The Sensor

There are more than 500 known color-centers in diamond [1]. This is mostly thanks to the diamond industry, which took great care in characterizing them. For magnetic field sensing, only those defects whose effective spin is non-zero are of significance. If we model the defect as a single spin, PG1hdGggbWF0aHNpemU9IjQwIj4KICAgIDxtb3Zlcj4KICAgICAgICA8bXRleHQ+UzwvbXRleHQ+CiAgICAgICAgPG1vPiYjeDIxOTI7PC9tbz4KICAgIDwvbW92ZXI+CjwvbWF0aD4=, which couples to the magnetic field through its Zeeman interaction term, leading to the following, basic Hamiltonian:

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

Here D is the crystal field tensor, also known in the atomic physics community as zero-field splitting, and PG1hdGggbWF0aHNpemU9IjQwIj4KICAgIDxtdGV4dD4mI3gzQjM7PC9tdGV4dD4KPC9tYXRoPg== is the gyromagnetic ratio, which, for an isolated electron, is equal to 28.02 GHz/T.

Some defects