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Nonlinear science.

Third and fourth-order exceptional points of Photon–phonon quantization in rare earth ions-doped microcrystals

Muhammad Usman, Zeeshan Mujahid, Lin Li, Guobin Liu, Zhijing Zhang, Fiza Latif, Muhammad Awais Shahid, Huanrong Fan, Yanpeng Zhang

Published Nov 6, 2025• 7 citations
Publisher
DOI
10.1016/j.nls.2025.100074

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The response of open physical systems has recently been recognized as a novel way to engineer non-Hermitian degeneracies, also known as exceptional points (EPs). We investigate the fourth-order parity-time (PT) and anti-parity-time (APT) symmetries for phase conjugation and self-diffraction under spontaneous six-wave mixing (SSWM) processes across various dressing schemes, including parallel, parallel-cascade, parallel-nested, pure-nested, cascade-nested, pure-cascade, and nested-cascade triple dressing schemes. Our investigation reveals that during the “self-diffraction” process sequential fourth-order non-Hermitian interactions between nested and cascade-nested triple dressing fields, where the photon dressing Rabi frequency exhibits dominance, lead to the sequential fourth-order quantization characterized by five EPs. Meanwhile, a sequential third-order PT–APT quantization is governed by six EPs under the dominance of the dephasing rate. Pure-cascade and nested-cascade triple dressing schemes exhibit a third-order quantization accompanied by four EPs. Additionally, the differential interplay between two dressing dephasing rates yields eight EPs in the pure-cascade triple dressing scheme. In the context of phase conjugation, pure-nested and cascade-nested dominated by the photon dressing Rabi frequency manifest a fourth-order PT–APT symmetric quantization characterized by two EPs. Simultaneously, a third-order PT–APT quantization characterized by six EPs results from an enhanced dephasing rate. Finally, three dressing schemes (parallel, parallel-nested, and parallel-cascade) exhibit second-order quantization arising from weakest non-Hermitian interaction. These outcomes are used to develop quantum memory devices with enhanced sensitivity in the atomic system.