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.
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.
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.
Measuring stochastic signals ("noise metrology") constitutes a central task in quantum sensing and the characterization of open quantum systems. Here we establish ultimate precision bounds for multiparameter estimation of stochastic signals encoded through Markovian Lindblad dynamics, allowing for arbitrary quantum control and noiseless ancillae. Although Markovianity enforces standard-quantum-limit scaling with sensing time T, our bounds reveal Heisenberg-type scaling in the number of dissipative channels, R: when the stochastic signal exhibits high-rank correlations across the R channels and the probe is entangled, the average variance (per parameter) scales no better than Ω(1/(TR2)). For collective k-body dissipation, R=Θ(Nk), signifying super-Heisenberg scaling with the system size N. We further show that, when the unknown parameters enter through the dissipative eigenrates, a Rapid Prepare-and-Measure (RPM) protocol that tracks many distinct quantum jumps in parallel attains these limits. In this regime, the estimation problem reduces to a multi-Poisson counting model, providing a conceptually clean route to optimal quantum noise metrology. We illustrate the breadth of the framework with applications to networked noise metrology, collective many-body dissipation, learning Pauli noise, and subdiffraction quantum imaging.
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.
Quantum entanglement is a powerful quantum resource for enhancing measurement precision beyond classical limit. % Here we propose an entanglement-enhanced symmetry-protected destructive many-body Ramsey interferometry for precise parameter estimation. % Through matching the symmetry of input states and Hamiltonian, the spectral shift of Ramsey spectroscopy caused by interparticle interaction, noise, decoherence and experimental imperfection can be mitigated for both time-independent and time-dependent signals, as explored in the companion Letter [S. Chen, et al., Ramsey Spectroscopy via Symmetry-Protected Destructive Many-Body Interferometry (submitted)]. % In this work, we show that symmetric entangled input states can further improve the measurement precision of symmetry-protected Ramsey spectroscopy without affecting the measurement accuracy. % Through inputting spin cat states and applying suitable interaction-based readout operations, the measurement precisions of time-independent and time-dependent signals can both approach the Heisenberg limit. % In particular, we systematically analyze how precision scaling and robustness depend on the input states, parameters, experimental imperfection and decoherence. % This work establishes a practical pathway to Heisenberg-limited quantum metrology with many-body Ramsey interferometry, offering resilience against realistic noise and imperfections.