Observation of Time-Domain Rabi Oscillations in the Landau-Zener Regime with a Single Electronic Spin

It is theoretically known that the quantum interference of a long sequence of Landau-Zener transitions can result in Rabi oscillations. Because of its stringent requirements, however, this phenomenon has never been experimentally observed in the time domain. Using a nitrogen-vacancy (NV) center spin in isotopically purified diamond, we observed the Rabi oscillations resulting from more than 100 Landau-Zener processes. Our results demonstrate favorable quantum controllability of NV centers, which could find applications in quantum metrology and quantum information processing.

Figure 1

(a) Schematic diagram of a NV center in the diamond lattice and the energy level diagram of the NV center. (b) Schematic diagram of Landau-Zener transition: when the energy levels undergo an avoided crossing, the quantum state undergoes a mixing process between the lower and the upper instantaneous eigenstates of the LZ Hamiltonian given by Eq. (2). This process is analogous to the operation of a beam splitter in optics experiments. (c) A single driving period contains four elementary rotations, which can be combined to produce a single effective rotation. On short time scales, one can see that each period involves four different rotations. On long time scales, the dynamics is described by the repeated application of the single-period rotation, as is the case for Rabi oscillations. (d) The pulse sequence used to drive Rabi oscillations in the LZ regime.

Figure 2

(a) Photoluminescence (PL) intensity of the optically detected magnetic resonance spectrum for the transition between the states $|0⟩$ and $|1⟩$ of the NV center (blue dots). The red curve is a fit with a single Lorentzian peak. (b) Results of a standard Ramsey experiment on the NV center. The results are fitted to the function $\exp [-{(t/T_2^{*})}^2]\cos (2\pi {\delta }_{f}t)$ (${\delta }_f=0.56\mathrm{MHz}$), where the oscillations are due to the detuning between the MW signal and the $|0⟩\leftrightarrow |1⟩$ transition. (c),(d) The occupation probability of the state $|0⟩$ for a double-passage experiment in the fast- and slow-passage regimes.

Figure 3

Rabi oscillations resulting from the interference of many LZ processes. (a) Fast-passage regime. The measured (upper curve) and numerically simulated (lower line) occupation probabilities $P_0$ of the state $|0⟩$ as a function of time. The experimental data here and those in (b) are offset along the $y$ axis for visibility. The Rabi frequency is about 1.49 MHz, which is consistent with numerical simulations. The parameters used in this case are $\mathrm{\Delta }=2\pi \times 5.57\mathrm{MHz}$, ${ϵ}_m=2\pi \times 100\mathrm{MHz}$, and $T=128\mathrm{ns}$. (b) Slow-passage regime. The same as in (a), except that dashed sinusoidal envelopes are added to show the oscillatory behavior, which corresponds to the ROs in the adiabatic basis. The parameters used in this case are $\mathrm{\Delta }=2\pi \times 9.60\mathrm{MHz}$, ${ϵ}_m=2\pi \times 50.4\mathrm{MHz}$, and $T=606\mathrm{ns}$.

Figure 4

Constructive versus destructive interferences in a single driving period. The parameters are the same as in Fig. 3, except for the sweep period being $T=149\mathrm{ns}$ in the case of destructive interference (pink line). The experimental results are shown in (a), while the results of numerical simulations are shown in (b). The case of destructive interference corresponds to the phenomenon of coherent destruction of tunneling (CDT).