PTrestoration via increased loss and gain in thePT-symmetric Aubry-André model

Abstract

In systems with "balanced loss and gain", the PT -symmetry is broken by increasing the nonhermiticity or the loss-gain strength. We show that finite lattices with oscillatory, PT -symmetric potentials exhibit a new class of PT -symmetry breaking and restoration. We obtain the PT phase diagram as a function of potential periodicity, which also controls the location complex eigenvalues in the lattice spectrum. We show that the sum of PT -potentials with nearby periodicities leads to PT -symmetry restoration, where the system goes from a PT -broken state to a PT -symmetric state as the average loss-gain strength is increased. We discuss the implications of this novel transition for the propagation of a light in an array of coupled waveguides.

Anderson localization in the non-Hermitian Aubry-André-Harper model with physical gain and loss

“…[33], a PT -symmetric Aubry-André model is discussed and the result shows that the physical gain and loss can affect the Anderson localization. In addition, it is found that the broken PT -symmetry can be restored via increased loss and gain in the Aubry-André model [34]. However, a general discussion of the nonHermitian AAH model, especially the influences of different configurations of physical gain and loss on the Anderson localization, is still lacking.…”

“…Recently, the Anderson localization has been studied in disordered optical lattices systems, where it was shown that the existence of physical gain and loss could enhance the localization of light [31,32]. Besides, the properties of PT -symmetry in non-Hermitian AubryAndré model have been investigated [33,34]. It is well known that the Aubry-André model or the Aubry-André-Harper (AAH) model will shows a phase transition from extended states to localized states (Anderson localization) when the lattice is incommensurate [35][36][37][38].…”

Electrical tunability due to coalescence of exceptional points in parity-time symmetric waveguides

“…The transition point is called the exceptional point (EP), at which two or more eigenvalues coincide. The existence of EPs have been investigated in various types of PT-symmetric physical systems [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], giving rise to a wide range of counterintuitive wave phenomena, such as loss-induced transparency [3], nonreciprocal Bloch oscillation [4], unidirectional invisibility [5][6][7], coexisting coherent perfect absorption and lasing [8,9], enhanced spontaneous emission [10], and enhanced nano-particle sensing [11].…”

“…The transition point is called the exceptional point (EP), at which two or more eigenvalues coincide. The existence of EPs have been investigated in various types of PT-symmetric physical systems [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19], giving rise to a wide range of counterintuitive wave phenomena, such as loss-induced transparency [3], nonreciprocal Bloch oscillation [4], unidirectional invisibility [5][6][7], coexisting coherent perfect absorption and lasing [8,9], enhanced spontaneous emission [10], and enhanced nano-particle sensing [11].Recently, there has been strong interest in more complex phenomena closely related to the occurrence of EPs in multistate systems and high-order EPs [10,[20][21][22][23][24][25][26][27]. Multiple optical waveguide systems [20,21] and photonic crystals [10,22] have been proposed for the realization of high-order EPs.…”

Exactly solvable $\mathcal{PT}$ -symmetric models in two dimensions

“…These studies are complemented by those of several continuum [10][11][12][13][14] and discrete [15][16][17][18][19][20][21][22] PT symmetric Hamiltonians. A PT Hamiltonian, continuum or discrete, typically consists of a Hermitian kinetic energy term H 0 and complex, PTsymmetric potential term V = V † .…”