The tunnel-time problem and a solid-state platform for quantum metrology via weak value enhancement*

We propose and construct a solid-state platform to explore the tunnel-time problem [1] which is related to the Larmor clock, and build upon this construct to provide for a weak-value enhancement for quantum metrology [2]. Quantum metrology that employs weak-values can potentially effectuate parameter estimation with an ultra-high sensitivity and has been typically explored across quantum optics setups. Recognizing the importance of sensitive parameter estimation in the solid-state, we propose a spintronic device platform to realize this. The setup estimates a very weak localized Zeeman splitting by exploiting a %Fabry-P'erot resonant tunneling enhanced magnetoresistance readout. We establish that this paradigm offers nearly optimal performance with a quantum Fisher information enhancement of about ten-thousand times that of single high-transmissivity barriers. The obtained signal also offers a high sensitivity in the presence of dephasing effects typically encountered in the solid state. These results put forth definitive possibilities in harnessing the inherent sensitivity of resonant tunneling for solid-state quantum metrology with potential applications, especially, in the sensitive detection of small induced Zeeman effects in quantum material heterostructures. 

[1] A. Mathew, K. Y. Camsari and B. Muralidharan, Phys. Rev. B, 105, 144418, (2022). 

[2] M. Subramanian, A. Mathew and B. Muralidharan, Phys. Rev. Applied (2023) (ArXiv: 2211.17060).