Non-Hermitian photonics promises exceptional topology of light

Midya, Bikashkali; Zhao, Han; Feng, Liang

doi:10.1038/s41467-018-05175-8

Cited by 167 publications

(111 citation statements)

References 15 publications

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“…The EP has many applications in optics [21][22][23][24][25][26][27], not limited to non-reciprocal energy transfer [23], unidirectional lasing [28,29], and optical sensing [30,31]. Bidirectional lasing alters to unidirectional lasing when approaching the EP [32]; the direction of lasing is controllable through adjusting the chiral mode of the micro resonator.…”

Section: Introductionmentioning

confidence: 99%

High-order exceptional points in supersymmetric arrays

Zhang

Jin

et al. 2020

Phys. Rev. A

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We employ the intertwining operator technique to synthesize a supersymmetric (SUSY) array of arbitrary size N . The synthesized SUSY system is equivalent to a spin-(N − 1)/2 under an effective magnetic field. By considering an additional imaginary magnetic field, we obtain a generalized parity-time-symmetric non-Hermitian Hamiltonian that describes a SUSY array of coupled resonators or waveguides under a gradient gain and loss; all the N energy levels coalesce at an exceptional point (EP), forming the isotropic high-order EP with N states coalescence (EPN). Near the EPN, the scaling exponent of phase rigidity for each eigenstate is (N − 1)/2; the eigen frequency response to the perturbation acting on the resonator or waveguide couplings is 1/N . Our findings reveal the importance of the intertwining operator technique for the spectral engineering and exemplify the practical application in non-Hermitian physics. arXiv:2003.07510v1 [quant-ph]

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Section: Introductionmentioning

confidence: 99%

High-order exceptional points in supersymmetric arrays

Zhang

Jin

et al. 2020

Phys. Rev. A

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“…In the neighboring asymmetric dimers, the asymmetric couplings with stronger and weaker coupling amplitudes are in the opposite directions, which is due to the difference in the one-way amplification and one-way attenuation. At µν = 0, the asymmetric couplings are unidirectional [164,177] and result in highly defective EPs. Notably, alternately introducing the gain and loss under inversion symmetry prevents the one-way amplification, one-way attenuation, and nonzero accumulation of imaginary flux.…”

Section: Discussionmentioning

confidence: 99%

“…3 represent the gapless phase with two symmetry protected EPs. The EPs possess distinct topology from that of DPs due to the bifurcation linking the Riemann surface [151][152][153][154][155][156][157][158][159][160][161][162][163][164][165].…”

Section: The Phase Diagram and Topological Characterizationmentioning

confidence: 99%

Inversion symmetric non-Hermitian Chern insulator

Jin

Song

2019

Phys. Rev. B

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We propose a two-dimensional non-Hermitian Chern insulator with inversion symmetry, which is anisotropic and has staggered gain and loss in both x and y directions. In this system, conventional bulk-boundary correspondence holds. The Chern number is a topological invariant that accurately predicts the topological phase transition and the existence of helical edge states in the topologically nontrivial phase. The band touching points are isolated and protected by the symmetry. The band touching affects the existence of helical edge states. Moreover, topologically protected helical edge states exist in the gapless phase for the system under open boundary condition in one direction. The detaching points between the edge states and the bulk states are predicted by the winding number associated with the vector field of average values of Pauli matrices. The non-Hermiticity also supports a topological phase with zero Chern number, where a pair of in-gap helical edge states exists. Our findings provide insights into the symmetry protected non-Hermitian topological insulators.

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“…Notably, the two coalescence eigenstates in H SSH and H † SSH are the two degenerate zero modes of the uniform ring, being orthogonal ψ − |ψ + = 0. The two coalescence eigenstates possess opposite chiralities classified by the type of EP [6,46,[56][57][58]. The non-Hermitian SSH ring H SSH engineered at the EP only supports the resonant transmission for the incident wave with one of two momenta k y = ±π/2.…”

Section: Chiral Scattering Centermentioning

confidence: 99%

“…Nonreciprocal photonics in the non-Hermitian physics are revealed to be useful for the applications in optics [40][41][42][43][44][45]. Non-Hermitian system at exceptional point (EP) has a coalescence state [6,46]. We propose an application of the PT -symmetric non-Hermitian Su-Schrieffer-Heeger (SSH) model at the EP [47][48][49][50][51][52][53], which exhibits unidirectionality without the assistance of magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Helical resonant transport and purified amplification at an exceptional point

2019

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We propose an application of a parity-time symmetric non-Hermitian Su-Schrieffer-Heeger (SSH) model by embedded it in a two-dimensional square lattice tube. The coalescence state at the exceptional point of non-Hermitian SSH model is chiral and selectively controls helical transport and amplification. Two typical helicity-dependent scattering dynamics are observed. If the incidence has an identical helicity with the embedded non-Hermitian SSH model, we observe a perfect transmission without reflection. However, if the incidence has an opposite helicity with the embedded non-Hermitian SSH model, except for a full transmission, we observe an amplified transmission with different helicity from the incidence; but the amplified reflection has identical helicity with the incidence. These intriguing features are completely unexpected in Hermitian system. Moreover, the helical amplification at high efficiency can be triggered by an arbitrary excitation. The different dynamics between incidences with opposite helicities are results of unidirectional tunneling, which is revealed to be capable of realizing without introducing magnetic field. We give a discussion about the helical dynamics under system imperfections. Our findings open a direction in all-optical device and provide perspectives in non-Hermitian transport. *

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Non-Hermitian photonics promises exceptional topology of light

Abstract: The band degeneracy, either the exceptional point of a non-Hermitian system or the Dirac point associated with a topological system, can feature distinct symmetry and topology. Their synergy will further produce more exotic topological effects in synthetic matter.

Cited by 167 publications

References 15 publications

High-order exceptional points in supersymmetric arrays

High-order exceptional points in supersymmetric arrays

Inversion symmetric non-Hermitian Chern insulator

Helical resonant transport and purified amplification at an exceptional point

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