In recent years, quantum lock-in detection has emerged as a promising technique to accurately detect weak signals submerged in background noise. However, the signal-to-noise ratio of existing protocols is severely limited by spectral leakage resulting from control operations implemented in pulse form. Here, we propose a general protocol for realizing quantum lock-in detection by employing successive quantum adiabatic evolution. In our protocol, the signal modulation is achieved by adiabatically controlling the time evolution of the quantum probe, which enables the implementation of triangular modulation functions. The realization of triangular-wave modulation fundamentally solves the problem of spectral leakage and facilitates the extraction of the complete characteristics of the target signals. We present a practical implementation scheme of adiabatic quantum lock-in detection based on nitrogen-vacancy centers in diamond, and demonstrate that the proposed protocol possesses strong resilience against experimental imperfections. Our results establish adiabatic quantum lock-in detection as a robust and experimentally accessible approach to detection of weak alternating signals in noisy environments, thus promoting the advance of real-world quantum sensing technologies.
In recent years, quantum lock-in detection has emerged as a promising technique to accurately detect weak signals submerged in background noise. However, the signal-to-noise ratio of existing protocols is severely limited by spectral leakage resulting from control operations implemented in pulse form. Here, we propose a general protocol for realizing quantum lock-in detection by employing successive quantum adiabatic evolution. In our protocol, the signal modulation is achieved by adiabatically controlling the time evolution of the quantum probe, which enables the implementation of triangular modulation functions. The realization of triangular-wave modulation fundamentally solves the problem of spectral leakage and facilitates the extraction of the complete characteristics of the target signals. We present a practical implementation scheme of adiabatic quantum lock-in detection based on nitrogen-vacancy centers in diamond, and demonstrate that the proposed protocol possesses strong resilience against experimental imperfections. Our results establish adiabatic quantum lock-in detection as a robust and experimentally accessible approach to detection of weak alternating signals in noisy environments, thus promoting the advance of real-world quantum sensing technologies.
Here we propose a general protocol for dual-channel lock-in detection of high-frequency ac signals. We find that the effect of a high-frequency target signal can be modulated through the application of rapidly oscillating driving fields. Based on this mechanism, we develop a quantum dual-channel lock-in detection protocol for high-frequency signals, which not only extends the accessible frequency range of quantum sensing but also enables the simultaneous estimation of the signal amplitude and initial phase. Furthermore, we present a feasible implementation scheme of the protocol based on nitrogen-vacancy centers in diamond. Numerical simulations demonstrate that the proposed protocol can effectively filter out background noise and significantly improve the signal-to-noise ratio. Our results provide a promising approach for realizing noise-resistant detection of weak signals in the high-frequency regime.
Abstract The detection of weak time-dependent alternating signals in a strongly noisy background is an important problem in physics and a critical task in metrology. Quantum lock-in amplifier can extract alternating signals within extreme noises by using suitable quantum resources, which has been widely used for magnetic field sensing, vector light shift detection, and force detection. In particular, entanglement-enhanced quantum lock-in amplifier can be realized via many-body quantum interferometry. The many-body lock-in measurement provides a feasible way to achieve high-precision detection of alternating signals, even in noisy environments. In this article, we review general protocol, experiment progresses and potential applications of quantum lock-in measurements.
Abstract Quantum lock-in amplifiers have been proposed to extract an alternating signal from a strong noise background. However, due to the typical target signal has unknown initial phase, it is challenging to extract complete information about the signal’s amplitude, frequency, and initial phase. Here, we present a general protocol for achieving a quantum double lock-in amplifier by employing two quantum mixers operating under orthogonal pulse sequences. To demonstrate the practical implementation, we discuss the experimental feasibility using a five-level double-Λ coherent population trapping system with Rb atoms. Here, each Λ structure acts as a quantum mixer, and two applied dynamical decoupling sequences serve as orthogonal reference signals. Notably, the system significantly reduces the total measurement time by nearly half and mitigates time-dependent systematic errors compared to conventional two-level systems. Furthermore, our quantum double lock-in amplifier is robust against experimental imperfections. This study establishes a pathway to alternating signal measurement, thereby facilitating the development of practical quantum sensing technologies.
Abstract Quantum systems are promising candidates for sensing of weak signals as they can be highly sensitive to external perturbations, thus providing excellent performance when estimating parameters of external fields. However, when trying to detect weak signals that are hidden by background noise, the signal-to-noise ratio is a more relevant metric than raw sensitivity. We identify, under modest assumptions about the statistical properties of the signal and noise, the optimal quantum control to detect an external signal in the presence of background noise using a quantum sensor. Interestingly, for white background noise, the optimal solution is the simple and well-known spin-locking control scheme. Using numerical techniques, we further generalize these results to the case of background noise with a Lorentzian spectrum. We show that for increasing correlation time, pulse based sequences, such as CPMG, are also close to the optimal control for detecting the signal, with the crossover dependent on the signal frequency. These results show that an optimal detection scheme can be easily implemented in near-term quantum sensors without the need for complicated pulse shaping.
Quantum sensing aims to detect signals with unparalleled sensitivity, potentially surpassing classical limitations. Solid-state spin defects, particularly nitrogen-vacancy centers in diamond, have emerged as promising platforms due to their long coherence time, optical addressability, high field sensitivity, and spatial and spectral resolution, making them ideal for sensing and imaging applications. Their compact size and robust performance under room temperature and ambient conditions further enhance their suitability for real-world applications. We provide an overview of quantum sensing principles and explore efforts to improve sensor functionality, including advanced sensing protocols, spatial imaging techniques, and integration with optical systems to enhance detection efficiency. We also highlight recent progress in the applications of these sensors across various use cases, including biomedical diagnostics, semiconductor device inspection, and industrial and military applications.
High-precision measurement of oscillating signal is a ubiquitous issue in fundamental science and a critical task in practical technologies. In quantum metrology, quantum lock-in detection provide an efficient method for measuring such signal. In general, when the initial phase of the oscillating signal is unknown,quantum double lock-in detection can effectively extract complete information about the signal's amplitude, frequency, and initial phase. Conventional quantum double lock-in detection requires two individual quantum interferometry, each of which must undergo state preparation and readout. However, the time for state preparation and readout need not be negligible in practical experiments. In particular, the time for state preparation is longer than the time for sensing. To save experimental resources, it is challenging to achieve quantum double lock-in detection just via a single quantum interferometry while still extracting complete information about the signal's amplitude, frequency, and initial phase. Here, we present a general protocol for achieving a quantum double lock-in detection just via a single quantum interferometry under a sequential orthogonal periodic multipulse sequences. In particular, if the input state is a Greenberger-Horne-Zeilinger state and two interaction-based operations are applied during interferometry, the measurement precisions for frequency, amplitude, and initial phase can both approach the Heisenberg limit. Our study paves a new way for measuring oscillating signals with a single quantum interferometry, and provides a feasible method for achieving Heisenberg-limited detection of alternating signals.