We investigate the striking properties that magnetoresistance of irradiated two-dimensional electron systems presents when their mobility is ultra-high ( \(\mu \gg 10^{7} cm^{2}V^{-1} s^{-1}\) ) and temperature is low ( \(T \sim 0.5\) K). Such as, an abrupt magnetoresistance collapse at low magnetic field and a resonance peak shift to the second harmonic ( \(2w_{c}=w\) ), \(w_{c}\) and w being the cyclotron and radiation frequencies, respectively. We appeal to the principle of quantum superposition of coherent states and find that Schrödinger cat states (even and odd) are key to explaining magnetoresistance at these extreme mobilities. On the one hand, the Schödinger cat state system oscillates as a whole with \(2w_{c}\) . Then, it would resonate with radiation at \(2w_{c}=w\) , thus being responsible for the shift of the resonance peak at the second harmonic. On the other hand, we find that Schrödinger cat states-based scattering processes give rise to a destructive effect when the odd states are involved, leading to a magnetoresistance collapse. The Aharonov-Bohm effect plays a central role in the latter, turning even cat states into odd ones. We show that ultra-high mobility two-dimensional electron systems could make a promising bosonic mode-based platform for quantum computing.
