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arXiv:2509.08291

Symmetry-protected many-body Ramsey spectroscopy: precision scaling and robustness

Chen Sijie, Jiahao Huang, Min Zhuang, Chaohong Lee

Published Sep 10, 2025• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2509.08291

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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.
Ramsey spectroscopy, a fundamental tool in both basic science and practical applications, is inevitably subject to several detrimental effects. % Here we propose a symmetry-protected destructive many-body interferometry (SPDMBI) for Ramsey spectroscopy, which successfully mitigates the spectral shift caused by interparticle interaction, noise, decoherence and experimental imperfection. % Through matching the symmetry of the input states and the Hamiltonian, the SPDMBI-based Ramsey spectroscopy yields an antisymmetric spectrum, whose antisymmetric point exactly determines the resonance frequency. % In such a Ramsey spectroscopy, the population difference under resonance is always zero, which is a result of destructive quantum interferometry. % To demonstrate its versatility, we showcase successful applications of symmetry-protected Ramsey spectroscopy in measuring both time-independent and time-dependent signals. % Our protocol can improve the performance of Ramsey spectroscopy, which offers a pathway for various high-precision quantum sensors.
Ramsey spectroscopy serves as a key tool for frequency measurement. Although entanglement can enhance the measurement precision, the atom-atom interaction required for entanglement generation may lead to a frequency shift. In addition, the spectra also suffer from light shift caused by the interaction between light and atoms. Thus, it is difficult to achieve high precision without inducing additional systematic errors. Here, we propose to realize high-precision entanglement-enhanced Ramsey spectroscopy with composite pulses. First, we utilize spin-squeezed states generated by one-axis twisting (OAT) dynamics to enhance the measurement precision. We find that by applying a suitable pulse after OAT, the resonant frequency can be inferred and the light shift can be reduced by using composite pulses. To increase the signal slope, we use anti-OAT dynamics to perform interaction-based readout after interrogation. By designing suitable composite pulses, it can significantly increase the signal response and further improve the measurement precision. Although both schemes can mitigate the light shift, it cannot be entirely eliminated. Thus, we develop the autobalanced entanglement-enhanced Ramsey spectroscopy. By using combination of different sequences with short and long interrogation times and feedback control, the light shift of both our protocols can be completely suppressed, which increases the measurement accuracy. Besides, we also investigate the effects of background atom-atom interaction and find that it only reduces the measurement precision without introducing additional frequency shift. Our study offers an alternative method for achieving precise frequency measurement, which has the potential to be of significant application in quantum sensors such as atomic clocks.
Ramsey interferometry is a widely used tool for precisely measuring transition frequencies between two energy levels of a quantum system, with applications in time keeping, precision spectroscopy, quantum optics, and quantum information. Often, the coherence time of the quantum system surpasses the one of the oscillator probing the system, thereby limiting the interrogation time and associated spectral resolution. Correlation spectroscopy overcomes this limitation by probing two quantum systems with the same noisy oscillator for a measurement of their transition frequency difference; this technique has enabled very precise comparisons of atomic clocks. Here, we extend correlation spectroscopy to the case of multiple quantum systems undergoing strong correlated dephasing. We model Ramsey correlation spectroscopy with N particles as a multiparameter phase estimation problem and demonstrate that multiparticle correlations can assist in reducing the measurement uncertainties even in the absence of entanglement. We derive precision limits and optimal sensing techniques for this problem and compare the performance of probe states and measurement with and without entanglement. Using one- and two-dimensional ion Coulomb crystals with up to 91 qubits, we experimentally demonstrate the advantage of measuring multiparticle correlations for reducing phase uncertainties and apply correlation spectroscopy to measure ion-ion distances, transition frequency shifts, laser-ion detunings, and path-length fluctuations. Our method can be straightforwardly implemented in experimental setups with globally coherent qubit control and qubit-resolved single-shot readout and is, thus, applicable to other physical systems such as neutral atoms in tweezer arrays. Published by the American Physical Society 2024
Quantum metrology studies the use of entanglement and other quantum resources to improve precision measurement. An interferometer using N independent particles to measure a parameter χ can achieve at best the "standard quantum limit" (SQL) of sensitivity δχ ∝ N-1/2. The same interferometer using N entangled particles can achieve in principle the "Heisenberg limit" δχ ∝ N-1, using exotic states, e.g., NooN states. Recent theoretical work argues that interactions among particles may be a valuable resource for quantum metrology, allowing scaling beyond the Heisenberg limit. Specifically, a k-particle interaction will produce sensitivity δχ ∝ N-kwith appropriate entangled states and δχ ∝ N-(k-1/2)even without entanglement. Here we demonstrate this "super-Heisenberg" scaling in a nonlinear, non-destructive measurement of the magnetisation of an atomic ensemble.
I analyze a metrological strategy for improving the precision of frequency estimation via Ramsey interferometry with strings of atoms in the presence of correlated dephasing. This strategy does not employ entangled states but rather a product state which evolves into a stationary state under the influence of correlated dephasing. It is shown that by using this state an improvement in precision compared to standard Ramsey interferometry can be gained. This improvement is not an improvement in scaling; i.e., the estimation precision has the same scaling with the number of atoms as the standard quantum limit but gains an improvement proportional to the free evolution time in the Ramsey interferometer. Since a stationary state is used, this evolution time can be substantially larger than in standard Ramsey interferometry which is limited by the coherence time of the atoms.
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.