Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Applied

Precision enhancement in quantum spatial measurement by squeezing-assisted weak-value amplification

ChaoXia Zhang, Yongchao Chen, Gang Chen, Hengxin Sun, Jing Zhang, Kui Liu, Rongguo Yang, Jiangrui Gao

Published Nov 25, 2024• 5 citations
Publisher

Abstract

Precision enhancement is demonstrated in an optical spatial measurement based on a weak-value amplification (WVA) system and splitlike detection, by injecting a ${\mathrm{TEM}}_{10}$ squeezed vacuum beam. We have experimentally realized high-precision optical spatial measurement beyond the shot-noise limit by using squeezing-assisted WVA. Based on the WVA technique, which can amplify the signal by increasing the number of photons that are injected into the interferometer, squeezed-beam injection can reduce the noise level and can further improve the signal-to-noise ratio (SNR). As a result, an SNR improvement of 2 dB, i.e., 1.3 times precision enhancement, can be achieved, and the obtained displacement and tilt sensitivity are $4.96\phantom{\rule{0.2em}{0ex}}\mathrm{fm}/\sqrt{\text{Hz}}$ and $0.39\phantom{\rule{0.2em}{0ex}}\mathrm{prad}/\sqrt{\text{Hz}}$, respectively, by using a 2-dB squeezed-beam injection and 2.6% postselection probability in the WVA process. Our work provides an effective method to accomplish higher precision in quantum spatial measurement, which has potential applications in gravitational wave interferometer calibration, super-resolution quantum imaging, etc.

DOI
10.1103/physrevapplied.22.054068

Related papers

Precision Enhancement in Spatial Measurement by Introducing Squeezed Light into Weak Value Amplification

Zhang, Chaoxia, Yongchao Chen, Chen, Gang +5 more

The precision enhancement is demonstrated in an optical spatial measurement based on weak value amplification (WVA) system and split-like detection, by injecting a TEM$_{10}$ squeezed vacuum beam. It is the first time to experimentally realize high-precision optical spatial measurement beyond the shot noise limit by using squeezing-assisted WVA. Based on the WVA technique, which can amplify the signal by increasing the number of photons that injected into the interferometer, squeezed beam injection can reduce the noise level and can further improve the signal-to-noise ratio(SNR). As a result, a SNR improvement of 2dB, i.e., 1.3 time precision enhancement, can be achieved, by using a 2dB squeezed beam injection and 2.6\% postselection probability in WVA process. Our work provides an effective method to accomplish higher precision in quantum spatial measurement, which has potential applications in gravitational wave interferometer calibration, super-resolution quantum imaging, etc.

arXiv:2311.16622•Nov 28, 2023•0 citations

Higher‐Order Spatially Squeezed Beam for Enhanced Spatial Measurements

Li Zhi, Hui Guo, Hongbo Liu +5 more

Abstract A scheme is proposed to realize high‐precision spatial measurement of laser beams beyond quantum limit using a novel quantum state called the order spatially squeezed state, which is the combination of a bright mode coherent state and squeezed vacuum mode state. An effective technique for the generation of a rectangular shape higher‐order mode squeezed light with a maximum mode order of 5 is experimentally demonstrated using a doubling resonated optical parametric amplifier. Furthermore, the fourth order tilt‐ and displacement‐squeezed beams are constructed and used to perform spatial tilt and displacement measurements, thereby improving the signal‐to‐noise ratio by 10 and 8.6 dB compared to the mode. The results indicate that high‐order spatially squeezed states enhance measurement precision beyond the shot noise limit and are more prominent in back‐action noise reduction. High‐precision spatial measurement has potential practical applications in high‐sensitivity atomic force microscope and super‐resolution quantum imaging.

Advanced Quantum Technologies•Sep 6, 2022•18 citations

Enhancement of the phase-measurement sensitivity beyond the standard quantum limit by a nonlinear interferometer

Z. Y. Ou

A nonlinear interferometer uses nonlinear elements as beam splitters to split and to recombine optical waves for interference. As a result, the interference fringe size has a nonlinear dependence on the intensity of the field for phase sensing and leads to an enhanced phase signal. In this paper, a practical scheme of nonlinear interferometry for precision phase measurement is analyzed with parametric amplifiers as the nonlinear beam splitters. It is found that the signal due to phase shift is enhanced by a factor of the amplification gain as compared to a linear interferometer with the same phase-sensing light intensity while the quantum noise is kept at the vacuum level, thus, effectively increasing the signal-to-noise ratio (SNR) beyond the standard quantum limit. Furthermore, the scheme is not as sensitive to the detection loss as the linear scheme with a squeezed state for noise reduction. However, losses inside the interferometer limit the enhancement factor in SNR. We apply the concept to a Michelson interferometer but with parametric amplifiers involved for gravitational-wave detection. We find that effective power is increased by the gain of the amplifiers without actually increasing the cycling power inside the interferometer. Furthermore, the full benefits with squeezed input and variational output or the combination of a quantum nondemolition interferometer for sensitivity beyond the standard quantum limit apply here with even better results. Such a nonlinear interferometer will find wide applications in precision measurements.

