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arXiv:1806.00057 · Physical Review A

Using interaction-based readouts to approach the ultimate limit of detection-noise robustness for quantum-enhanced metrology in collective spin systems

Simon A. Haine

Published Sep 28, 2018• 48 citations
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Abstract

We consider the role of detection noise in quantum-enhanced metrology in collective spin systems and derive a fundamental bound for the maximum obtainable sensitivity for a given level of added detection noise. We then present an interaction-based readout utilizing the commonly used one-axis twisting scheme that approaches this bound for states generated via several commonly considered methods of generating quantum enhancement, such as one-axis twisting, two-axis countertwisting, twist-and-turn squeezing, quantum nondemolition measurements, and adiabatically scanning through a quantum phase transition. We demonstrate that our method performs significantly better than other recently proposed interaction-based readouts. These results may help provide improved sensitivity for quantum-sensing devices in the presence of unavoidable detection noise.

DOI
10.1103/physreva.98.030303

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We consider the role of detection noise in quantum-enhanced metrology in collective spin systems and derive a fundamental bound for the maximum obtainable sensitivity for a given level of added detection noise. We then present an interaction-based readout utilizing the commonly used one-axis twisting scheme that approaches this bound for states generated via several commonly considered methods of generating quantum enhancement, such as one-axis twisting, two-axis countertwisting, twist-and-turn squeezing, quantum nondemolition measurements, and adiabatically scanning through a quantum phase transition. We demonstrate that our method performs significantly better than other recently proposed interaction-based readouts. These results may help provide improved sensitivity for quantum-sensing devices in the presence of unavoidable detection noise.
We consider the role of detection noise in quantum-enhanced metrology in collective spin systems, and derive a fundamental bound for the maximum obtainable sensitivity for a given level of added detection noise. We then present an interaction-based readout utilising the commonly used one-axis twisting scheme that approaches this bound for states generated via several commonly considered methods of generating quantum enhancement, such as one-axis twisting, two-axis counter-twisting, twist-and-turn squeezing, quantum non-demolition measurements, and adiabatically scanning through a quantum phase transition. We demonstrate that this method performs significantly better than other recently proposed interaction-based readouts. These results may help provide improved sensitivity for quantum sensing devices in the presence of unavoidable detection noise.
Spin cat states are promising candidates for quantum-enhanced measurement. Here, we analytically show that the ultimate measurement precision of spin cat states approaches the Heisenberg limit, where the uncertainty is inversely proportional to the total particle number. In order to fully exploit their metrological ability, we propose to use the interaction-based readout for implementing phase estimation. It is demonstrated that the interaction-based readout enables spin cat states to saturate their ultimate precision bounds. The interaction-based readout comprises a one-axis twisting, two $\frac{\ensuremath{\pi}}{2}$ pulses, and a population measurement, which can be realized via current experimental techniques. Compared with the twisting echo scheme on spin squeezed states, our scheme with spin cat states is more robust against detection noise. Our scheme may pave an experimentally feasible way to achieve Heisenberg-limited metrology with non-Gaussian entangled states.
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.
Interference provides a fundamental mechanism for generating and manipulating entanglement in many-body quantum systems. Here, we develop an interference framework in which the nonlinear dynamics of collective spin-12\tfrac{1}{2}21​ ensembles are mapped onto phase accumulation and self-interference in phase space, providing a direct and physically transparent description of entanglement formation. Within this framework, one-axis twisting produces Greenberger-Horne-Zeilinger (GHZ) states, while two-axis twisting generates multi-component GHZ superpositions relevant for multiparameter quantum metrology. Building on this interference-based description, we analyze metrological performance under realistic Markovian noise, including local and collective emission, pumping, and dephasing, and examine the role of Hamiltonian control based on linear and nonlinear interactions. We show that the optimal control enhances sensitivity in both single- and multiparameter estimation across noise-dependent regimes. These results establish interference as a unifying principle linking nonlinear dynamics, entanglement generation, and metrological performance. This framework offers a broadly applicable route to robust quantum-enhanced sensing in noisy many-body systems.
Entanglement-enhanced atom interferometry has the potential of surpassing the standard quantum limit and eventually reaching the ultimate Heisenberg bound. The experimental progress is, however, hindered by various technical noise sources, including the noise in the detection of the output quantum state. The influence of detection noise can be largely overcome by exploiting echo schemes, where the entanglement-generating interaction is repeated after the interferometer sequence. Here, we propose an echo protocol that uses two-axis countertwisting as the main nonlinear interaction. We demonstrate that the scheme is robust to detection noise and its performance is superior compared to the already demonstrated one-axis twisting echo scheme. In particular, the sensitivity maintains the Heisenberg scaling in the limit of a large particle number. Finally, we show that the protocol can be implemented with spinor Bose-Einstein condensates. Our results thus outline a realistic approach to mitigate the detection noise in quantum-enhanced interferometry.
Cavity QED is a promising avenue for the deterministic generation of entangled and spin-squeezed states for quantum metrology. One archetypal scheme generates squeezing via collective one-axis twisting interactions. However, we show that in implementations using optical transitions in long-lived atoms the achievable squeezing is fundamentally limited by collectively enhanced emission into the cavity mode which is generated in parallel with the cavity-mediated spin-spin interactions. We propose an alternative scheme which generates a squeezed state that is protected from collective emission, and investigate its sensitivity to realistic sources of experimental noise and imperfections.