Non-Hermitian bidirectional robust transport

Abstract

Transport of quantum or classical waves in open systems is known to be strongly affected by non-Hermitian terms that arise from an effective description of system-enviroment interaction. A simple and paradigmatic example of non-Hermitian transport, originally introduced by Hatano and Nelson two decades ago [N. Hatano and D.R. Nelson, Phys. Rev. Lett. 77, 570 (1996)], is the hopping dynamics of a quantum particle on a one-dimensional tight-binding lattice in the presence of an imaginary vectorial potential. The imaginary gauge field can prevent Anderson localization via non-Hermitian delocalization, opening up a mobility region and realizing robust transport immune to disorder and backscattering. Like for robust transport of topologically-protected edge states in quantum Hall and topological insulator systems, non-Hermitian robust transport in the HatanoNelson model is unidirectional. However, there is not any physical impediment to observe robust bidirectional non-Hermitian transport. Here it is shown that in a quasi-one dimensional zigzag lattice, with non-Hermitian (imaginary) hopping amplitudes and a synthetic gauge field, robust transport immune to backscattering can occur bidirectionally along the lattice.

Controllable unidirectional transport and light trapping using a one-dimensional lattice with non-Hermitian coupling

“…It seems somewhat similar to the case in Ref. [28] that the relative position can be adjusted by the phase φ. However, due to the movable imaginary part of the dispersion relation, a filter with selectable wave numbers can be realized, as shown in the next section.…”

“…is invariable versus φ. Note that a purely dissipative optical system requires γ ≥ 2β [28]. Moreover, we point out that a Hermitian lattice arises when γ = β = 0.…”

“…if |U b | is much larger than J and energy E (in modulus) of the system (−2κ ≤ |E| ≤ 2κ) [27,28]. Then the equivalent evolution equations can be read i da n dt = U ef f,n a n + J 1 a n+1 + J 2 a n−1…”

Dynamical topological invariant for the non-Hermitian Rice-Mele model

“…The non-Hermiticy arises from asymmetry factor λ, which has been proposed to be realized in experiment [17]. We note that the Hamiltonian preserves timereversal (T ) symmetry.…”

Quantum dynamics of a parity-time-symmetric kicked particle in a 1D box

“…PT-symmetric analog of such system could be realized in a cavity with the losses. Another option, putting the system in a transverse beam propagation inside a passive optical resonator with combined phase and loss gratings, was discussed, e.g., [30]. An optical waveguide which is driven ny PTsymmetric optical field can be considered as another version of the model we are going to treat.…”