree of freedom does not break the PT symmetry of the system. The optical path-length difference introduced through the coupling process induces a nonreciprocal coupling phase factor, which effectively realizes a synthetic magnetic flux in the closed configuration formed by the four coupled primary resonators.
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