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 A

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

Z. Y. Ou

Published Feb 14, 2012• 195 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.85.023815

Related papers

Quantum metrology with parametric amplifier-based photon correlation interferometers

Florian Hudelist, Jia Kong, Cunjin Liu +3 more

Conventional interferometers usually utilize beam splitters for wave splitting and recombination. These interferometers are widely used for precision measurement. Their sensitivity for phase measurement is limited by the shot noise, which can be suppressed with squeezed states of light. Here we study a new type of interferometer in which the beam splitting and recombination elements are parametric amplifiers. We observe an improvement of 4.1±0.3 dB in signal-to-noise ratio compared with a conventional interferometer under the same operating condition, which is a 1.6-fold enhancement in rms phase measurement sensitivity beyond the shot noise limit. The improvement is due to signal enhancement. Combined with the squeezed state technique for shot noise suppression, this interferometer promises further improvement in sensitivity. Furthermore, because nonlinear processes are involved in this interferometer, we can couple a variety of different waves and form new types of hybrid interferometers, opening a door for many applications in metrology. Interferometers play a key role in precision measurements and metrology. Here, the authors demonstrate a new type of interferometer that replaces the standard beam splitter elements with parametric amplifiers, which provides enhanced performance compared with a Mach–Zehnder interferometer.

Nature Communications•Jan 29, 2014•438 citations

High sensitivity quantum Michelson interferometer

Zuo Xiao-Jie, Sun Ying-Rong, Yan Zhi-Hui +1 more

Michelson interferometer can be applied to not only the building block of the fundamental research of physics, but also the precise measurement, such as the direct observation of gravity wave signal. Therefore, high performance Michelson interferometer is the key step towards the implementation of direct observation of weak gravity wave signal. Recently, the vacuum noise was reduced by injecting squeezed vacuum into the unused port of Michelson interferomter, and the phase signal optical field in Mach-Zender interferometer is amplified based on the four-wave mixing in hot Rubidium atom. Here we study high sensitivity quantum Michelson interferometer. In the Michelson interferometer, the linear optical beam splitter is replaced by a non-degenerated optical parametric amplifier to realize the splitting and combining of optical fields, and the squeezed vacuum is also injected into the unused port of interferomter, so that the high signal-to-noise ratio and high sensitivity of phase measurement can be realized. Due to the inevitable optical losses, the losses inside and outside the Michelson interferometer are considered in our theoretical model. We investigate the influences of the losses inside and outside the Michelson interferometer on the sensitivity of phase measurement. By theoretical calculation, we analyze the dependence of sensitivity of phase measurement on system parameters, such as intensity of optical fields for phase sensing, gain factor of non-degenerated optical parametric amplifier, the losses inside and outside the Michelson interferometer, and the squeezing parameter of input squeezed vacuum, and thus the condition of high sensitivity nonlinear Michelson interferometer can be obtained. In a broad system parametric range, the quantum Michaleson interferometer can surpass standard quantum limit, and the nonlinear Michaleson interferometer with squeezed state injection can provide the optimal sensitivity for phase measurement. The nonlinear Michelson interferometer with squeezed state is suitable for weak signal measurement. While the gain factor of non-degenerated optical parametric amplifier is large enough, the nonlinear Michelson interferometer without injecting the squeezed vacuum can still reach the optimal sensitivity, which reduces the use of quantum resources. When the phase sensing optical field is strong, the linear Michelson interferometer with injecting the squeezed vacuum can also reach the optimal sensitivity, and the sensitivity is robust for both losses inside and outside the interferometer. All the kinds of interferometers are more sensitive to the loss inside the interferometer than outside the interferometer, and the sensitivity of phase measurement can be improved by reducing the loss inside the interferometer. Our result provides direct reference of experimental implementation of high performance interferometer for high precision quantum metrology.

Acta Physica Sinica•Jan 1, 2018•3 citations

High-Sensitivity Quantum-Enhanced Interferometers

Juan Li Yu, Yinhua Wu, Liang Nie +1 more

High-sensitivity interferometers are one of the basic tools for precision measurement, and their sensitivity is limited by their shot noise limit (SNL), which is determined by vacuum fluctuations of the probe field. The quantum interferometer with novel structures can break the SNL and measure the weak signals, such as the direct observation of gravity wave signal. Combining classical interferometers and the optical parametric amplifier (OPA) can enhance the signal; meanwhile, the quantum noise is kept at the vacuum level, so that the sensitivity of the nonlinear interferometer beyond the SNL can be achieved. By analyzing in detail the influence of system parameters on the precision of quantum metrology, including the intensity of optical fields for phase sensing, the gain factor of OPA, and the losses inside and outside the interferometers, the application conditions of high-sensitivity nonlinear quantum interferometers are obtained. Quantum interferometer-based OPAs provide the direct references for the practical development of quantum precise measurement.

