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arXiv:1804.03971 · Physical Review A

Achieving Heisenberg-limited metrology with spin cat states via interaction-based readout

Jiahao Huang, Min Zhuang, Bo Lü, Yongguan Ke, Chaohong Lee

Published Jul 23, 2018• 49 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.98.012129

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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 \ensuremathπ2\frac{\ensuremath{\pi}}{2}2\ensuremathπ​ 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.
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.
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 propose an approach to quantum phase estimation that can attain precision near the Heisenberg limit without requiring single-particle-resolved state detection. We show that the "one-axis twisting" interaction, well known for generating spin squeezing in atomic ensembles, can also amplify the output signal of an entanglement-enhanced interferometer to facilitate readout. Applying this interaction-based readout to oversqueezed, non-Gaussian states yields a Heisenberg scaling in phase sensitivity, which persists in the presence of detection noise as large as the quantum projection noise of an unentangled ensemble. Even in dissipative implementations-e.g., employing light-mediated interactions in an optical cavity or Rydberg dressing-the method significantly relaxes the detection resolution required for spectroscopy beyond the standard quantum limit.
Detection noise poses a challenge for achieving Heisenberg-limited phase estimation. We discuss a "twisting echo" protocol1 that addresses this problem by using interactions to amplify a spectroscopic signal. The echo protocol enables phase sensitivity near the Heisenberg limit while permitting detection noise on the order of the quantum noise of an unentangled state. For comparison with conventional schemes requiring direct detection of entangled states, we calculate the dependence of metrological gain on detection noise in Ramsey spectroscopy with squeezed, twin Fock, and GHZ states. The twisting echo outperforms all of these alternatives if the detection uncertainty is at or above the single-atom level.
Abstract Spin squeezing is a key resource in quantum metrology, allowing improvements of measurement signal-to-noise ratio. Its generation is a challenging task because the experimental realization of the required squeezing interaction remains difficult. Here, we propose a generic scheme to synthesize spin squeezing in non-squeezing systems. By using periodical rotation pulses, the original non-squeezing interaction can be transformed into squeezing interaction, with significantly enhanced interaction strength. The sign of the interaction coefficient is also flippable, facilitating time-reversal readout protocol for nonlinear interferometers. The generated spin squeezing is capable of achieving the Heisenberg limit with measurement precision ∝ 1/N for N particles and its robustness to noises of pulse areas and separations has been verified as well. This work offers a path to extending the scope of Heisenberg-limited quantum precision measurements in non-squeezing systems.