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 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.
Achieving high-precision detection of time-dependent signals within noise is a ubiquitous issue in physics and a critical task in metrology.Lock-in amplifiers are detectors that can extract alternating signals within extreme noise via a known carrier frequency.Here we present a protocol for achieving an entanglement-enhanced lock-in amplifier via use of many-body multipulse quantum interferometry.The many-body quantum lock-in amplifier is implemented by application of a periodic multi-π -pulse sequence during the interrogation.Our analytic results show that, by our choosing suitable input states and readout operations, the frequency and amplitude of an unknown alternating field can be simultaneously extracted via population measurements.The lock-in point can be determined via the symmetry of the signal during a single interrogation time or the time-averaged signals for multiple interrogation times.We find that the measurement signal at the lock-in point is independent of the interrogation time.In particular, if we input spin cat states and apply interaction-based readout operations, the measurement precisions for frequency and amplitude can both approach the Heisenberg limit.Moreover, our many-body quantum amplifier is also robust with regard to extreme stochastic noise.Our study paves a new way for measuring time-dependent signals with many-body quantum systems, and provides a feasible method for achieving Heisenberg-limited detection of alternating signals.
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.
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 sinusoidal modulation functions. The realization of sinusoidal-wave modulation substantially mitigates 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.
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.
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 Quantum lock-in detection (QLID), a cornerstone technique in quantum metrology, enables precise extraction of oscillating signals from noise by leveraging dynamical decoupling to suppress unwanted spectral components. Beyond this, many-body quantum entanglement serves as a critical resource for surpassing the standard quantum limit in precision measurements. Here we report the first experimental realization of entanglement-enhanced QLID using two 40Ca+ ions confined in a linear Paul trap. The system is initialized into a maximally entangled Greenberger-Horne-Zeilinger state via a Mϕlmer-Sϕrensen gate, followed by the application of periodic multipulse sequences to implement QLID. Compared to non-entangled states (e.g., a product state), our work demonstrates frequency measurement precision scaling as 1/N with particle number (N) , achieving the Heisenberg scaling. Remarkably, the precision in the time domain approaches a super-Heisenberg scaling (i.e., 1/T2), significantly outperforming conventional bounds. To enhance practical applicability, we further optimize multipulse sequences to improve robustness against rotation angle inaccuracies and detuning errors. This work establishes QLID as a powerful paradigm for quantum sensing and provides a concrete pathway to Heisenberg-limited detection of oscillating signals in realistic settings.