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arXiv:2510.25870 · PRX Quantum

Optimal Displacement Sensing with Spin-Dependent Squeezed States

Liam J. Bond, Christophe H. Valahu, Athreya Shankar, Ting Rei Tan, Arghavan Safavi-Naini

Published Apr 28, 2026• 0 citations
arXivHTMLPDF

Abstract

Displacement sensing is a fundamental task in metrology. However, the development of quantum-enhanced sensors that fully utilize the available degrees of freedom in many-body quantum systems remains an outstanding challenge. We propose many-body displacement sensing schemes that use spin-dependent squeezed (SDS) states—hybrid spin-boson states whose bosonic squeezed quadrature is conditioned on an auxiliary spin. We prove that SDS states are , i.e., their quantum Cramér-Rao bound saturates the Heisenberg limit. We propose explicit measurement sequences that can be readily implemented in systems such as trapped ions. We also introduce a scalable state-preparation protocol and numerically demonstrate the preparation of 8.7 dB of spin-dependent squeezing 15 times faster than the standard approach using second-order sidebands in trapped ions. The potential applications of our sensing protocols range from measuring single-photon scattering to searches for dark matter.

DOI
10.1103/mhvv-pr5d

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Displacement sensing is a fundamental task in metrology. However, the development of quantum-enhanced sensors that fully utilize the available degrees of freedom in many-body quantum systems remains an outstanding challenge. We propose many-body displacement sensing schemes that use spin-dependent squeezed (SDS) states—hybrid spin-boson states whose bosonic squeezed quadrature is conditioned on an auxiliary spin. We prove that SDS states are , i.e., their quantum Cramér-Rao bound saturates the Heisenberg limit. We propose explicit measurement sequences that can be readily implemented in systems such as trapped ions. We also introduce a scalable state-preparation protocol and numerically demonstrate the preparation of 8.7 dB of spin-dependent squeezing 15 times faster than the standard approach using second-order sidebands in trapped ions. The potential applications of our sensing protocols range from measuring single-photon scattering to searches for dark matter.
Atom interferometers are reaching sensitivities fundamentally constrained by quantum fluctuations. A main challenge is to integrate entanglement into quantum sensing protocols to enhance precision while ensuring robustness against noise and systematics. Here, we theoretically investigate differential phase measurements with two atom interferometers using spin-squeezed states, accounting for common-mode phase noise spanning the full 2π2π2π range. We estimate the differential signal using model-free ellipse fitting, a robust method requiring no device calibration and resilient to additional noise sources. Our results show that spin-squeezing enables sensitivities below the standard quantum limit. Specifically, we identify optimal squeezed states that minimize the differential phase variance, scaling as N−2/3N^{-2/3}N−2/3, while eliminating bias inherent in ellipse fitting methods. We benchmark our protocol against the Cramér-Rao bound and compare it with hybrid methods that incorporate auxiliary classical sensors. Our findings provide a pathway to robust and high-precision atom interferometry, in realistic noisy environments and using readily available states and estimation methods.
Abstract Atom interferometers are reaching sensitivities fundamentally constrained by quantum fluctuations. A main challenge is to integrate entanglement into quantum sensing protocols to enhance precision while ensuring robustness against noise and systematics. Here, we theoretically investigate differential phase measurements with two atom interferometers using spin-squeezed states of N atoms, accounting for common-mode phase noise spanning the full 2 π range. We estimate the differential signal using model-free ellipse fitting, a robust method requiring no device calibration and resilient to additional noise sources. Our results show that spin-squeezing enables sensitivities below the standard quantum limit (SQL). Specifically, we identify optimal squeezed states that minimize the differential phase uncertainty, scaling as N − 2 / 3 , thus overcoming the SQL by a factor N 1 / 6 , while eliminating the bias inherent in ellipse fitting methods. We benchmark our protocol against the Cramér–Rao bound and compare it with hybrid methods that incorporate auxiliary classical sensors. Our findings provide a pathway to robust and high-precision atom interferometry, in realistic noisy environments and using readily available states and estimation methods.
We theoretically investigate prospects for the creation of nonclassical spin states in trapped ion arrays by coupling to a squeezed state of the collective motion of the ions. The correlations of the generated spin states can be tailored for quantum-enhanced sensing of global or differential rotations of subensembles of the spins by working with specific vibrational modes of the ion array. We propose a pair of protocols to utilize the generated states and demonstrate their viability even for small systems, while assessing limitations imposed by spin-motion entanglement and technical noise. Our work suggests new opportunities for the preparation of many-body states with tailored correlations for quantum-enhanced metrology in spin-boson systems.
Achieving measurement precision beyond the standard quantum limit (SQL) is a fundamental object in quantum metrology. In this manuscript, we propose a streamlined protocol for weak signal sensing in a trapped-ion spin-oscillator system that simultaneously exploits detuned motional squeezing and spin-oscillator entanglement. By combining these two quantum resources, the phase accumulation in this spin system is significantly accelerated, as a result achieving an exponential improvement in the sensitivity over unsqueezed cases. Remarkably, we show that the significant metrological gain provided by our protocol persists in noisy environments, with the sensitivity remaining below the SQL. In particular, our protocol retains a distinct advantage in the short interrogation time regime, thus demonstrating the practical potential in quantum-enhanced sensing.
Many-body quantum chaos has immense potential as a tool to accelerate the preparation of entangled states and overcome challenges due to decoherence and technical noise. Here, we study how chaos in the paradigmatic Dicke model, which describes the uniform coupling of an ensemble of qubits to a common bosonic mode, can enable the rapid generation of non-Gaussian entangled spin-boson states without fine-tuning of system parameters or initial conditions. However, the complexity of these states means that unlocking their utility for quantum-enhanced sensing with standard protocols would require the measurement of complex or typically inaccessible observables. To address this challenge, we develop a sensing scheme based on interaction-based readout that enables us to implement near-optimal quantum-enhanced metrology of global spin rotations or bosonic displacements using only spin measurements. We show that our approach is robust to technical noise and imperfections and thus opens new opportunities to exploit complex entangled states generated by chaotic dynamics in current quantum science platforms such as trapped-ion and cavity-QED experiments.
Twist-untwist protocols for quantum metrology consist of a serial application of (1) unitary nonlinear dynamics (e.g., spin squeezing or Kerr nonlinearity), (2) parameterized dynamics $U(\ensuremath{\phi})$ (e.g., a collective rotation or phase space displacement), and (3) time reversed application of step 1. Such protocols are known to produce states that allow Heisenberg scaling for experimentally accessible estimators of $\ensuremath{\phi}$ even when the nonlinearities are applied for times much shorter than required to produce Schr\"odinger cat states. In this work, we prove that, asymptotically in the number of particles, twist-untwist protocols provide the lowest estimation error among quantum metrology protocols that utilize two calls to a weakly nonlinear evolution and a readout involving only first and second moments of a total spin operator $\stackrel{P\vec}{n}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{P\vec}{J}$. We consider the following physical settings: all-to-all interactions generated by one-axis twisting Jz2{J}_{z}^{2}Jz2​ (e.g., interacting Bose gases), constant finite range spin-spin interactions of distinguishable or bosonic atoms (e.g., trapped ions or Rydberg atoms, or lattice bosons). In these settings, we further show that the optimal twist-untwist protocols asymptotically achieve 85% and 92% of the respective quantum Cram\'er-Rao bounds. We show that the error of a twist-untwist protocol can be decreased by a factor of LLL without an increase in the noise of the spin measurement if the twist-untwist protocol can be noiselessly iterated as an LLL layer quantum alternating operator ansatz.