In order to comprehensively study the spin dynamics of a two-level quantum system, it is critical to calibrate each eigenstate. In the case of nitrogen vacancy (NV) centers in diamond, we calibrate the photoluminescence intensity (*IPL*) for each spin eigenstate to accurately determine the *ms* = 0 and *ms* = -1 population (*P*).

We employ an adiabatic passage to produce a precise spin-flip that is independent of the Rabi oscillation. This is done by applying a moderate driving field with a frequency strongly de-tuned from the spin resonance and subsequently sweeping the frequency adiabatically through the resonance causing the spin to flip. This procedure can be mapped as a Landau-Zener transition in the rotating frame with the probability of remaining in the *ms* = 0 state given by the Landau-Zener formula:

where *H1* is the amplitude of the driving microwave field in units of the on-resonance Rabi frequency, and is the Landau velocity, or sweep rate of the frequency.

To verify our adiabatic passage calibration, we measure *IPL* as we sweep through the *ms* = 0 to *ms* = -1 transition. For this measurement, we hold *H1* constant at 29 MHz and sweep 300 MHz with various sweep durations to vary the Landau velocity. The result is shown below.

The data are fit to a simple exponential decay (red line) with a decay constant of 0.020 ± 0.001 ns-1, close to calculated value of 0.018 ns-1 given by the Landau-Zener formula. Next we fix the sweep duration to 600 ns ( = 0.5 MHz/ns), well into the adiabatic regime, and perform partial adiabatic passages. We stop the experiment at increasingly longer times and project the spin to see the progress of the spin-flip, shown below.

As expected, the spin flips as the driving frequency passes through resonance. In our work on strongly-driven NV centers, we use this technique to calibrate the measured *IPL* level with the value of *P* = 1 defined after initialization and *P* = 0 after adiabatic passage.

To learn more about our studies, please refer to "Gigahertz Dynamics of a Strongly Driven Single Quantum Spin", G. D. Fuchs, V. V. Dobrovitski, D. M. Toyli, F. J. Heremans, and D. D. Awschalom, *Science ***326**, 1520 (2009).