Photonic shielding in giant resonator system

Abstract

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