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Starting from the basics of quantum device theory using the Keldysh non-equilibrium Green’s function (NEGF) approach, we will present a solid-state implementation of the Larmor clock [4] that exploits tunnel magnetoresistance to “distill” information on how long itinerant spins take to traverse a barrier embedded in it. We provide a direct mapping between the magnetoresistance signals and the tunneling times that aligns well with the interpretation in terms of generalized quantum measurements and quantum weak values [3]. 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 in the presence of phase breaking effects that are intrinsic to solid-state systems. We show that the magnetoresistance signal reliably “distills” the details of the “tick” that has passed as the electrons tunnel through the embedded barrier, when subject to momentum and phase relaxation processes. Our ideas can be further generalized for applications involving quantum weak values, with many possibilities that can be envisioned using the emerging properties of quantum materials.

References:
[1] R. Ramos et.al., Nature, 583,529, (2020).
[2] D. C. Spierings and A. M. Steinberg, Phys. Rev. Lett., 127, 133001, (2021).
[3] A. M. Steinberg, Phys. Rev. Lett., 74, 2405, (1995).
[4] A. Mathew, K. Y. Camsari and B. Muralidharan, Phys. Rev. B, 105, 144418, (2022).