A solid state test bed for quantum time keeping and quantum weak values

In this work, we propose the use of the magnetoresistance phenomenon for quantum time keeping via a solid-state device realization of the Larmor clock. Specifying the spin dependent tunneling process as a generalized measurement, we describe how to utilize standard magnetoresistance measurements on this set up to distill the embedded information on the quantum weak values that describe the traversal time inside the barrier. Our results using the Keldysh non-equilibrium Green's function technique are synergetic with the Larmor clock in the coherent limit. We further analyze the proposed transport signatures and the resulting interpretations of the traversal time and the measurement back action in the limit of weak phase breaking decoherence effects. Furthermore, in the limit of weak Zeeman fields, and a suitably engineered pre-selection, we demonstrate how to minimize the measurement back action. The device ideas that we suggest here can thus be extended to open up a spintronics test bed to investigate quantum weak value amplification and possibly facilitate the use of magnetoresistance effects in quantum metrology.