Proposal for a solid-state magnetoresistive Larmor quantum clock

We propose a solid-state implementation of the Larmor clock that exploits tunnel magnetoresistance to distill information on how long itinerant spins take to traverse a barrier embedded in it. Keeping in mind that the tunneling time innately involves pristine preselection and postselection, our proposal takes into account the detrimental aspects of multiple reflections by incorporating multiple contacts, multiple current measurements, and suitably defined magnetoresistance signals. Our analysis provides a direct mapping between the magnetoresistance signals and the tunneling times and aligns well with the interpretation in terms of generalized quantum measurements and quantum weak values. By means of an engineered preselection in one of the ferromagnetic contacts, we also elucidate how one can make the measurement “weak” by minimizing the backaction, whereas keeping the tunneling time unchanged. We then analyze the resulting interpretations of the tunneling time and the measurement backaction in the presence of phase breaking effects that are intrinsic to solid-state systems. We unravel that whereas the time-keeping aspect of the Larmor clock is reasonably undeterred due to momentum and phase relaxation processes, it degrades significantly in the presence of spin dephasing. We believe that the ideas presented here also open up a fructuous solid-state platform to encompass emerging ideas in quantum technology, such as quantum weak values and its applications that are currently exclusive to quantum optics and cold atoms.