Photonics•Jun 29, 2023•2 citations

Phase-measurement sensitivity beyond the standard quantum limit in an interferometer consisting of a parametric amplifier and a beam splitter

Jia Kong, Z. Y. Ou, Weiping Zhang

We analyze a nonconventional interferometer that is formed with a parametric amplifier and a beam splitter for beam splitting and recombination. Because the outputs from a parametric amplifier are entangled and their quantum noise is correlated, the employment of the beam splitter will superimpose the two quantum fields and the destructive interference will lead to the subtraction of the quantum noise and to noise reduction in the output of the interferometer and hence an improvement of the signal-to-noise ratio (SNR) beyond the standard quantum limit or the shot noise limit. Furthermore, the injection of a squeezed state into the idler port of the parametric amplifier will lead to further improvement of the SNR. We will discuss the possibility of reaching the Heisenberg limit in such an interferometer. We find that the injection of a coherent state will degrade the performance in reaching the Heisenberg limit, whereas a squeezed state injection can improve it by a factor of 2 at best.

Physical Review A•Feb 20, 2013•44 citations

Realization of a nonlinear interferometer with parametric amplifiers

Jietai Jing, Cunjin Liu, Zhifan Zhou +2 more

We construct an interferometer with parametric amplifiers as beam splitters. Because of the gain in the parametric amplifiers, the maximum output intensity of the interferometer can be much bigger than the input intensity as well as the intensity inside the interferometer (the phase sensing intensity). We find that the fringe intensity depends quadratically on the intensity of the phase sensing field at high gain. This type of nonlinear interferometer has better sensitivity than the traditional linear interferometer made of beam splitters with the same phase sensing intensity.

Applied Physics Letters•Jul 4, 2011•197 citations

Quantum Interferometer Combining Squeezing and Parametric Amplification

Xiaojie Zuo, Zhihui Yan, Yanni Feng +4 more

High precision interferometers are the building blocks of precision metrology and the ultimate interferometric sensitivity is limited by the quantum noise. Here, we propose and experimentally demonstrate a compact quantum interferometer involving two optical parametric amplifiers and the squeezed states generated within the interferometer are directly used for the phase-sensing quantum state. By both squeezing shot noise and amplifying phase-sensing intensity the sensitivity improvement of 4.86±0.24 dB beyond the standard quantum limit is deterministically realized and a minimum detectable phase smaller than that of all present interferometers under the same phase-sensing intensity is achieved. This interferometric system has significantly potential applications in a variety of measurements for tiny variances of physical quantities.

