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1. Wave Excitation and Dynamics in Non-Hermitian Disordered Systems

   https://doi.org/10.1103/PhysRevResearch.4.013102  

   Huang, Y.; Kang, Yuhao; Genack, Azriel Z. (February 2022, Physical review research)

   Dynamic and steady-state aspects of wave propagation are deeply connected in lossless open systems ‎in which the scattering matrix is unitary. There is then an equivalence among the energy excited within ‎the medium through all channels, the Wigner time delay, which is the sum of dwell times in all ‎channels coupled to the medium, and the density of states. But these equivalences fall away in the ‎presence of material loss or gain. In this paper, we use microwave measurements, numerical ‎simulations, and theoretical analysis to discover the changing relationships among fundamental wave ‎properties with loss and gain, and their dependence upon dimensionality and spectral overlap. We ‎begin with the demonstrations that the transmission time in random 1D media is equal to the density ‎of states even in the presence of ultrastrong absorption and that its ensemble average is independent ‎of the strengths of scattering and absorption. In contrast, the Wigner time becomes imaginary in the ‎presence of loss, with real and imaginary parts that fall with absorption. In multichannel media, the ‎transmission time remains equal to the density of states and is independent of the scattering strength ‎in unitary systems but falls with absorption to a degree that increases with the strengths of absorption ‎and scattering, and the number of channels coupled to the medium. We show that the relationships ‎between key propagation variables in non-Hermitian systems can be understood in terms of the ‎singularities of the phase of the determinant of the transmission matrix. The poles of the transmission ‎matrix are the same as those of the scattering matrix, but the transmission zeros are fundamentally ‎different. Whereas the zeros of the scattering matrix are the complex conjugates of the poles, the ‎transmission zeros are topological: in unitary systems they occur only singly on the real axis or as ‎conjugate pairs. We follow the evolution and statistics of zeros in the complex plane as random ‎samples are deformed. The sensitivity of the spacing of zeros in the complex plane with deformation ‎of the sample has a square-root singularity at a zero point at which two single zeros and a complex ‎pair interconvert. The transmission time is a sum of Lorentzian functions associated with poles and ‎zeros. The sum over poles is the density of states with an average that is independent of scattering ‎and dissipation. But the sum over zeros changes with loss, gain, scattering strength and the number of ‎channels in ways that make it possible to control ultranarrow spectral features in transmission and ‎transmission time. We show that the field, including the contribution of the still coherent incident ‎wave, is a sum over modal partial fractions with amplitudes that are independent of loss and gain. The ‎energy excited may be expressed in terms of the resonances of the medium and is equal to the dwell ‎time even in the presence of loss or gain.‎ 

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2. Exact Fisher zeros and thermofield dynamics across a quantum critical point

   https://doi.org/10.1103/PhysRevResearch.6.043139  

   Liu, Yang; Lv, Songtai; Meng, Yuchen; Tan, Zefan; Zhao, Erhai; Zou, Haiyuan (November 2024, Physical Review Research)

   By setting the inverse temperature $\beta$ loose to occupy the complex plane, Fisher showed that the zeros of the complex partition function $Z$, if approaching the real $\beta$ axis, reveal a thermodynamic phase transition. More recently, Fisher zeros were used to mark the dynamical phase transition in quench dynamics. It remains unclear, however, how Fisher zeros can be employed to better understand quantum phase transitions or the nonunitary dynamics of open quantum systems. Here we answer this question by a comprehensive analysis of the analytically continued one-dimensional transverse field Ising model. We exhaust all the Fisher zeros to show that in the thermodynamic limit they congregate into a remarkably simple pattern in the form of continuous open or closed lines. These Fisher lines evolve smoothly as the coupling constant is tuned, and a qualitative change identifies the quantum critical point. By exploiting the connection between $Z$ and the thermofield double states, we obtain analytical expressions for the short- and long-time dynamics of the survival amplitude, including its scaling behavior at the quantum critical point. We point out $Z$ can be realized and probed in monitored quantum circuits. The exact analytical results are corroborated by the numerical tensor renormalization group. We further show that similar patterns of Fisher zeros also emerge in other spin models. Therefore, the approach outlined may serve as a powerful tool for interacting quantum systems. 

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3. Reflectionless excitation of arbitrary photonic structures: a general theory

   https://doi.org/10.1515/nanoph-2020-0403  

   Stone, A. Douglas; Sweeney, William R.; Hsu, Chia Wei; Wisal, Kabish; Wang, Zeyu (October 2020, Nanophotonics)

   null (Ed.)

