Coherent coupling of a trapped electron to a distant superconducting microwave cavity

We theoretically investigate the coupling of a single electron in a planar Penning trap with a remote superconducting microwave (MW) cavity. Coupling frequencies around Ω = 2 π · 1 MHz can be reached with resonators with a loaded quality factor of Q = 10 5, allowing for the strong coupling regime. The electron and the cavity form a system of two coupled quantum harmonic oscillators. This is a hybrid and linear microwave quantum network. We show that the coherent interaction can be sustained over distances of a few mm up to several cm. Similar to classical linear MW circuits, the coherent quantum exchange of photons is ruled by the impedances of the electron and the cavity. As one concrete application, we discuss the entanglement of the cyclotron motions of two electrons located in two separate traps.