Parity‐Time Symmetry in Non‐Hermitian Complex Optical Media

Gupta, Samit Kumar; Zou, Yi; Zhu, Xinhua; Lu, Ming‐Hui; Zhang, Lijian; Li, Xiaoping; Chen, Yan‐Feng

doi:10.1002/adma.201903639

Cited by 93 publications

(37 citation statements)

References 302 publications

(494 reference statements)

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“…The exceptional point (EP) in a non-Hermitian system occurs when eigenstates coalesce [1][2][3], and usually associates with the non-Hermitian phase transition [4,5]. In a parity-time (PT ) symmetric non-Hermitian coupled system, the PT symmetry of eigenstates spontaneously breaks at the EP [6][7][8][9][10][11][12][13][14][15][16], which determines the exact PTsymmetric phase and the broken PT -symmetric phase in this system.…”

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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“…The photonic topological system can be described by the effective Hamiltonian consisting of two subsystems for the pseudospin states with opposite helicity 12 , 13 , 15 , 27 , 28 . In the presence of loss, the effective Hamiltonian of the system is non-Hermitian and the eigenvalue spectrum is no longer real 29 – 31 . The effect of loss is typically mitigated or compensated by gain.…”

Section: Introductionmentioning

confidence: 99%

Parity-time phase transition in photonic crystals with $$C_{6v}$$ symmetry

Jiang

Chen

Chern

2020

Sci Rep

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We investigate the parity-time (PT) phase transition in photonic crystals with $$C_{6v}$$ C 6 v symmetry, with balanced gain and loss on dielectric rods in the triangular lattice. A two-level non-Hermitian model that incorporates the gain and loss in the tight-binding approximation was employed to describe the dispersion of the PT symmetric system. In the unbroken PT phase, the double Dirac cone feature associated with the $$C_{6v}$$ C 6 v symmetry is preserved, with a frequency shift of second order due to the presence of gain and loss. The helical edge states with real eigenfrequencies can exist in the common band gap for two topologically distinct lattices. In the broken PT phase, the non-Hermitian perturbation deforms the dispersion by merging the frequency bands into complex conjugate pairs and forming the exceptional contours that feature the PT phase transition. In this situation, the band gap closes and the edge states are mixed with the bulk states.

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“…Exploring novel quantum phase or QPT [44][45][46][47][48][49][50][51][52] in non-Hermitian systems becomes an attractive topic. Motivated by the recent development of non-Hermitian quantum mechanics [53], both in theoretical and experimental aspects [26,[54][55][56][57][58][59][60][61][62][63][64][65][66], in this paper we investigate the QPTs in non-Hermitian regime. The purpose of the present work is to present a simple non-Hermitian model to demonstrate alternative type of QPT, which driven by a local parameter.…”

Section: Introductionmentioning

confidence: 99%

Semilocalization transition driven by a single asymmetrical tunneling

Wang¹,

Zhang²,

Song³

2020

Phys. Rev. A

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A local impurity usually only strongly affects few single-particle energy levels, thus cannot induce a quantum phase transition (QPT), or any macroscopic quantum phenomena in a many-body system within the Hermitian regime. However, it may happen for a non-Hermitian impurity. We investigate the many-body ground state property of a one-dimensional tight-binding ring with an embedded single asymmetrical dimer based on exact solutions. We introduce the concept of semi-localization state to describe a new quantum phase, which is a crossover from extended to localized state. The peculiar feature is that the decay length is of the order of the system size, rather than fixed as a usual localized state. In addition, the spectral statistics is non-analytic as asymmetrical hopping strengths vary, resulting a sudden charge of the ground state. The distinguishing feature of such a QPT is that the density of ground state energy varies smoothly due to unbroken symmetry. However, there are other observables, such as the groundstate center of mass and average current, exhibit the behavior of second-order QPT. This behavior stems from time-reversal symmetry breaking of macroscopic number of single-particle eigen states.

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Parity‐Time Symmetry in Non‐Hermitian Complex Optical Media

Cited by 93 publications

References 302 publications

High-order exceptional points in supersymmetric arrays

High-order exceptional points in supersymmetric arrays

Parity-time phase transition in photonic crystals with $$C_{6v}$$ symmetry

Semilocalization transition driven by a single asymmetrical tunneling

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