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# Floquet control of global $PT$ symmetry in 2D arrays of quadrimer waveguides

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posted on 2023-11-30, 19:10 authored by Bo Zhu, Honghua Zhong, Jun Jia, Fuqiu Ye, Libin FuManipulating the global $PT$ symmetry of a non-Hermitian composite system is a rather significative and challenging task. Here, we investigate Floquet control of global $PT$ symmetry in 2D arrays of quadrimer waveguides with transverse periodic structure along $x$-axis and longitudinal periodic modulation along $z$-axis. For unmodulated case with inhomogeneous inter- and intra- quadrimer coupling strength $\kappa_1

eq\kappa$, in addition to conventional global $PT$-symmetric phase and $PT$-symmetry-breaking phase, we find that there is exotic phase where global $PT$ symmetry is broken under open boundary condition, whereas it still is unbroken under periodical boundary condition. The boundary of phase is analytically given as $\kappa_1\geq\kappa+\sqrt{2}$ and $1\leq\gamma\leq2$, where there exists a pair of zero-energy edge states with purely imaginary energy eigenvalues localized at the left boundary, whereas other $4N-2$ eigenvalues are real. Especially, the domain of the exotic phase can be manipulated narrow and even disappeared by tuning modulation parameter. More interestingly, whether or not the array has initial global $PT$ symmetry, periodic modulation not only can restore the broken global $PT$ symmetry, but also can control it by tuning modulation amplitude. Therefore, the global property of transverse periodic structure of such a 2D array can be manipulated by only tuning modulation amplitude of longitudinal periodic modulation.

eq\kappa$, in addition to conventional global $PT$-symmetric phase and $PT$-symmetry-breaking phase, we find that there is exotic phase where global $PT$ symmetry is broken under open boundary condition, whereas it still is unbroken under periodical boundary condition. The boundary of phase is analytically given as $\kappa_1\geq\kappa+\sqrt{2}$ and $1\leq\gamma\leq2$, where there exists a pair of zero-energy edge states with purely imaginary energy eigenvalues localized at the left boundary, whereas other $4N-2$ eigenvalues are real. Especially, the domain of the exotic phase can be manipulated narrow and even disappeared by tuning modulation parameter. More interestingly, whether or not the array has initial global $PT$ symmetry, periodic modulation not only can restore the broken global $PT$ symmetry, but also can control it by tuning modulation amplitude. Therefore, the global property of transverse periodic structure of such a 2D array can be manipulated by only tuning modulation amplitude of longitudinal periodic modulation.