Non-Hermitian quantum rings

Abstract

We investigate the spectral and dynamical properties of a quantum particle constrained on a ring threaded by a magnetic flux in presence of a complex (non-Hermitian) potential. For a static magnetic flux, the quantum states of the particle on the ring can be mapped into the Bloch states of a complex crystal, and magnetic flux tuning enables to probe the spectral features of the complex crystal, including the appearance of exceptional points. For a time-varying (linearly-ramped) magnetic flux, Zener tunneling among energy states is realized owing to the induced electromotive force. As compared to the Hermitian case, striking effects are observed in the non-Hermitian case, such as a highly asymmetric behavior of particle motion when reversing the direction of the magnetic flux and field-induced delayed transparency.

$\mathcal {PT}$-symmetric optical superlattices

“…Complex crystals show rather unusual scattering and transport properties as compared to ordinary crystals, such as violation of the Friedel's law of Bragg scattering [37,38,44], double refraction and nonreciprocal diffraction [17], unidirectional Bloch oscillations [47], unidirectional invisibility [48,49,50,51,52], and invisible defects [53,54]. Complex crystals described by tight-binding Hamiltonians with complex site energies and/or hopping rates have been investigated in several recent works (see, for instance, [8,9,10,11,27,29,53,55,56,57,58,59,60,61] and references therein). Most of previous studies on non-Hermitian lattices have been limited to consider periodic or bi-periodic crystals, inhomogenous lattices, or lattices in presence of localized defects or disorder.…”

Bloch oscillations in non-Hermitian lattices with trajectories in the complex plane

“…However, in strongly non-Hermitian potentials the band structure can become imaginary, and in this case it is not clear whether and how the semiclassical picture of BOs can be extended to account for a complex energy lattice band. Several examples of tight-binding lattice models that show a non-vanishing imaginary part of the band dispersion curve have been discussed in many works, including the Hatano-Nelson model describing the hopping motion of a quantum particle in a linear tight-binding lattice with an imaginary vector potential [45][46][47][48], the nonHermitian extension of the Su-Schrieffer-Heeger tightbinding model [49][50][51], PT -symmetric binary superlattices [36,52], and the PT -symmetric Aubry-Andre model [53]. Lattice bands with a non vanishing imaginary part could be realized in synthetic temporal optical crystals, waveguide lattices, coupled-resonator optical waveguides, microwave resonator chains, etc.…”

Amplitude control of a quantum state in a non-Hermitian Rice-Mele model driven by an external field

“…The imaginary part of the Berry phase is significant for a propagating particle since it may be utilized to directly amplify or attenuate the particle probability. Very recently, the spectral and dynamical properties of * songtc@nankai.edu.cn a quantum particle constrained on a ring threaded by a time-varying magnetic flux in the presence of a complex (non-Hermitian) potential are investigated [26]. It has been demonstrated that several striking effects are observed in the non-Hermitian case in comparison with the Hermitian one.…”