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The “Tick” Embedded in a Magneto-resistance Signal

The tunneling time problem – the question on how long a particle spends inside a forbidden region, has puzzled physicists since the inception of quantum mechanics. Following recent ground-breaking experiments using cold atoms [1,2], this topic that innately involves quantum weak values and connections with generalized von Neumann measurements [3], can be made accessible to a broader class of experimental platforms, especially those involving condensed matter physics.

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.


[1] R. Ramos, 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).


Prof. Bhaskaran Muralidharan obtained his B.Tech in Engineering Physics from the Indian Institute of technology (IIT) Bombay in 2001, his M. S. and Ph. D in Electrical Engineering from Purdue University, West Lafayette, USA in 2003 and 2008 respectively. Between 2008-2012, he was a post-doctoral associate at the Massachusetts Institute of Technology (MIT) and at the Institute for theoretical Physics at the University of Regensburg, Germany. Since 2012, he has been a faculty in the Department of Electrical Engineering at IIT Bombay, where he is currently a full Professor. His core research area is computational quantum transport and its applications to modeling and simulation of “Beyond Moore” devices. His research output spans diverse areas of emerging nanoscale devices, ultimately built on top of a broad and fundamental foundation of utilizing quantum engineering for novel functionalities. He was also the recipient of the APS-IUSSTF professorship award in 2014, the Shastri Indo-Canada fellowship 2019 and the SERB-STAR award in 2019. He is also a recipient of the Excellence in Teaching Award in IIT Bombay. He is also an Associate Editor in the IEEE Transactions on Nanotechnology, on the Editorial board of Scientific Reports and Materials for Quantum Technology (IOP).

Host: Arun Paramekanti
Event series  CQIQC SeminarsQO/AMO Seminars