Fig. 3: The protocol.
From: Achieving the ultimate precision limit with a weakly interacting quantum probe
The NV and the nuclear spins are initialized at the x direction. The nuclei are then allowed, using an appropriate pulse sequence, to propagate according to the free Hamiltonian H0 for a time t, which results in a rotation by θ = ωNt around the z-axis. Then, by changing the external pulse sequence, the system propagates under the interaction Hamiltonian H1 for a duration of τ. This results in a rotation of the nuclei around the x-axis by an angle of ±ϕ = ± 2gτ depending on the sensor’s state. The sensor will experience an effective dephasing depending on the extent of its entanglement with the ensemble.
