Theory of Entanglement-Assisted Gradiometry via Spin Singlet Transport Bottlenecks in Semiconductor Device Transport

We present a quantitative theory for entanglement-assisted sensing of magnetic field gradients with Lindblad simulations of spin singlet transport bottlenecks of spin defects. While spatially separated optically addressable spin centers have been demonstrated to sense field gradients [1,2], techniques employing electrical readout without microwaves or optical components would offer significant size, weight, and power (SWaP) advantages [3,4]. We propose such a technique, based on spin-selective transport through entangled singlet bottlenecks, where singlet-triplet mixing is induced by magnetic field gradients. We calculate the signal expected for the particular model of a deep level divacancy in spatial proximity to a shallow phosphorus donor in silicon carbide. In the absence of external fields, we show that this deep-shallow spin pair can naturally evolve into an entangled spin singlet steady-state bottleneck, despite the spin mixing induced by the phosphorus nuclear spin. We first discuss the experimental conditions under which the entangled singlet state forms. Finally, we predict the gradiometry sensitivity of this spin pair and show the dependence of the sensitivity on defect coherence times, spin Hamiltonian parameters, and electrical transport rates.

[1] Shin et. al., J. Appl. Phys. 112, 124519 (2012).

[2] Y. Masuyama et al., Sensors 21(3), 977 (2021).

[3] Cochrane et al., Sci Rep 6, 37077 (2016).

[4] Moxim et al., J. Appl. Phys. 135, 155703 (2024).