Floquet control of global <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math> symmetry in quadrimer waveguide arrays
Bo Zhu, Honghua Zhong, Jun Jia, Fuqiu Ye, Libin Fu
Abstract
Manipulating the global $\mathcal{PT}$ symmetry of a non-Hermitian composite system is a rather significative and challenging task. Here, we investigate Floquet control of global $\mathcal{PT}$ symmetry in quadrimer waveguide arrays with transverse periodic structure along the $x$ axis and longitudinal periodic modulation along the $z$ axis. For the unmodulated case with inhomogeneous inter- and intraquadrimer coupling strength ${\ensuremath{\kappa}}_{1}\ensuremath{\ne}\ensuremath{\kappa}$, in addition to the conventional global $\mathcal{PT}$ symmetric phase and the $\mathcal{PT}$ symmetry breaking phase, we find that there is an exotic phase in which global $\mathcal{PT}$ symmetry is broken under open boundary condition, whereas it still is unbroken under periodical boundary condition. Especially, the domain of the exotic phase induced by boundary effect can shrink and even disappear by tuning modulation parameter. More interestingly, whether or not the array has initial global $\mathcal{PT}$ symmetry, periodic modulation can not only restore the broken global $\mathcal{PT}$ symmetry, but also control it by tuning modulation amplitude. Therefore, the global property of transverse periodic structure of such an array can be manipulated by only tuning modulation amplitude of longitudinal periodic modulation.