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Register a new userPassive $mathcal{PT}$-symmetry breaking transitions without exceptional points in dissipative photonic systems
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Over the past decade, parity-time ($mathcal{PT}$)-symmetric Hamiltonians have been experimentally realized in classical, optical settings with balanced gain and loss, or in quantum systems with localized loss. In both realizations, the $mathcal{PT}$-symmetry breaking transition occurs at the exceptional point of the non-Hermitian Hamiltonian, where its eigenvalues and the corresponding eigenvectors both coincide. Here, we show that in lossy systems, the $mathcal{PT}$ transition is a phenomenon that broadly occurs without an attendant exceptional point, and is driven by the potential asymmetry between the neutral and the lossy regions. With experimentally realizable quantum models in mind, we investigate dimer and trimer waveguide configurations with one lossy waveguide. We validate the tight-binding model results by using the beam propagation method analysis. Our results pave a robust way toward studying the interplay between passive $mathcal{PT}$ transitions and quantum effects in dissipative photonic configurations.
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Exceptional points in non-Hermitian systems have recently been shown to possess nontrivial topological properties, and to give rise to many exotic physical phenomena. However, most studies thus far have focused on isolated exceptional points or one-dimensional lines of exceptional points. Here, we substantially expand the space of exceptional systems by designing two-dimensional surfaces of exceptional points, and find that symmetries are a key element to protect such exceptional surfaces. We construct them using symmetry-preserving non-Hermitian deformations of topological nodal lines, and analyze the associated symmetry, topology, and physical consequences. As a potential realization, we simulate a parity-time-symmetric 3D photonic crystal and indeed find the emergence of exceptional surfaces. Our work paves the way for future explorations of systems of exceptional points in higher dimensions.
We demonstrate the existence of exceptional points of degeneracy (EPD) of periodic eigenstates in non-Hermitian coupled chains of dipolar scatterers. Guided modes supported by these structures can exhibit an EPD in their dispersion diagram at which two or more Bloch eigenstates coalesce, in both their eigenvectors and eigenvalues. We show a second-order modal EPD associated with the parity-time ($cal{PT}$) symmetry condition, at which each particle pair in the double chain exhibits balanced gain and loss. Furthermore, we also demonstrate a fourth-order EPD occurring at the band edge. Such degeneracy condition was previously referred to as a degenerate band edge in lossless anisotropic photonic crystals. Here, we rigorously show it under the occurrence of gain and loss balance for a discrete guiding system. We identify a more general regime of gain and loss balance showing that $cal{PT}$-symmetry is not necessary to realize EPDs. Furthermore, we investigate the degree of detuning of the EPD when the geometrical symmetry or balanced condition is broken. These findings open unprecedented avenues toward superior light localization and transport with application to high-Q resonators utilized in sensors, filters, low-threshold switching and lasing.
Standard exceptional points (EPs) are non-Hermitian degeneracies that occur in open systems. At an EP, the Taylor series expansion becomes singular and fails to converge -- a feature that was exploited for several applications. Here, we theoretically introduce and experimentally demonstrate a new class of parity-time symmetric systems [implemented using radio frequency (rf) circuits] that combine EPs with another type of mathematical singularity associated with the poles of complex functions. These nearly divergent exceptional points can exhibit an unprecedentedly large eigenvalue bifurcation beyond those obtained by standard EPs. Our results pave the way for building a new generation of telemetering and sensing devices with superior performance.
Non-Hermitian systems, with symmetric or antisymmetric Hamiltonians under the parity-time ($mathcal{PT}$) operations, can have entirely real eigenvalues. This fact has led to surprising discoveries such as loss-induced lasing and topological energy transfer. A merit of anti-$mathcal{PT}$ systems is free of gain, but in recent efforts on making anti-$mathcal{PT}$ devices, nonlinearity is still required. Here, counterintuitively, we show how to achieve anti-$mathcal{PT}$ symmetry and its spontaneous breaking in a linear device by spinning a lossy resonator. Compared with a Hermitian spinning device, significantly enhanced optical isolation and ultrasensitive nanoparticle sensing are achievable in the anti-$mathcal{PT}$-broken phase. In a broader view, our work provides a new tool to study anti-$mathcal{PT}$ physics, with such a wide range of applications as anti-$mathcal{PT}$ lasers, anti-$mathcal{PT}$ gyroscopes, and anti-$mathcal{PT}$ topological photonics or optomechanics.
We study symmetries of open bosonic systems in the presence of laser pumping. Non-Hermitian Hamiltonians describing these systems can be parity-time (${cal{PT}}$) symmetric in special cases only. Systems exhibiting this symmetry are characterised by real-valued energy spectra and can display exceptional points, where a symmetry-breaking transition occurs. We demonstrate that there is a more general type of symmetry, i.e., rotation-time (${cal{RT}}$) symmetry. We observe that ${cal{RT}}$-symmetric non-Hermitian Hamiltonians exhibit real-valued energy spectra which can be made singular by symmetry breaking. To calculate the spectra of the studied bosonic non-diagonalisable Hamiltonians we apply diagonalisation methods based on bosonic algebra. Finally, we list a versatile set rules allowing to immediately identifying or constructing ${cal{RT}}$-symmetric Hamiltonians. We believe that our results on the ${cal{RT}}$-symmetric class of bosonic systems and their spectral singularities can lead to new applications inspired by those of the ${cal{PT}}$-symmetric systems.
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