Landau-Zener-Stückelberg-Majorana interferometry of a superconducting qubit in front of a mirror

We investigate the Landau-Zener-St\\uckelberg-Majorana interferometry of a superconducting qubit in a semi-infinite transmission line terminated by a mirror. The transmon-type qubit is at the node of the resonant electromagnetic (EM) field, ``hiding'' from the EM field. We modulate the resonant frequency of the qubit by applying a sinusoidal flux pump. We perform spectroscopy by measuring the reflection coefficient of a weak probe in the system. Remarkable interference patterns emerge in the spectrum, which can be interpreted as multiphoton resonances in the dressed qubit. Our calculations agree well with the experiments.