High-sensitivity double-quantum magnetometry in diamond via quantum control

Figure  1.  Coherent operation of a single NV center in diamond. (a) Pulsed ODMR spectrum of a single $ ^{{\text{14}}}{\text{NV}} $ center at a bias magnetic field of 21 Gauss. A single resonant spectral line splits into three lines with intervals of 2.16 MHz because of the unpolarized $ ^{{\text{14}}}{\text{N}} $ nuclear spin hyperfine coupling with nitrogen NV electron spin. (b-c) Rabi oscillation of electron spin for the transition $ \left| {0,0} \right\rangle \leftrightarrow \left| {1,0} \right\rangle $ with different MW power. For low MW power, the Rabi oscillation can be fitted with a simple cosine function. When the MW power is increased three times, the frequency of Rabi oscillation cannot be easily determined for experimental results. The laser power at 532 nm is 0.7 mW in our experiment.

Figure  2.  Rabi oscillation with shaped MW pulse. (a) MW sequence scheme of amplitude modulation. The gray region denotes carrier frequency (${\omega = }{{f}_{\text{2}}}$). The blue dash line denotes the modulation function $A(t) = {\varOmega _0}\left[ {2{\rm cos}(\Delta t) + 1} \right]$，where ${\varOmega _0} = 0.558$ MHz. (b) Rabi oscillation of NV center driving by the amplitude modulation of the MW pulse. The time scale for the $\pi$ gate is 920 ns.

Figure  3.  Ramsey sensing results. (a) Pulse sequence for the Ramsey sensing protocol. A DC magnetic field is applied along the NV center axis. (b–c) Ramsey fringes of the NV center driven with or without amplitude modulation of MW pulse. Here, the MW pulse addresses the target transition $ \left| {0,0} \right\rangle \leftrightarrow \left| {1,0} \right\rangle $. The duration time of the $\pi/2$ gate is 460 ns. By fitting experimental results with theory, the coherent time for both cases is $ T_2^* \approx 4 $ ${\text{μs}}$. However, the signal contrast of our sharp sequence is improved approximately three times compared with the traditional method. The Rabi frequency for the traditional Ramsey is set as ${\varOmega _0} = 0.558$ MHz.

Figure  4.  DQ Ramsey sensing protocol and results. (a) Pulse sequence for the DQ Ramsey sensing protocol. Compared with the SQ Ramsey sequence, the $\pi$ gate (denoted with orange) needs to be applied after preparing the electron spin into a superposition state $ \left( {\left| 0 \right\rangle + \left| 1 \right\rangle } \right)/\sqrt 2 $. The frequency of the $\pi$ gate is in resonance with the transition $ \left| {0,0} \right\rangle \leftrightarrow \left| { - 1,0} \right\rangle $. Then, the probe state $ \left( {\left| { - 1} \right\rangle + \left| 1 \right\rangle } \right)/\sqrt 2 $ for the detection of the DC magnetic field is obtained. (b) DQ Ramsey sensing results as a function of sensing time (τ) and DC magnetic-field change. (c) DQ Ramsey results with fixed amplitude of DC magnetic field, which corresponds to the blue dashed line in Fig. 4 (b). The coherence time for DQ Ramsey is $ T_{2,DQ}^* \approx 2 $ ${\text{μs}}$. (d) DQ Ramsey results (denoted by red dots) as a function of the amplitude of DC magnetic field with fixed sensing time (τ=1 ${\text{μs}}$) for out shaped MW pulse. The blue square corresponds to the rectangular MW pulse. (e) Measured sensitivity of a single NV spin magnetometer over a range of sensing time after repeating $ N = 1.5 \times {10^6} $ times.