Fig. 2: Metastable dynamics of a ¹⁴N nuclear spin induced by sequential RIMs of a nearby NV electron spin.

a, b Typical PL time trace of an NV center under sequential RIMs and the corresponding distribution of the measurement results. The total and average photon counts are shown on the left and right axes, respectively. The duration of free evolution, τ = 374 ns. The number of measurement repetition m is 5 k, 60 k, 250 k, 600 k from top to bottom. When m = 5 k, it is difficult to distinguish the nuclear spin quantum states. When m = 60 k, the jump signal is concentrated in two distinct photon count intervals. As m increases further to 250 k, the overlap between the two distribution peaks becomes more pronounced. When m exceeds the metastable region, the photon counting peaks gradually merge. The blue envelopes in (b) indicate the normalized numerical simulation results. c Numerical results. The evolution of the nuclear spin state fidelity under sequential RIMs. The initial thermal state of the nuclear spin is polarized to either the dark state \({| 1\left.\right\rangle }_{n}\left\langle \right.1|\) or the bright state \(({| 0\left.\right\rangle }_{n}\left\langle \right.0|+{| -1\left.\right\rangle }_{n}\left\langle \right.-1| )/2\). The solid lines are fits to the simulation results. The fidelity F_D,B quantifies how close the quantum states represented by the trajectories are to the ideal dark or bright states, respectively. d The channel spectrum, with one fixed point, two metastable points and six decaying points. The right pane is a magnified view of the spectrum near the metastable points, and the deviations of their eigenvalues from 1 (1 − ∣λ∣) are shown accordingly. The metastable region and the underlying channel spectrum gap are marked with blue shades in (c) and (d), respectively. Monte Carlo simulations are conducted with a tilt angle θ = 8.8° and 3000 samples.