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arXiv:2312.01684 · Physical Review A

Orbital-angular-momentum-enhanced phase estimation using non-Gaussian states with photon loss

Yong-Jian Chen, Jinwei Gao, Jin‐Xuan Han, Zhonghui Yuan, Ruo-Qi Li, Yongyuan Jiang, Jie Song

Published Aug 22, 2023• 6 citations
arXivHTMLPDF

Abstract

This study investigates the use of orbital angular momentum (OAM) to enhance phase estimation in Mach-Zehnder interferometers by employing non-Gaussian states as input resources in the presence of noise. Our research demonstrates that non-Gaussian states, particularly the photon-subtraction-then-addition state, exhibit the best sensitivity in the presence of symmetric noise. Additionally, a higher order of the Bose operator of non-Gaussian states provides better sensitivity for symmetric noise. OAM can mitigate the deterioration of noise, making it possible to estimate small phase shifts $\ensuremath{\theta}\ensuremath{\rightarrow}0$. OAM enhances the resolution and sensitivity of all input states and mitigates the deterioration caused by photon loss. Additionally, OAM enhances the resolution and sensitivity of all input states, enabling the sensitivity to approach the $1/N$ limit even under significant photon loss (e.g., $50%$ symmetric photon loss). These results hold promise for enhancing the sensitivity and robustness of quantum metrology, particularly in the presence of significant photon loss.

DOI
10.1103/physreva.108.022613

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Abstract The precision of quantum measurements can be effectively improved by using both photon-added non-Gaussian operations and Kerr nonlinear phase shift. Here, we employ a coherent state mixed with a photon-added squeezed vacuum state as the input to a Mach–Zehnder interferometer with parity detection, thereby achieving a significant enhancement in phase measurement precision. Our research focuses on the phase sensitivity of linear phase shift under both ideal conditions and photon loss, as well as quantum Fisher information (QFI). The results demonstrate that employing the photon addition operations can markedly enhance phase sensitivity and QFI, and under optimal conditions, the measurement precision can approach the Heisenberg limit for the linear phase shift case. In addition, we delve deeper into the scenario of replacing the linear phase shift with a Kerr nonlinear one and systematically analyze the QFI under both ideal and photon loss conditions. By comparison, it is evident that employing both the photon addition operations and the Kerr nonlinear phase shift can further significantly enhance phase measurement precision while effectively improving the system’s robustness against photon loss. These findings are instrumental in facilitating the development and practical application of quantum metrology.
Quantum metrology aims to achieve measurement precision that surpasses classical limits in the estimation of physical parameters. In realistic conditions, however, its advantage can be diminished by interactions between a quantum system and its environment. This necessitates careful design of quantum resources that can sustain enhanced performance even under noise. Here, we investigate how a quantum non-Gaussian operation can provide an advantage in noisy quantum metrology. Specifically, we examine the effect of single-photon subtraction applied to a two-mode squeezed vacuum state in the task of phase estimation using a Mach–Zehnder interferometer under photon loss. The single-photon subtraction can be implemented either before or after the first beam splitter in the interferometer. By evaluating the quantum Fisher information for both the original and the photon-subtracted states, we assess the potential enhancement in sensing precision. We show that the enhancement occurs when photon subtraction is performed before the first beam splitter, provided that loss acts only on the signal mode. Our findings shed light on the role of non-Gaussian operations in noisy quantum metrology, clarifying when photon subtraction can yield a genuine advantage over Gaussian resources.
Based on the conventional Mach-Zehnder interferometer, we propose a metrological scheme to improve phase sensitivity. In this scheme, we use a coherent state and a squeezed vacuum state as input states, employ multi-photon-subtraction operations and make intensity-detection or homodyne-detection. We study phase sensitivity, quantum Fisher information and quantum Cramér-Rao bound under both ideal and lossy conditions. The results indicate that choosing an appropriate detection method and photon subtraction scheme can significantly enhance the phase sensitivity and robustness against photon losses. Even under lossy conditions, the multi-photon subtraction schemes can surpass the standard quantum limit. Notably, the homodyne detection method can even break through the Heisenberg limit. Moreover, increasing the number of photon-subtracted can enhance both phase sensitivity and quantum Fisher information. This research highlights the significant value of this scheme in quantum precision measurement.
Lights carrying orbital angular momentum (OAM) have potential applications in precise rotation measurement, especially in remote sensing. Interferometers, especially nonlinear quantum interferometers, have also been proven to greatly improve the measurement accuracy in quantum metrology. By combining these two techniques, we theoretically propose a new atom-light hybrid Sagnac interferometer with OAM lights to advance the precision of the rotation measurement. A rotation sensitivity below standard quantum limit is achieved due to the enhancement of the quantum correlation of the interferometer even with 96% photon losses. This makes our protocol robustness to the photon loss. Furthermore, combining the slow light effect brings us at least four orders of magnitude of sensitivity better than the earth rotation rate. This new type interferometer has potential applications in high precision rotation sensing.
Quantum metrology employs quantum resources to achieve measurement precision beyond classical limits. This work investigates a Mach--Zehnder interferometer incorporating a Kerr nonlinear phase shifter, with photon-added two-mode squeezed coherent states generated via four-wave mixing as input. We demonstrate that increasing both the photon-addition order and the input resource strength systematically enhances phase sensitivity, quantum Fisher information, and the corresponding quantum Cramér--Rao bound. The proposed system not only surpasses the standard quantum limit but also approaches or exceeds the Heisenberg limit for linear phase shifts, while Kerr nonlinearity enables surpassing the super-Heisenberg limit. Furthermore, the scheme exhibits enhanced robustness against photon loss, providing a promising pathway toward practical high-precision quantum metrology applications.
Lights carrying orbital angular momentum (OAM) have potential applications in precise rotation measurement, especially in remote sensing. Interferometers, especially nonlinear quantum interferometers, have also been proven to greatly improve the measurement accuracy in quantum metrology. By combining these two techniques, we theoretically propose a new atom-light hybrid Sagnac interferometer with OAM lights to advance the precision of the rotation measurement. A rotation sensitivity below standard quantum limit is achieved due to the enhancement of the quantum correlation of the interferometer even with 96% photon losses. This makes our protocol robustness to the photon loss. Furthermore, combining the slow light effect brings us at least four orders of magnitude of sensitivity better than the earth rotation rate. This new type interferometer has potential applications in high precision rotation sensing.