Physical Review A•Feb 14, 2012•195 citations

Approaching Quantum-Limited Metrology with Imperfect Detectors by Using Weak-Value Amplification

Liang Xu, Zexuan Liu, Animesh Datta +4 more

Weak-value amplification (WVA) is a metrological protocol that amplifies ultrasmall physical effects. However, the amplified outcomes necessarily occur with highly suppressed probabilities, leading to the extensive debate on whether the overall measurement precision is improved in comparison to that of conventional measurement (CM). Here, we experimentally demonstrate the unambiguous advantages of WVA that overcome practical limitations including noise and saturation of photodetection and maintain a shot-noise-scaling precision for a large range of input light intensity well beyond the dynamic range of the photodetector. The precision achieved by WVA is 6 times higher than that of CM in our setup. Our results clear the way for the widespread use of WVA in applications involving the measurement of small signals including precision metrology and commercial sensors.

arXiv:2005.03629•Physical Review Letters•Aug 17, 2020•97 citations

Mechanism of suppressing noise intensity of squeezed state enhancement

Ruotao ZHANG, Wenhui Zhang

This research focuses on advanced noise suppression technologies for high-precision measurement systems, particularly addressing the limitations of classical noise reducing approaches. The noise level of laser sources is a crucial factor that directly affects the measurement sensitivity in applications such as gravitational wave detection and biomedical imaging. Classical feedback control technologies are effective but often encounter a bottleneck resulting from the classical noise suppression limits. To cope with these challenges, a novel method integrating quantum squeezed light with classical feedback control systems to reduce intensity noise is proposed in this work. By employing an amplitude-squeezed light field, a quantum-enhanced feedback control model is developed, thereby theoretically examining the influence of both the feedback loop gain and the degree of squeezing on the noise suppression performance. The results show that the injection of squeezed light significantly reduces the intensity noise, approaching the shot noise limit (SNL), thereby improving the system sensitivity beyond the classical noise reduction boundaries. Specifically, –10 dB squeezed state injection into the feedback system yields an additional noise suppression of approximately 8.97 dB, exceeding what is achievable using classical feedback alone. This demonstrates that the potential of the proposed method can enhance measurement precision close to the quantum noise limits without increasing the laser power. The analysis highlights the asymmetric noise suppression effects between the inner feedback loop and outer feedback loop. Although the outer loop benefits significantly from the squeezed light injection and achieves noise levels that are unattainable by classical feedback methods, the inner loop shows relatively minor improvements. This asymmetry is attributed to the inherent characteristics of quantum squeezing and the limitations of the feedback loop design. Further investigation into the individual noise components reveals that the primary contributors to the intensity noise include input noise, photodetector noise, and beam splitter-induced vacuum fluctuations. The injection of squeezed light effectively mitigates these vacuum fluctuations, which are typically a major noise source in high-precision laser systems. Theoretical research results show that the use of squeezed light in feedback control systems can effectively enhance noise suppression, equivalent to a nine fold increase in detected optical power, without the physical drawbacks of increasing laser power such as thermal noise. In conclusion, this study provides a theoretical validation of combining quantum squeezed states with classical feedback control to exceed classical noise suppression limits. The integration of a –10 dB squeezed state demonstrates a significant noise reduction, showing that this hybrid approach could revolutionize noise management in precision measurement applications. The results pave the way for further exploring quantum-enhanced control technologies in fields such as gravitational wave detection, quantum communication, and advanced optical sensing, providing a pathway for improving sensitivity and noise suppression without increasing additional power requirements.