   Abstract We outline and interpret a recently developed theory of impedance matching or reflectionless excitation of arbitrary finite photonic structures in any dimension. The theory includes both the case of guided wave and free-space excitation. It describes the necessary and sufficient conditions for perfectly reflectionless excitation to be possible and specifies how many physical parameters must be tuned to achieve this. In the absence of geometric symmetries, such as parity and time-reversal, the product of parity and time-reversal, or rotational symmetry, the tuning of at least one structural parameter will be necessary to achieve reflectionless excitation. The theory employs a recently identified set of complex frequency solutions of the Maxwell equations as a starting point, which are defined by having zero reflection into a chosen set of input channels, and which are referred to as R-zeros. Tuning is generically necessary in order to move an R-zero to the real frequency axis, where it becomes a physical steady-state impedance-matched solution, which we refer to as a reflectionless scattering mode (RSM). In addition, except in single-channel systems, the RSM corresponds to a particular input wavefront, and any other wavefront will generally not be reflectionless. It is useful to consider the theory as representing a generalization of the concept of critical coupling of a resonator, but it holds in arbitrary dimension, for arbitrary number of channels, and even when resonances are not spectrally isolated. In a structure with parity and time-reversal symmetry (a real dielectric function) or with parity–time symmetry, generically a subset of the R-zeros has real frequencies, and reflectionless states exist at discrete frequencies without tuning. However, they do not exist within every spectral range, as they do in the special case of the Fabry–Pérot or two-mirror resonator, due to a spontaneous symmetry-breaking phenomenon when two RSMs meet. Such symmetry-breaking transitions correspond to a new kind of exceptional point, only recently identified, at which the shape of the reflection and transmission resonance lineshape is flattened. Numerical examples of RSMs are given for one-dimensional multimirror cavities, a two-dimensional multiwaveguide junction, and a multimode waveguide functioning as a perfect mode converter. Two solution methods to find R-zeros and RSMs are discussed. The first one is a straightforward generalization of the complex scaling or perfectly matched layer method and is applicable in a number of important cases; the second one involves a mode-specific boundary matching method that has only recently been demonstrated and can be applied to all geometries for which the theory is valid, including free space and multimode waveguide problems of the type solved here. 

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4. Complex-frequency excitations in photonics and wave physics

   https://doi.org/10.1126/science.ado4128  

   Kim, Seunghwi; Krasnok, Alex; Alù, Andrea (March 2025, Science)

   Closed, lossless optical cavities are characterized by a Hamiltonian that obeys Hermiticity, resulting in strictly real-valued resonance frequencies. By contrast, non-Hermitian wave systems are characterized by Hamiltonians with poles and zeros at complex frequencies, whose control through precise engineering of material loss and gain can lead to exotic scattering phenomena. Notably, excitation signals that oscillate at complex-valued frequencies can mimic the emergence of gain and loss, facilitating access to these non-Hermitian responses without material modifications. These findings have been advancing the fundamental understanding of wave-matter interactions and are enabling breakthroughs in metamaterials, imaging, sensing, and computing. This Review examines theoretical advances and experimental discoveries in this emerging field, demonstrating how tailored time-domain excitations offer new opportunities for wave manipulation and control. 

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5. Cascaded PT-symmetric artificial sheets: multimodal manipulation of self-dual emitter-absorber singularities, and unidirectional and bidirectional reflectionless transparencies

   https://doi.org/10.1088/1361-6463/ac3300  

   Yang, Minye; Ye, Zhilu; Farhat, Mohamed; Chen, Pai-Yen (November 2021, Journal of Physics D: Applied Physics)

   Abstract We introduce cascaded parity-time (PT)-symmetric artificial sheets (e.g. metasurfaces or frequency selective surfaces) that may exhibit multiple higher-order laser-absorber modes and bidirectional reflectionless transmission resonances within the PT-broken phase, as well as a unidirectional reflectionless transmission resonance associated with the exceptional point (EP). We derive the explicit expressions of the gain–loss parameter required for obtaining these modes and their intriguing physical properties. By exploiting the cascaded PT structures, the gain–loss threshold for the self-dual laser-absorber operation can be remarkably lowered, while the EP remains unaltered. We further study interferometric sensing based on such a multimodal laser-absorber and demonstrate that its sensitivity may be exceptionally high and proportional to the number of metasurfaces along the light propagation direction. 

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