arXiv:2005.01911•Physical Review Letters•May 1, 2020•78 citations
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.
Conventional interferometers usually utilize beam splitters for wave splitting and recombination. These interferometers are widely used for precision measurement. Their sensitivity for phase measurement is limited by the shot noise, which can be suppressed with squeezed states of light. Here we study a new type of interferometer in which the beam splitting and recombination elements are parametric amplifiers. We observe an improvement of 4.1±0.3 dB in signal-to-noise ratio compared with a conventional interferometer under the same operating condition, which is a 1.6-fold enhancement in rms phase measurement sensitivity beyond the shot noise limit. The improvement is due to signal enhancement. Combined with the squeezed state technique for shot noise suppression, this interferometer promises further improvement in sensitivity. Furthermore, because nonlinear processes are involved in this interferometer, we can couple a variety of different waves and form new types of hybrid interferometers, opening a door for many applications in metrology. Interferometers play a key role in precision measurements and metrology. Here, the authors demonstrate a new type of interferometer that replaces the standard beam splitter elements with parametric amplifiers, which provides enhanced performance compared with a Mach–Zehnder interferometer.
Michelson interferometer can be applied to not only the building block of the fundamental research of physics, but also the precise measurement, such as the direct observation of gravity wave signal. Therefore, high performance Michelson interferometer is the key step towards the implementation of direct observation of weak gravity wave signal. Recently, the vacuum noise was reduced by injecting squeezed vacuum into the unused port of Michelson interferomter, and the phase signal optical field in Mach-Zender interferometer is amplified based on the four-wave mixing in hot Rubidium atom. Here we study high sensitivity quantum Michelson interferometer. In the Michelson interferometer, the linear optical beam splitter is replaced by a non-degenerated optical parametric amplifier to realize the splitting and combining of optical fields, and the squeezed vacuum is also injected into the unused port of interferomter, so that the high signal-to-noise ratio and high sensitivity of phase measurement can be realized. Due to the inevitable optical losses, the losses inside and outside the Michelson interferometer are considered in our theoretical model. We investigate the influences of the losses inside and outside the Michelson interferometer on the sensitivity of phase measurement. By theoretical calculation, we analyze the dependence of sensitivity of phase measurement on system parameters, such as intensity of optical fields for phase sensing, gain factor of non-degenerated optical parametric amplifier, the losses inside and outside the Michelson interferometer, and the squeezing parameter of input squeezed vacuum, and thus the condition of high sensitivity nonlinear Michelson interferometer can be obtained. In a broad system parametric range, the quantum Michaleson interferometer can surpass standard quantum limit, and the nonlinear Michaleson interferometer with squeezed state injection can provide the optimal sensitivity for phase measurement. The nonlinear Michelson interferometer with squeezed state is suitable for weak signal measurement. While the gain factor of non-degenerated optical parametric amplifier is large enough, the nonlinear Michelson interferometer without injecting the squeezed vacuum can still reach the optimal sensitivity, which reduces the use of quantum resources. When the phase sensing optical field is strong, the linear Michelson interferometer with injecting the squeezed vacuum can also reach the optimal sensitivity, and the sensitivity is robust for both losses inside and outside the interferometer. All the kinds of interferometers are more sensitive to the loss inside the interferometer than outside the interferometer, and the sensitivity of phase measurement can be improved by reducing the loss inside the interferometer. Our result provides direct reference of experimental implementation of high performance interferometer for high precision quantum metrology.
High-sensitivity interferometers are one of the basic tools for precision measurement, and their sensitivity is limited by their shot noise limit (SNL), which is determined by vacuum fluctuations of the probe field. The quantum interferometer with novel structures can break the SNL and measure the weak signals, such as the direct observation of gravity wave signal. Combining classical interferometers and the optical parametric amplifier (OPA) can enhance the signal; meanwhile, the quantum noise is kept at the vacuum level, so that the sensitivity of the nonlinear interferometer beyond the SNL can be achieved. By analyzing in detail the influence of system parameters on the precision of quantum metrology, including the intensity of optical fields for phase sensing, the gain factor of OPA, and the losses inside and outside the interferometers, the application conditions of high-sensitivity nonlinear quantum interferometers are obtained. Quantum interferometer-based OPAs provide the direct references for the practical development of quantum precise measurement.
We analyze a nonconventional interferometer that is formed with a parametric amplifier and a beam splitter for beam splitting and recombination. Because the outputs from a parametric amplifier are entangled and their quantum noise is correlated, the employment of the beam splitter will superimpose the two quantum fields and the destructive interference will lead to the subtraction of the quantum noise and to noise reduction in the output of the interferometer and hence an improvement of the signal-to-noise ratio (SNR) beyond the standard quantum limit or the shot noise limit. Furthermore, the injection of a squeezed state into the idler port of the parametric amplifier will lead to further improvement of the SNR. We will discuss the possibility of reaching the Heisenberg limit in such an interferometer. We find that the injection of a coherent state will degrade the performance in reaching the Heisenberg limit, whereas a squeezed state injection can improve it by a factor of 2 at best.
We construct an interferometer with parametric amplifiers as beam splitters. Because of the gain in the parametric amplifiers, the maximum output intensity of the interferometer can be much bigger than the input intensity as well as the intensity inside the interferometer (the phase sensing intensity). We find that the fringe intensity depends quadratically on the intensity of the phase sensing field at high gain. This type of nonlinear interferometer has better sensitivity than the traditional linear interferometer made of beam splitters with the same phase sensing intensity.
High precision interferometers are the building blocks of precision metrology and the ultimate interferometric sensitivity is limited by the quantum noise. Here, we propose and experimentally demonstrate a compact quantum interferometer involving two optical parametric amplifiers and the squeezed states generated within the interferometer are directly used for the phase-sensing quantum state. By both squeezing shot noise and amplifying phase-sensing intensity the sensitivity improvement of 4.86±0.24 dB beyond the standard quantum limit is deterministically realized and a minimum detectable phase smaller than that of all present interferometers under the same phase-sensing intensity is achieved. This interferometric system has significantly potential applications in a variety of measurements for tiny variances of physical quantities.