Acta Physica Sinica•Jan 1, 2025•1 citation

Precision measurement beyond the shot-noise limit

Min Xiao, Ling-An Wu, H. J. Kimble

Improvements in precision beyond the limit set by the vacuum state or zero-point fluctuations of the field are reported for two optical experiments. Both experiments employ the squeezed light from an optical parametric oscillator to reduce the level of fluctuations in one of two quadrature phase amplitudes below the shot-noise level (SNL). The first experiment follows the work of Caves1 on precision interferometry with squeezed states. An increase in signal-to-noise of 2.5 dB relative to the SNL is demonstrated for the detection of phase modulation in a Mach-Zehnder interferometer. In the second experiment amplitude modulation is encoded on a weak signal beam with an acoustooptic modulator. For the case of a squeezed signal beam compared with a beam in a coherent state, an improvement in sensitivity of 2.5 dB is achieved for the detection of amplitude changes of the field. The observed increases in sensitivity in both experiments are currently limited by simple linear losses in propagation and detection and not by the degree of available squeezing.

Annual Meeting Optical Society of America•Jan 1, 1987•3 citations
Precision enhancement is demonstrated in an optical spatial measurement based on a weak-value amplification (WVA) system and splitlike detection, by injecting a TEM10{\mathrm{TEM}}_{10}TEM10​ squeezed vacuum beam. We have experimentally realized high-precision optical spatial measurement beyond the shot-noise limit by using squeezing-assisted WVA. Based on the WVA technique, which can amplify the signal by increasing the number of photons that are injected into the interferometer, squeezed-beam injection can reduce the noise level and can further improve the signal-to-noise ratio (SNR). As a result, an SNR improvement of 2 dB, i.e., 1.3 times precision enhancement, can be achieved, and the obtained displacement and tilt sensitivity are 4.96fm/Hz4.96\phantom{\rule{0.2em}{0ex}}\mathrm{fm}/\sqrt{\text{Hz}}4.96fm/Hz​ and 0.39prad/Hz0.39\phantom{\rule{0.2em}{0ex}}\mathrm{prad}/\sqrt{\text{Hz}}0.39prad/Hz​, respectively, by using a 2-dB squeezed-beam injection and 2.6% postselection probability in the WVA process. Our work provides an effective method to accomplish higher precision in quantum spatial measurement, which has potential applications in gravitational wave interferometer calibration, super-resolution quantum imaging, etc.
The precision enhancement is demonstrated in an optical spatial measurement based on weak value amplification (WVA) system and split-like detection, by injecting a TEM10_{10}10​ squeezed vacuum beam. It is the first time to experimentally realize high-precision optical spatial measurement beyond the shot noise limit by using squeezing-assisted WVA. Based on the WVA technique, which can amplify the signal by increasing the number of photons that injected into the interferometer, squeezed beam injection can reduce the noise level and can further improve the signal-to-noise ratio(SNR). As a result, a SNR improvement of 2dB, i.e., 1.3 time precision enhancement, can be achieved, by using a 2dB squeezed beam injection and 2.6\% postselection probability in WVA process. Our work provides an effective method to accomplish higher precision in quantum spatial measurement, which has potential applications in gravitational wave interferometer calibration, super-resolution quantum imaging, etc.
Abstract A scheme is proposed to realize high‐precision spatial measurement of laser beams beyond quantum limit using a novel quantum state called the order spatially squeezed state, which is the combination of a bright mode coherent state and squeezed vacuum mode state. An effective technique for the generation of a rectangular shape higher‐order mode squeezed light with a maximum mode order of 5 is experimentally demonstrated using a doubling resonated optical parametric amplifier. Furthermore, the fourth order tilt‐ and displacement‐squeezed beams are constructed and used to perform spatial tilt and displacement measurements, thereby improving the signal‐to‐noise ratio by 10 and 8.6 dB compared to the mode. The results indicate that high‐order spatially squeezed states enhance measurement precision beyond the shot noise limit and are more prominent in back‐action noise reduction. High‐precision spatial measurement has potential practical applications in high‐sensitivity atomic force microscope and super‐resolution quantum imaging.
A nonlinear interferometer uses nonlinear elements as beam splitters to split and to recombine optical waves for interference. As a result, the interference fringe size has a nonlinear dependence on the intensity of the field for phase sensing and leads to an enhanced phase signal. In this paper, a practical scheme of nonlinear interferometry for precision phase measurement is analyzed with parametric amplifiers as the nonlinear beam splitters. It is found that the signal due to phase shift is enhanced by a factor of the amplification gain as compared to a linear interferometer with the same phase-sensing light intensity while the quantum noise is kept at the vacuum level, thus, effectively increasing the signal-to-noise ratio (SNR) beyond the standard quantum limit. Furthermore, the scheme is not as sensitive to the detection loss as the linear scheme with a squeezed state for noise reduction. However, losses inside the interferometer limit the enhancement factor in SNR. We apply the concept to a Michelson interferometer but with parametric amplifiers involved for gravitational-wave detection. We find that effective power is increased by the gain of the amplifiers without actually increasing the cycling power inside the interferometer. Furthermore, the full benefits with squeezed input and variational output or the combination of a quantum nondemolition interferometer for sensitivity beyond the standard quantum limit apply here with even better results. Such a nonlinear interferometer will find wide applications in precision measurements.
