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Register a new userHigher-order exceptional point in a cavity magnonics system
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We propose to realize the pseudo-Hermiticity in a cavity magnonics system consisting of the Kittel modes in two small yttrium-iron-garnet spheres coupled to a microwave cavity mode. The effective gain of the cavity can be achieved using the coherent perfect absorption of the two input fields fed into the cavity. With certain constraints of the parameters, the Hamiltonian of the system has the pseudo-Hermiticity and its eigenvalues can be either all real or one real and other two constituting a complex-conjugate pair. By varying the coupling strengths between the two Kittel modes and the cavity mode, we find the existence of the third-order exceptional point in the parameter space, in addition to the usual second-order exceptional point existing in the system with parity-time symmetry. Also, we show that these exceptional points can be demonstrated by measuring the output spectrum of the cavity.
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Exceptional points (EPs), at which both eigenvalues and eigenvectors coalesce, are ubiquitous and unique features of non-Hermitian systems. Second-order EPs are by far the most studied due to their abundance, requiring only the tuning of two real parameters, which is less than the three parameters needed to generically find ordinary Hermitian eigenvalue degeneracies. Higher-order EPs generically require more fine-tuning, and are thus assumed to play a much less prominent role. Here, however, we illuminate how physically relevant symmetries make higher-order EPs dramatically more abundant and conceptually richer. More saliently, third-order EPs generically require only two real tuning parameters in presence of either $PT$ symmetry or a generalized chiral symmetry. Remarkably, we find that these different symmetries yield topologically distinct types of EPs. We illustrate our findings in simple models, and show how third-order EPs with a generic $sim k^{1/3}$ dispersion are protected by PT-symmetry, while third-order EPs with a $sim k^{1/2}$ dispersion are protected by the chiral symmetry emerging in non-Hermitian Lieb lattice models. More generally, we identify stable, weak, and fragile aspects of symmetry-protected higher-order EPs, and tease out their concomitant phenomenology.
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