Detection of Quantum Signals Free of Classical Noise via Quantum Correlation

Extracting useful signals is key to both classical and quantum technologies. Conventional noise filtering methods rely on different patterns of signal and noise in frequency or time domains, thus limiting their scope of application, especially in quantum sensing. Here, we propose a signal-nature-based (not signal-pattern-based) approach which singles out a quantum signal from its classical noise background by employing the intrinsic quantum nature of the system. We design a novel protocol to extract the quantum correlation signal and use it to single out the signal of a remote nuclear spin from its overwhelming classical noise backgrounds, which is impossible to be accomplished by conventional filter methods. Our Letter demonstrates the quantum or classical nature as a new degree of freedom in quantum sensing. The further generalization of this quantum nature-based method opens a new direction in quantum research.

Figure 1

Illustration of the quantum nature-based method. Comparison between traditional DSP methods which are based on pattern-dependent noise filters (upper), and the quantum-nature-based filtering method (lower). The latter can filter out arbitrary classical noise without resorting to a specific pattern of noise in the frequency or time domain. (b) The semiclassical picture of the QC protocol and (c) the semiclassical picture of the CC protocol. The difference between the QC and CC protocols is that the rotation operation is absent in the QC protocols. The final signal of these protocols is the expectation value of ${\widehat{\sigma }}_y$ of the sensor after these operations. Phase randomization denotes the incoherent operation that eliminates the $x\text{−}y$ components of the sensor while keeping its $z$ components.

Figure 2

Experimental implementation of the $\mathrm{QC}/\mathrm{CC}$ protocol: (a) Left graph: The sketch map of the nitrogen vacancy (NV) center in diamond. The NV center is coupled with the surrounding ${}^{13}\mathrm{C}$ nuclear spins through dipolar-dipolar interaction; The middle graph: The optical initialization and operation of the NV center; The right graph: the energy structure of the ground state of the NV center. (b) The experimental implementation of the protocol. In these pictures, the green rectangle denotes the laser pulse to initialize or read out the NV spin. The phase randomization part aims to eliminate the information on the phase of the NV center by randomizing the phase while keeping its population. It is realized by a $z$-direction rotation dc pulse with random rotating angles (see Supplemental Material [24]). This method can be generalized to most types of sensors. The purple (orange) rectangle denotes the $\pi /2$ microwave pulse with axis being $y(x)$.

Figure 3

Verification of the quantumness of QC signal. (a) The $\mathrm{QC}/\mathrm{CC}$ signals from a sensor under the classical ac magnetic field. Left: the detected QC $(\mathrm{orange}\mathrm{scatters})/\mathrm{CC}$ (purple scatters) correlation signals in the time domain; Right: the detected $\mathrm{QC}/\mathrm{CC}$ signals in the frequency domain. (b) The $\mathrm{QC}/\mathrm{CC}$ signals from a sensor coupled with nuclear spins. Upper: the sequence to measure $\mathrm{QC}/\mathrm{CC}$ signal of a polarized nuclear spin. We use the method of Ref. [44] to polarize the nuclear spin bath. The electron polarization is transferred to the bath by repeating a partial swap gate (denoted by $\beta$) (see Ref. [44]). Lower: The Fourier transform of the $\mathrm{QC}/\mathrm{CC}$ signal. Here the magnetic field is $B_z=504\mathrm{G}$.

Figure 4

The demonstration of the pattern-independent quantum sensing. (a) Filters out a single frequency classical noise. (b) Filters out classical color noise. Here the magnetic field is $B_z=504\mathrm{G}$. The hyperfine coupling between the nuclear spin and sensor is 60.4 kHz.