Tilt Measurement at the Quantum Cramer–Rao Bound Using a Higher-Order Hermite–Gaussian Mode
The quantum Cramer–Rao bound (QCRB) provides an ultimate precision limit in parameter estimation. The sensitivity of spatial measurements can be improved by using the higher-order Hermite–Gaussian mode. However, to date, the QCRB-saturating tilt measurement has not been realized. Here, we experiment...
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MDPI AG
2023-05-01
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| Series: | Photonics |
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| Online Access: | https://www.mdpi.com/2304-6732/10/5/584 |
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| author | Zhi Li Yijian Wang Hengxin Sun Kui Liu Jiangrui Gao |
| author_facet | Zhi Li Yijian Wang Hengxin Sun Kui Liu Jiangrui Gao |
| author_sort | Zhi Li |
| collection | DOAJ |
| description | The quantum Cramer–Rao bound (QCRB) provides an ultimate precision limit in parameter estimation. The sensitivity of spatial measurements can be improved by using the higher-order Hermite–Gaussian mode. However, to date, the QCRB-saturating tilt measurement has not been realized. Here, we experimentally demonstrate tilt measurements using a higher-order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><msub><mi>G</mi><mn>40</mn></msub></mrow></semantics></math></inline-formula> mode as the probe beam. Using the balanced homodyne detection with an optimal local beam, which involves the superposition of high-order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><msub><mi>G</mi><mn>30</mn></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><msub><mi>G</mi><mn>50</mn></msub></mrow></semantics></math></inline-formula> modes, we demonstrate the precision of the tilt measurement approaching the QCRB. The signal-to-noise ratio of the tilt measurement is enhanced by 9.2 dB compared with the traditional method using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><msub><mi>G</mi><mn>00</mn></msub></mrow></semantics></math></inline-formula> as the probe beam. This scheme is more practical and robust to losses, which has potential applications in areas such as laser interferometer gravitational-wave observatories and high-sensitivity atomic force microscopes. |
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| last_indexed | 2024-03-11T03:23:10Z |
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| spelling | doaj.art-2de5e535ae5442be944b15af53e601102023-11-18T02:54:49ZengMDPI AGPhotonics2304-67322023-05-0110558410.3390/photonics10050584Tilt Measurement at the Quantum Cramer–Rao Bound Using a Higher-Order Hermite–Gaussian ModeZhi Li0Yijian Wang1Hengxin Sun2Kui Liu3Jiangrui Gao4State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, ChinaState Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, ChinaState Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, ChinaState Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, ChinaState Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, ChinaThe quantum Cramer–Rao bound (QCRB) provides an ultimate precision limit in parameter estimation. The sensitivity of spatial measurements can be improved by using the higher-order Hermite–Gaussian mode. However, to date, the QCRB-saturating tilt measurement has not been realized. Here, we experimentally demonstrate tilt measurements using a higher-order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><msub><mi>G</mi><mn>40</mn></msub></mrow></semantics></math></inline-formula> mode as the probe beam. Using the balanced homodyne detection with an optimal local beam, which involves the superposition of high-order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><msub><mi>G</mi><mn>30</mn></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><msub><mi>G</mi><mn>50</mn></msub></mrow></semantics></math></inline-formula> modes, we demonstrate the precision of the tilt measurement approaching the QCRB. The signal-to-noise ratio of the tilt measurement is enhanced by 9.2 dB compared with the traditional method using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><msub><mi>G</mi><mn>00</mn></msub></mrow></semantics></math></inline-formula> as the probe beam. This scheme is more practical and robust to losses, which has potential applications in areas such as laser interferometer gravitational-wave observatories and high-sensitivity atomic force microscopes.https://www.mdpi.com/2304-6732/10/5/584high-order Hermite–Gaussian modetilt measurementquantum Cramer–Rao boundhomodyne detection |
| spellingShingle | Zhi Li Yijian Wang Hengxin Sun Kui Liu Jiangrui Gao Tilt Measurement at the Quantum Cramer–Rao Bound Using a Higher-Order Hermite–Gaussian Mode Photonics high-order Hermite–Gaussian mode tilt measurement quantum Cramer–Rao bound homodyne detection |
| title | Tilt Measurement at the Quantum Cramer–Rao Bound Using a Higher-Order Hermite–Gaussian Mode |
| title_full | Tilt Measurement at the Quantum Cramer–Rao Bound Using a Higher-Order Hermite–Gaussian Mode |
| title_fullStr | Tilt Measurement at the Quantum Cramer–Rao Bound Using a Higher-Order Hermite–Gaussian Mode |
| title_full_unstemmed | Tilt Measurement at the Quantum Cramer–Rao Bound Using a Higher-Order Hermite–Gaussian Mode |
| title_short | Tilt Measurement at the Quantum Cramer–Rao Bound Using a Higher-Order Hermite–Gaussian Mode |
| title_sort | tilt measurement at the quantum cramer rao bound using a higher order hermite gaussian mode |
| topic | high-order Hermite–Gaussian mode tilt measurement quantum Cramer–Rao bound homodyne detection |
| url | https://www.mdpi.com/2304-6732/10/5/584 |
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