Weak-value amplification (WVA) is a metrological protocol that amplifies ultrasmall physical effects. However, the amplified outcomes necessarily occur with highly suppressed probabilities, leading to the extensive debate on whether the overall measurement precision is improved in comparison to that of conventional measurement (CM). Here, we experimentally demonstrate the unambiguous advantages of WVA that overcome practical limitations including noise and saturation of photodetection and maintain a shot-noise-scaling precision for a large range of input light intensity well beyond the dynamic range of the photodetector. The precision achieved by WVA is 6 times higher than that of CM in our setup. Our results clear the way for the widespread use of WVA in applications involving the measurement of small signals including precision metrology and commercial sensors.
This research focuses on advanced noise suppression technologies for high-precision measurement systems, particularly addressing the limitations of classical noise reducing approaches. The noise level of laser sources is a crucial factor that directly affects the measurement sensitivity in applications such as gravitational wave detection and biomedical imaging. Classical feedback control technologies are effective but often encounter a bottleneck resulting from the classical noise suppression limits. To cope with these challenges, a novel method integrating quantum squeezed light with classical feedback control systems to reduce intensity noise is proposed in this work. By employing an amplitude-squeezed light field, a quantum-enhanced feedback control model is developed, thereby theoretically examining the influence of both the feedback loop gain and the degree of squeezing on the noise suppression performance. The results show that the injection of squeezed light significantly reduces the intensity noise, approaching the shot noise limit (SNL), thereby improving the system sensitivity beyond the classical noise reduction boundaries. Specifically, –10 dB squeezed state injection into the feedback system yields an additional noise suppression of approximately 8.97 dB, exceeding what is achievable using classical feedback alone. This demonstrates that the potential of the proposed method can enhance measurement precision close to the quantum noise limits without increasing the laser power. The analysis highlights the asymmetric noise suppression effects between the inner feedback loop and outer feedback loop. Although the outer loop benefits significantly from the squeezed light injection and achieves noise levels that are unattainable by classical feedback methods, the inner loop shows relatively minor improvements. This asymmetry is attributed to the inherent characteristics of quantum squeezing and the limitations of the feedback loop design. Further investigation into the individual noise components reveals that the primary contributors to the intensity noise include input noise, photodetector noise, and beam splitter-induced vacuum fluctuations. The injection of squeezed light effectively mitigates these vacuum fluctuations, which are typically a major noise source in high-precision laser systems. Theoretical research results show that the use of squeezed light in feedback control systems can effectively enhance noise suppression, equivalent to a nine fold increase in detected optical power, without the physical drawbacks of increasing laser power such as thermal noise. In conclusion, this study provides a theoretical validation of combining quantum squeezed states with classical feedback control to exceed classical noise suppression limits. The integration of a –10 dB squeezed state demonstrates a significant noise reduction, showing that this hybrid approach could revolutionize noise management in precision measurement applications. The results pave the way for further exploring quantum-enhanced control technologies in fields such as gravitational wave detection, quantum communication, and advanced optical sensing, providing a pathway for improving sensitivity and noise suppression without increasing additional power requirements.
Improvements in precision beyond the limit set by the vacuum state or zero-point fluctuations of the field are reported for two optical experiments. Both experiments employ the squeezed light from an optical parametric oscillator to reduce the level of fluctuations in one of two quadrature phase amplitudes below the shot-noise level (SNL). The first experiment follows the work of Caves1 on precision interferometry with squeezed states. An increase in signal-to-noise of 2.5 dB relative to the SNL is demonstrated for the detection of phase modulation in a Mach-Zehnder interferometer. In the second experiment amplitude modulation is encoded on a weak signal beam with an acoustooptic modulator. For the case of a squeezed signal beam compared with a beam in a coherent state, an improvement in sensitivity of 2.5 dB is achieved for the detection of amplitude changes of the field. The observed increases in sensitivity in both experiments are currently limited by simple linear losses in propagation and detection and not by the degree of available squeezing.