Non-Hermitian Hamiltonians, which effectively describe dissipative systems,<br>and analogue gravity models, which simulate properties of gravitational<br>objects, comprise seemingly different areas of current research. Here, we<br>investigate the interplay between the two by relating parity-time-symmetric<br>dissipative Weyl-type Hamiltonians to analogue Schwarzschild black holes<br>emitting Hawking radiation. We show that the exceptional points of these<br>Hamiltonians form tilted cones mimicking the behavior of the light cone of a<br>radially infalling observer approaching a black hole horizon. We further<br>investigate the presence of tunneling processes, reminiscent of those happening<br>in black holes, in a concrete example model. We interpret the non-trivial<br>result as the purely thermal contribution to analogue Hawking radiation in a<br>Schwarzschild black hole. Assuming that our particular Hamiltonian models a<br>photonic crystal of experimental relevance, we argue that the loss from the<br>latter in the form of thermal radiation can be interpreted as the blackbody<br>contribution to analogue black hole radiation when measuring at the exceptional<br>cone. As such, these systems are promising candidates for black hole analogue<br>models.
Protection of all nondefective twofold degeneracies by antiunitary symmetries in non-Hermitian systems
Sharareh Sayyad
Physical Review Research
4
(4)
043213
(2022)
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Non-Hermitian degeneracies are classified as defective exceptional points (EPs) and nondefective de- generacies. While in defective EPs, both eigenvalues and eigenvectors coalesce, nondefective degeneracies are characterized merely by the emergence of degenerate eigenvalues. It is also known that all degeneracies are either symmetryprotected or accidental. In this paper, I prove that antiunitary symmetries protect all nondefective twofold degeneracies. By developing a 2D non-Hermitian tight-binding model, I have demonstrated that these symmetries comprise various symmetry operations, such as discrete or spatial point-group symmetries and Wick’s rotation in the non-Hermitian parameter space. Introducing these composite symmetries, I present the protection of nondefective degeneracies in various parameter regimes of my model. This work paves the way to stabilizing nondefective degeneracies and offers a new perspective on understanding non-Hermitian band crossings.
Bound states and photon emission in non-Hermitian nanophotonics
Zongping Gong,
Miguel Bello,
Daniel Malz,
Flore K. Kunst
Physical Review A
106
053517
(2022)
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We establish a general framework for studying the bound states and the photon-emission dynamics of quantum emitters coupled to structured nanophotonic lattices with engineered dissipation (loss). In the single-excitation sector, the system can be described exactly by a non-Hermitian formalism. We have pointed out in the accompanying letter [Gong,et al., arXiv:2205.05479] that a single emitter coupled to a one-dimensional non-Hermitian lattice may already exhibit anomalous behaviors without Hermitian counterparts. Here we provide further detail on these observations. We also present several additional examples on the cases with multiple quantum emitters or in higher dimensions. Our work unveils the tip of the iceberg of the rich non-Hermitian phenomena in dissipative nanophotonic systems.
Anomalous Behaviors of Quantum Emitters in Non-Hermitian Baths
Zongping Gong,
Miguel Bello Gamboa,
Daniel Malz,
Flore K. Kunst
Both non-Hermitian systems and the behaviour of emitters coupled to<br>structured baths have been studied intensely in recent years. Here we study the<br>interplay of these paradigmatic settings. In a series of examples, we show that<br>a single quantum emitter coupled to a non-Hermitian bath displays a number of<br>unconventional behaviours, many without Hermitian counterpart. We first<br>consider a unidirectional hopping lattice whose complex dispersion forms a<br>loop. We identify peculiar bound states inside the loop as a manifestation of<br>the non-Hermitian skin effect. In the same setting, emitted photons may display<br>spatial amplification markedly distinct from free propagation, which can be<br>understood with the help of the generalized Brillouin zone. We then consider a<br>nearest-neighbor lattice with alternating loss. We find that the long-time<br>emitter decay always follows a power law, which is usually invisible for<br>Hermitian baths. Our work points toward a rich landscape of anomalous quantum<br>emitter dynamics induced by non-Hermitian baths.
Bound states and photon emission in non-Hermitian nanophotonics
Zongping Gong,
Miguel Bello,
Daniel Malz,
Flore K. Kunst
Physical Review A
106
053517
(2022)
| Journal
| PDF
Realizing exceptional points of any order in the presence of symmetry
Sharareh Sayyad,
Flore K. Kunst
Physical Review Research
4
(2)
023130
(2022)
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Exceptional points~(EPs) appear as degeneracies in the spectrum of non-Hermitian matrices at which the eigenvectors coalesce. In general, an EP of order n may find room to emerge if 2(n−1) real constraints are imposed. Our results show that these constraints can be expressed in terms of the determinant and traces of the non-Hermitian matrix. Our findings further reveal that the total number of constraints may reduce in the presence of unitary and antiunitary symmetries. Additionally, we draw generic conclusions for the low-energy dispersion of the EPs. Based on our calculations, we show that in odd dimensions the presence of sublattice or pseudo-chiral symmetry enforces nth order EPs to disperse with the (n−1)th root. For two-, three- and four-band systems, we explicitly present the constraints needed for the occurrence of EPs in terms of system parameters and classify EPs based on their low-energy dispersion relations.
Anomalous Behaviors of Quantum Emitters in Non-Hermitian Baths
Zongping Gong,
Miguel Bello,
Daniel Malz,
Flore K. Kunst
Physical Review Letters
129
223601
(2022)
| Journal
| PDF
Both non-Hermitian systems and the behaviour of emitters coupled to structured baths have been studied intensely in recent years. Here we study the interplay of these paradigmatic settings. In a series of examples, we show that a single quantum emitter coupled to a non-Hermitian bath displays a number of unconventional behaviours, many without Hermitian counterpart. We first consider a unidirectional hopping lattice whose complex dispersion forms a loop. We identify peculiar bound states inside the loop as a manifestation of the non-Hermitian skin effect. In the same setting, emitted photons may display spatial amplification markedly distinct from free propagation, which can be understood with the help of the generalized Brillouin zone. We then consider a nearest-neighbor lattice with alternating loss. We find that the long-time emitter decay always follows a power law, which is usually invisible for Hermitian baths. Our work points toward a rich landscape of anomalous quantum emitter dynamics induced by non-Hermitian baths.
Upon combining dissipative and nonlinear effects in a bipartite lattice of cavity polaritons, dissipatively stabilized bulk gap solitons emerge, which create a topological interface.
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Max Planck Institute for the Science of Light Staudtstr. 2 91058 Erlangen, Germany
