Figure 1

(a) Spin energy-level diagram for the NV-center GS and ES. Zero energy is aligned with both $|0{⟩}_{\mathrm{GS}}$ and $|0{⟩}_{\mathrm{ES}}$. There are nuclear spin sublevels in both the GS and ES (not resolved), with nuclear spin $I=1/2$ since we fabricated our NV center by ion implanting ${}^{15}\mathrm{N}$ ions [11]. At $B=1276\mathrm{G}$, the transition $|0{⟩}_{\mathrm{GS}}\to |-1{⟩}_{\mathrm{GS}}$ is labeled with a short blue arrow while the transition $|0{⟩}_{\mathrm{ES}}\to |-1{⟩}_{\mathrm{ES}}$ is labeled with a longer purple arrow. (b) Measurement diagram for Ramsey and QPT experiments. Optically, the NV center is initialized into $|0{⟩}_{\mathrm{GS}}$ by pumping with a 532 nm laser followed by waiting for fluorescence decay. The pulsed laser, which was tuned to 583 nm in the experiment, has a pulse period of 132 ns and pulse duration of 5–10 ps. For each laser pulse, there is a probability ($P_{\mathrm{ES}}$) of the NV center being excited. Using time-correlated single-photon-counting electronics, we bin photons collected in two windows marked with dashed black boxes. The first provides a reference for $P_{\mathrm{ES}}$ of the initialized spin state, whereas the second forms the signal. Gaussian ESR pulses are applied before and after the optical pulse that corresponds with “signal” collection. (c) Plot of an actual ESR pulse waveform used to prepare and read out states in Ramsey and QPT experiments. The first pulse to manipulate the spin in the GS has carrier frequency $f_{\mathrm{GS}}=0.65\mathrm{GHz}$ and a full width at half maximum (FWHM) of $\approx 3.3\mathrm{ns}$, whereas the second pulse that maps the transverse spin state onto the $Z$ axis has carrier frequency $f_{\mathrm{ES}}=2.14\mathrm{GHz}$, a $\mathrm{FWHM}\approx 0.67\mathrm{ns}$, and is timed shortly after the laser pulse. Bloch sphere representations of the spin state indicate how the spin precession rate of the superposition state changes before and after the optical excitation. The small black vertical arrow in the first Block sphere represents the strength of the effective field of the spin in the GS relative to the effective field in the ES, which is shown with a larger vertical arrow and faster Larmor precession.Reuse & Permissions

Figure 2

Points are Ramsey data from fluorescence measurements, normalized to the fluorescence level of $|0⟩$ ($P_{|0⟩}=1$) and $|-1⟩$ ($P_{|0⟩}=0$). The solid red curve is a fit to the data. The dashed black curve is the simulation, assuming no free parameters as described in the text and the Supplemental Material [24].Reuse & Permissions

Figure 3

(a) Graphical representation of ${\chi }_{\mathrm{phys}}$ for the first point of QPT with $t_{\mathrm{ES}}=0.59\pm 0.03\mathrm{ns}$. (b) Phase angle $\varphi$ as a function of $t_{\mathrm{ES}}$. The Gaussian envelope of the $\pi /2_{\mathrm{ES}}$ pulses used for $S_x$ and $S_Y$ measurement in QPT are indicated above each point. Inset: polar plot of $\varphi$, with a radius corresponding to $F$ for the experiment (blue circles) and the simulation (purple triangles). The random error in $\varphi$ due to photon shot noise is $\approx 5°$, determined by Monte Carlo integration. The total uncertainty in $\varphi$ is larger due to other experimental contributions (see the Supplemental Material [24]). (c) $F$ as a function of $t_{\mathrm{ES}}$ for each QPT measurement (blue circles) and simulation (purple triangles). The error bars are also calculated with Monte Carlo integration using the photon shot noise statistics, and do not include other sources of uncertainty such as ESR pulse errors. The dashed lines are linear guides to the eye for visual extrapolation back to the $t_{\mathrm{ES}}=0$.Reuse & Permissions