Phase-sensitive quantum spectroscopy with high-frequency resolution

Classical sensors for spectrum analysis are widely used but lack micro- or nanoscale spatial resolution. On the other hand, quantum sensors, capable of working with nanoscale precision, do not provide precise frequency resolution over a wide range of frequencies. Using a single spin in diamond, we present a measurement protocol for quantum probes which enables full signal reconstruction on a nanoscale spatial resolution up to potentially 100 GHz. We achieve $58\mathrm{nT}/\sqrt{\mathrm{Hz}}$ amplitude and $0.095\mathrm{rad}/\sqrt{\mathrm{Hz}}$ phase sensitivity and a relative frequency uncertainty of ${10}^{-12}$ for a 1.51 GHz signal within 10 s of integration. This technique opens the way to quantum spectrum analysis methods with potential applications in electron spin detection and nanocircuitry in quantum technologies.

Figure 1

Nanoscale high-frequency sensing. (a) Confocal setting for sensing with a single NV center in diamond. The right panel shows its level structure and the lower panel the pulse sequence for high-frequency Qdyne. (1) The NV center is excited with a green laser and the fluorescence is collected. (2) Population decay via a metastable state initializes the NV center in $|0\rangle$. (3) A DC shift can be applied to drive the sensor out of resonance with respect to the signal. The offset is turned off for a time $\tau$ to allow interaction with the sensor. The single sequence length of duration $T_L$ is repeated many times. (b) Working principle of the high-frequency Qdyne method. After preparation of $|{+}_i\rangle$ with a $\pi /2$ pulse around the $x$ axis the final state after signal interaction depends on the signal phase $\varphi$. A signal interaction resulting in a $\pi /2$ rotation is shown. The states are shown on the Bloch sphere in the rotating frame of the local oscillator. (c) Measurement of a 1.510 82 GHz signal. In a sampling time of 10 s, $3\times {10}^6$ samples are taken that correspond to $1.5\times {10}^6$ frequency channels in the FFT (only every 2000th point is shown). Lower plot: Zoom around the peak. (d) Measurement with a signal being applied only during the sensing period (top) and having a continuous signal without (center) and with a DC shift (bottom). The $x$ axis is the absolute value $\delta =|{\delta }_0|$ of the beat note of Eq. (5).

Figure 2

Full signal reconstruction. (a), (c), (d) Signal frequency, strength, and phase estimation. Measuring all three parameters allows full reconstruction of the signal. In (a) the difference between the estimated frequency $\nu$ and the signal frequency ${\nu }_{\mathrm{sig}}$ is displayed. (b) Linewidth (full width at half maximum) $\mathrm{\Delta }\nu =1/T$. The insets show the uncertainty of the respective estimation (error bars) as the 95% confidence intervals of the fit parameters. (a), (b) scale with $T^{-3/2}$ and (c), (d) with $T^{-1/2}$.

Figure 3

(a) Noise floor in dependence on integration time. Amplitude sensitivity of the measurement is obtained from a fit of slope $T^{-1/2}$ that gives a $58\mathrm{nT}$ noise floor at $T=1\mathrm{s}$. (b) Example of signal strength ambiguities for an interaction length ${\tau }_{\mathrm{ref}}=31.3\mathrm{ns}$. These ambiguities are lifted when the interaction time is changed. (c) Sensitivity in dependence on the signal frequency. Signals of strength $6.5\mu \mathrm{T}$ with varying frequency are detected. All other measurement parameters are kept constant.