Optical structures with local {\cal PT} -symmetry

Abstract

We propose a new class of optical synthetic materials that are described by non-Hermitian Hamiltonians. The building blocks of such systems are coupled PT-symmetric elements (dimers), with coupling t. Despite the lack of global PT-symmetry, these systems have a robust parameter region of real spectra (exact phase) even in cases where the complex refractive index n = β + iγ of each PT dimer is random. The validity of our proposition is confirmed for representative cases where we calculate the borders of the exact phase in terms of β, γ and t.

$\mathcal {PT}$-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.…”

PT symmetric Aubry–Andre model

“…In this case, the system would be no longer PT symmetric and the corresponding energy eigenvalues are not real. Bendix et al studied a disordered system by considering a pair of N coupled dimers with impurities (γ n , −γ n ) [14]. They noted that the system is not PT symmetric as a whole (global symmetry), but it possesses a local P d T symmetry that admits real spectrum.…”

“…The critical number of non-Hermitian degree is shown to be different for planar and circular array configurations [11] and it can be increased if impurities and tunneling energy are made position-dependent in an extended lattice [12]. However, γ P T decreases with increasing the lattice sites [13][14][15][16], hence the PT symmetric phase is fragile. An important consequence of PT symmetric optical systems is the power oscillations.…”

Non-unitary Evolution of Quantum Logics

“…Non-Hermitian Hamiltonians [1] find many applications in diverse areas of physics such as for example, optics [2,3], solid state physics [4], decoherence [5], the quantum to classical limit, and final equilibrium [6]. Decoherence and relaxation times can be defined using non-unitary evolutions, pole theory, and non-Hermitic Hamiltonians [6,15].…”