Photonic shielding in giant resonator system

<sec>In the traditional quantum optics and waveguide electrodynamics, atom is usually considered as a point like dipole. However, successful coupling between superconducting transmon surface acoustic wave gives birth to giant atom, which interacts with via more than two points. In setup, dipole approximation breaks down nonlocal light-matter interaction, it brings lots of unconventional effects, are presented by phase interference. As simplification, resonator, supports equal energy interval, can be regarded linear version atom. Like system, resonator also coupled array sites.</sec> <sec>According interference effect, we study control in cavities waveguide. For three-resonator reveal characteristics steady state Heisenberg-Langevin equations when driving dissipation both present. such coherently controlled adjusting difference <inline-formula><tex-math id="M2">\begin{document}$\phi$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="9-20230049_M2.jpg"/><graphic xlink:href="9-20230049_M2.png"/></alternatives></inline-formula> classical fields. We analytically give existence condition dark cavity. The results show that only middle cavity ideal, one realize flash shielding. Furthermore, generalize above three system multiple investigate photonic find number resonators id="M3">\begin{document}$4n+1\, n\in Z$\end{document}</tex-math><alternatives><graphic xlink:href="9-20230049_M3.jpg"/><graphic xlink:href="9-20230049_M3.png"/></alternatives></inline-formula>, bidirectional shielding occurs, is, shield vice versa. On contrary, there id="M4">\begin{document}$4n+3$\end{document}</tex-math><alternatives><graphic xlink:href="9-20230049_M4.jpg"/><graphic xlink:href="9-20230049_M4.png"/></alternatives></inline-formula> regime, directional happens, waveguide, but cannot resonator.</sec> <sec>The interesting comes from effect. That field injects photons into propagate different directions. overlapped photon carrying undergoes destructive acts resonator. hope based scheme applied device designing.</sec>