Non-Hermitian transparency and one-way transport in low-dimensional lattices by an imaginary gauge field

Abstract

Unidirectional and robust transport is generally observed at the edge of two-or three-dimensional quantum Hall and topological insulator systems. A hallmark of these systems is topological protection, i.e. the existence of propagative edge states that cannot be scattered by imperfections or disorder in the system. A different and less explored form of robust transport arises in non-Hermitian systems in the presence of an imaginary gauge field. As compared to topologically-protected transport in quantum Hall and topological insulator systems, robust non-Hermitian transport can be observed in lower dimensional (i.e. one dimensional) systems. In this work the transport properties of one-dimensional tight-binding lattices with an imaginary gauge field are theoretically investigated, and the physical mechanism underlying robust one-way transport is highlighted. Back scattering is here forbidden because reflected waves are evanescent rather than propagative. Remarkably, the spectral transmission of the non-Hermitian lattice is shown to be mapped into the one of the corresponding Hermitian lattice, i.e. without the gauge field, but computed in the complex plane. In particular, at large values of the gauge field the spectral transmittance becomes equal to one, even in the presence of disorder or lattice imperfections. This phenomenon can be referred to as one-way non-Hermitian transparency. Robust one-way transport can be also realized in a more realistic setting, namely in heterostructure systems, in which a non-Hermitian disordered lattice is embedded between two homogeneous Hermitian lattices. Such a double heterostructure realizes asymmetric (non-reciprocal) wave transmission. A physical implementation of non-Hermtian transparency, based on light transport in a chain of optical microring resonators, is suggested.

Tight-binding lattices with an oscillating imaginary gauge field

“…Imaginary gauge fields were introduced in a pioneering paper by Hatano and Nelson [6] to study non-Hermitian Anderson localization in disordered lattices, which raised a lively interest [11,12]. Recently, the proposal to implement artificial imaginary gauge fields in integrated photonics using coupled optical microrings with tailored gain and loss regions [13,14] has renewed the interest in the HatanoNelson model, paving the way toward an experimental demonstration of non-Hermitian Anderson delocalization transition. Such previous studies, however, are limited to consider stationary imaginary gauge fields.…”

“…Such a result was subsequently revisited by several authors [11] and connected to the problem of the spectrum of tridiagonal random matrices and random Dirac fermion models [12]. Recently, an optical implementation of the Hatano-Nelson model with an artificial maginary gauge field, based on a chain of coupled optical microrings with tailored gain and loss regions, was suggested [13] and the phenomenon of non-Hermitian transparency was disclosed [14]. In such previous studies [6,[11][12][13][14][15] the imaginary gauge field was considered stationary.…”

“…Recently, an optical implementation of the Hatano-Nelson model with an artificial maginary gauge field, based on a chain of coupled optical microrings with tailored gain and loss regions, was suggested [13] and the phenomenon of non-Hermitian transparency was disclosed [14]. In such previous studies [6,[11][12][13][14][15] the imaginary gauge field was considered stationary. However, it is well known that in ordinary tight-binding Hermitian quantum models oscillating electric and/or magnetic fields can deeply change the hopping dynamics via Peierls' substitution with important applications to coherent quantum state storage, dynamic decoupling and decoherence control (see, for instance, [16] and references * stefano.longhi@polimi.it therein).…”

Active topological photonics

“…Regarding line-gapped systems, the topological transition in this case is explained by the winding number of the Q matrix based on the biorthogonal projection operator [132,133,140]. Furthermore, imaginary gauge fields [135,[142][143][144], which indicate paired effective amplification in one way and attenuation to the other, are presented as an intelligible interpretation of these anomalous properties. The skin effect will hence stem from some symmetry breaking induced by non-Hermiticity [135,145].…”

One-way light transport controlled by synthetic magnetic fluxes and ${\mathscr{P}}{\mathscr{T}}$-symmetric resonators

“…The imaginary gauge field results in nonreciprocal photon tunneling, and leads to asymmetric amplification and attenuation of the counter-propagating waves. Light transport is robust, being insensitive to disorders and imperfections under a non-Hermitian delocalization [11,12]. The light propagation in one direction is shape-preserving and accompanied by persistent amplification.…”