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arXiv:2304.05471 · Physical Review Letters

Squeezed Superradiance Enables Robust Entanglement-Enhanced Metrology Even with Highly Imperfect Readout

Martin Koppenhöfer, Peter Groszkowski, Aashish A. Clerk

Published Aug 8, 2023• 11 citations
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Abstract

Quantum metrology protocols using entangled states of large spin ensembles attempt to achieve measurement sensitivities surpassing the standard quantum limit (SQL), but in many cases they are severely limited by even small amounts of technical noise associated with imperfect sensor readout. Amplification strategies based on time-reversed coherent spin-squeezing dynamics have been devised to mitigate this issue, but are unfortunately very sensitive to dissipation, requiring a large single-spin cooperativity to be effective. Here, we propose a new dissipative protocol that combines amplification and squeezed fluctuations. It enables the use of entangled spin states for sensing well beyond the SQL even in the presence of significant readout noise. Further, it has a strong resilience against undesired single-spin dissipation, requiring only a large collective cooperativity to be effective.

DOI
10.1103/physrevlett.131.060802

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Quantum metrology protocols using entangled states of large spin ensembles attempt to achieve measurement sensitivities surpassing the standard quantum limit (SQL), but in many cases they are severely limited by even small amounts of technical noise associated with imperfect sensor readout. Amplification strategies based on time-reversed coherent spin-squeezing dynamics have been devised to mitigate this issue, but are unfortunately very sensitive to dissipation, requiring a large single-spin cooperativity to be effective. Here, we propose a new dissipative protocol that combines amplification and squeezed fluctuations. It enables the use of entangled spin states for sensing well beyond the SQL even in the presence of significant readout noise. Further, it has a strong resilience against undesired single-spin dissipation, requiring only a large collective cooperativity to be effective.
Quantum metrology protocols exploiting ensembles of N two-level systems and Ramsey-style measurements are ubiquitous.However, in many cases excess readout noise severely degrades the measurement sensitivity; in particular in sensors based on ensembles of solid-state defect spins.We present a dissipative "spin-amplification" protocol that allows us to dramatically improve the sensitivity of such schemes, even in the presence of realistic intrinsic dissipation and noise.Our method is based on exploiting collective (i.e., superradiant) spin decay, an effect that is usually seen as a nuisance because it limits spin-squeezing protocols.We show that our approach can allow a system with a highly imperfect spin readout to approach standard-quantum-limit-like scaling in N within a factor of 2, without needing to change the actual readout mechanism.Our ideas are compatible with several state-of-the-art experimental platforms where an ensemble of solid-state spins (NV centers, SiV centers) is coupled to a common microwave or mechanical mode.
The sensitivity of quantum sensors is fundamentally constrained by the standard quantum limit (SQL) arising from intrinsic quantum fluctuations. While non-classical resources like squeezing or entanglement can surpass this limit, their utility is often restricted by the extreme fragility of entangled states and the complexity of their preparation. Quantum criticality offers a compelling alternative by harnessing divergent susceptibility to amplify signals without requiring fragile non-classical resources. However, the practical benefit of this approach has remained controversial due to the potential for the simultaneous amplification of quantum noise. Here, we demonstrate a universal protocol for noiseless critical sensing by engineering a light-driven atomic ensemble near a dynamical critical point. Analogous to a Kapitza pendulum near its inverted orientation, the spin system enters a non-equilibrium regime where the signal susceptibility diverges while the quantum noise periodically recedes to its coherent baseline. We exploit this ``noise ebbing'' to create a built-in noiseless amplifier, demonstrating a 3.3 dB metrological gain over the SQL in an atomic magnetometer. Our implementation exhibits intrinsic robustness against common experimental imperfections such as detection losses, establishing non-equilibrium critical dynamics as a practical and versatile paradigm for surpassing the fundamental limits of quantum sensing.
Spin squeezing can increase the sensitivity of interferometric measurements of small signals in large spin ensembles beyond the standard quantum limit. In many practical settings, the ideal metrological gain is limited by imperfect readout of the sensor. To overcome this issue, protocols based on time reversal of unitary one-axis-twist (OAT) spin-squeezing dynamics have been proposed. Such protocols mitigate readout noise and, when implemented using cavity feedback, have been argued to also be robust against dissipation as long as the collective cooperativity of the system is sufficiently large [Davis et al., Phys. Rev. Lett. 116, 053601 (2016)]. Here, we perform a careful systematic study of dissipative effects on three different implementations of a OAT twist-untwist sensing scheme (based on symmetric as well as asymmetric cavity feedback and on a Tavis-Cummings interaction). Our full treatment shows that the three approaches have markedly different properties and resilience when subject to dissipation. Moreover, the metrological gain for an implementation using symmetric cavity feedback is more sensitive to undesired dissipation than was previously appreciated.
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.
Balancing high sensitivity with a broad dynamic range is a fundamental challenge in measurement science, as improving one often compromises the other. While traditional quantum metrology has prioritized enhancing local sensitivity, a large dynamic range is crucial for applications such as atomic clocks, where extended phase interrogation times contribute to wider phase range. In this Letter, we introduce a novel quantum deamplification mechanism that extends dynamic range at a minimal cost of sensitivity. Our approach uses two sequential spin-squeezing operations to generate and detect an entangled probe state, respectively. We demonstrate that the optimal quantum interferometer limit can be approached through two-axis countertwisting dynamics. Further expansion of dynamic range is possible by using sequential quantum deamplification interspersed with phase encoding processes. Additionally, we show that robustness against detection noise can be enhanced by a hybrid sensing scheme that combines quantum deamplification with quantum amplification. Our protocol is within the reach of state-of-the-art atomic-molecular-optical platforms, offering a scalable, noise-resilient pathway for entanglement-enhanced metrology.
Useful quantum metrology requires nonclassical states with a high particle number and (close to) the optimal exploitation of the state's quantum correlations. Unfortunately, the single-particle detection resolution demanded by conventional protocols, such as spin squeezing via one-axis twisting, places severe limits on the particle number. Additionally, the challenge of finding optimal measurements (that saturate the quantum Cramér-Rao bound) for an arbitrary nonclassical state limits most metrological protocols to only moderate levels of quantum enhancement. "Interaction-based readout" protocols have been shown to allow optimal interferometry or to provide robustness against detection noise at the expense of optimality. In this Letter, we prove that one has great flexibility in constructing an optimal protocol, thereby allowing it to also be robust to detection noise. This requires the full probability distribution of outcomes in an optimal measurement basis, which is typically easily accessible and can be determined from specific criteria we provide. Additionally, we quantify the robustness of several classes of interaction-based readouts under realistic experimental constraints. We determine that optimal and robust quantum metrology is achievable in current spin-squeezing experiments.