Theory of Optically Detected Magnetic Resonance of a Silicon Vacancy in SiC Nanoparticles—A Quantum Sensor of Magnetic Fields

Magnetometers are used in virtually every aspect of our lives: from navigation, the detection of submarines and underwater debris, archaeological and geological surveys, to our mobile phones and in the exploration of our solar system [1-2]. Recently, solid-state magnetometers have stimulated particular interest due to their smaller size, weight, and power (SWaP) compared to existing magnetometers [3], and their potential to self-calibrate [4]; two attractive features which improve the efficiency of any device carrying a magnetometer, especially spacecraft. However, extensive research must be completed to optimize this new technology for widespread commercial use, and a detailed theory is the first step in this process.<br/><br/>Silicon Carbide nanoparticles containing defects with optically addressable spin states are available in a variety of sizes and crystal structures [5-8]. This creates the perfect playground for optimizing the spin-photon interaction for the purpose of quantum sensing of magnetic fields. In this work we model optically detected magnetic resonance (ODMR) of the silicon vacancy (V_Si) in silicon carbide,<br/>a budding candidate for solid-state quantum magnetometry, using Lindblad master equations. The silicon vacancy can be thought of as a S = 3/2 synthetic atom, and its spin states are sensitive to magnetic fields via the Zeeman effect. In ODMR, magnetic resonances of the Zeeman field are detected by extrema in the normalized photoluminescence signal when a transverse microwave field is applied. The photoluminescence is calculated from the steady-state density matrix populations and compared to recent experimental results [9-11].<br/><br/>We acknowledge support from NSF DMR-1921877.<br/><br/>[1] Budker, D., Romalis, M. Optical magnetometry. <i>Nature Phys</i> <b>3</b>, 227–234 (2007).<br/>[2] Ness, N.F. Magnetometers for space research. <i>Space Sci Rev</i> <b>11</b>, 459–554 (1970).<br/>[3] Kraus, H., Soltamov, V., Fuchs, F. et al. Magnetic field and temperature sensing with atomic-scale spin defects in silicon carbide. <i>Sci Rep</i> <b>4</b>, 5303 (2014).<br/>[4] Cochrane, C., Blacksberg, J., Anders, M. et al. Vectorized magnetometer for space applications using electrical readout of atomic scale defects in silicon carbide. <i>Sci Rep</i> <b>6</b>, 37077 (2016).<br/>[5] Beke, D., Valenta, J., Károlyházy, G. et al. Room-Temperature Defect Qubits in Ultrasmall Nanocrystals. <i>J. Phys. Chem. Lett.</i> <b>11</b> 1675-1681 (2020).<br/>[6] Castelletto, S., Almutairi, A.F.M., Thalassinos, G. et al. Fluorescent color centers in laser ablated 4H-SiC nanoparticles. <i>Optics Letters</i> <b>42</b> 1297-1300 (2017).<br/>[7] Castelletto, S., Johnson, B., Zachreson, C. et al. Room Temperature Quantum Emission from Cubic Silicon Carbide Nanoparticles. <i>ACS Nano</i> <b>8</b> 7938-7947 (2014).<br/>[8] Widmann, M., Lee, S., Rendler, T. et al. Coherent control of single spins in silicon carbide at room temperature. <i>Nature Materials</i> <b>14</b> 164-168 (2015).<br/>[9] Kraus, H., Soltamov, V., Riedel, D. et al. Room-temperature quantum microwave emitters based on spin defects in silicon carbide. <i>Nature Phys</i> <b>10</b>, 157–162 (2014).<br/>[10] Fischer, M., Sperlich, A., Kraus, H. et al. Highly Efficient Optical Pumping of Spin Defects in Silicon Carbide for Stimulated Microwave Emission. <i>Phys. Rev. Applied</i> <b>9</b>, 054006 (2018).<br/>[11] Cochrane, C., Kraus, H., Neudeck, P. et al. Magnetic Field Sensing with 4H SiC Diodes: N vs P Implantation. <i>MSF</i> <b>924</b> 988-992 (2018).