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

arXiv:2004.14266 · Physical Review Letters

SU(2)-in-SU(1,1) Nested Interferometer for High Sensitivity, Loss-Tolerant Quantum Metrology

Wei Du, Jia Kong, Guzhi Bao, Peiyu Yang, Jun Jia, Sheng Ming, Chun-Hua Yuan, J. F. Chen, Z. Y. Ou, Morgan W. Mitchell, Weiping Zhang

Published Jan 20, 2022• 52 citations
arXivHTMLPDF

Abstract

We present experimental and theoretical results on a new interferometer topology that nests a SU(2) interferometer, e.g., a Mach-Zehnder or Michelson interferometer, inside a SU(1,1) interferometer, i.e., a Mach-Zehnder interferometer with parametric amplifiers in place of beam splitters. This SU(2)-in-SU(1,1) nested interferometer (SISNI) simultaneously achieves a high signal-to-noise ratio (SNR), sensitivity beyond the standard quantum limit (SQL) and tolerance to photon losses external to the interferometer, e.g., in detectors. We implement a SISNI using parametric amplification by four-wave mixing (FWM) in Rb vapor and a laser-fed Mach-Zehnder SU(2) interferometer. We observe path-length sensitivity with SNR 2.2 dB beyond the SQL at power levels (and thus SNR) 2 orders of magnitude beyond those of previous loss-tolerant interferometers. We find experimentally the optimal FWM gains and find agreement with a minimal quantum noise model for the FWM process. The results suggest ways to boost the in-practice sensitivity of high-power interferometers, e.g., gravitational wave interferometers, and may enable high-sensitivity, quantum-enhanced interferometry at wavelengths for which efficient detectors are not available.

DOI
10.1103/physrevlett.128.033601

Related papers

SU(2)-in-SU(1,1) nested interferometer

Wei Du, Jia Kong, Jun Fang Jia +6 more

The use of squeezing and entanglement allows advanced interferometers to detect signals that would otherwise be buried in quantum mechanical noise. High sensitivity instruments including magnetometers and gravitational wave detectors have shown enhanced signal-to-noise ratio (SNR) by injecting single-mode squeezed light into SU(2) interferometers, e.g. the Mach-Zehnder or Michelson topologies. The quantum enhancement in this approach is sensitive to losses, which break the fragile quantum correlations in the squeezed state. In contrast, SU(1,1) interferometers achieve quantum enhancement by noiseless amplification; they noiselessly increase the signal rather than reducing the quantum noise. Prior work on SU(1,1) interferometers has shown quantum-enhanced SNR11 and insensitivity to losses but to date has been limited to low powers and thus low SNR. Here we introduce a new interferometer topology, the SU(2)-in-SU(1,1) nested interferometer, that combines quantum enhancement, the high SNR possible with a SU(2) interferometer, and the loss tolerance of the SU(1,1) approach. We implement this interferometer using four-wave mixing in a hot atomic vapor and demonstrate 2:2(5) dB of quantum SNR enhancement, in a system with a phase variance nearly two orders of magnitude below that of any previous loss-tolerant enhancement scheme. The new interferometer enables new possibilities such as beyond-shot-noise sensing with wavelengths for which efficient detectors are not available.

•Apr 30, 2020•2 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

SU(1,1) interferometry via four-wave mixing in Rb

Travis Horrom, Brian E. Anderson, Prasoon Gupta +1 more

Quantum-enhanced precision measurements have emerged as one of the most useful applications of quantum optics. Exploiting quantum states of light and quantum processes, classical measurement limits can be surpassed, leading to improvements in areas including clocks, spectroscopy, magnetometry, and imaging. One measurement where straightforward quantum enhancements are possible is phase sensing with an interferometer. One can inject squeezed vacuum states into the dark port of the beamsplitter in a traditional interferometer to reduce the quantum noise and reach phase sensitivities beyond the shot noise limit. An alternate approach is to replace the beamsplitters of an interferometer with nonlinear parametric amplifiers, which produce nonclassical states of light that can be used to surpass classical performance. This so called SU(1,1) interferometer can theoretically approach sensitivities that scale as 1/n, the Heisenberg limit where n is the interior phase sensing photon number, compared to the shot noise limit of 1/ √ n for a traditional interferometer [1]. I will present our group’s experimental progress in testing a Mach-Zender SU(1,1) interferometer using four-wave mixers (4WMs) in hot Rb atoms as the parametric beamsplitters. The 4WM process generates entangled twin beams which serve as the two arms of the interferometer, and are then recombined in a second 4WM cell, resulting in a phase-sensitive output. We will extend the work done on this interferometer [2, 3] by performing a detailed analysis of the output signal to noise through homodyne measurements, and will attempt to observe the better-than-shot-noise scaling of the sensitivity. We will also consider the various difficulties of this optical interferometer such as the susceptibility to loss and imperfect mode-matching within the interferometer. Our group is also considering an analogous SU(1,1) interferometer in a cold atom system. Collisions in a spinor Bose-Einstein condensate of sodium atoms give rise to a 4WM process that produces spin states of the atoms which are entangled in atom number. These interactions can be controlled to set up an SU(1,1) atom interferometer, where the relevant measurements are now atomic population differences rather than photon intensities. These enhancements can lead to drastic improvements in atomic spin interferometry [3, 4].

•Jan 1, 2015•3 citations

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

Quantum dense metrology by an SU(2)-in-SU(1,1) nested interferometer

Wei Du, J. F. Chen, Z. Y. Ou +1 more

With the help of quantum entanglement, quantum dense metrology (QDM) is a technique that can make joint estimates of two conjugate quantities such as phase and amplitude modulations of an optical field, with an accuracy beating the standard quantum limit simultaneously. SU(1,1) interferometers (SUIs) can realize QDM with detection loss tolerance but is limited in absolute sensitivity. Here, we present a QDM scheme with a linear or SU(2) interferometer nested inside an SUI. By using a degenerate SUI and controlling the phase angle of the phase-sensitive amplifiers in the SUI, we can achieve the optimum quantum enhancement in the measurement precision of an arbitrary mixture of phase and amplitude modulation.

arXiv:2002.02195•Applied Physics Letters•Jul 13, 2020•22 citations

Sensitivity Evaluation of SU(1,1) Interferometers with Arbitrary Input Probe State and Homodyne Detections

Sonu Jana, Dhruv Baheti, Paul Grossiord +3 more

We provide a general theoretical derivation of the phase sensitivity achieved by SU(1,1) interferometers under homodyne detection. The general expressions obtained accommodate arbitrary input states and include internal and external losses. In this systematic review, both full SU(1,1) interferometers with two parametric amplifiers and the truncated interferometers with only one parametric amplifier are examined. We investigate scenarios involving both single-output ports and joint homodyne detection, and consider parametric amplifiers with equal gains or with a boosted gain second amplifier. Our analytical formulation provides physical insight and understanding of the improvements in the sensitivity, which are shown to originate from noise reduction and/or signal amplification, depending on the configurations and practical implementations. Surprisingly, the configuration with single-output mode detection and parametric amplifiers with equal gains exhibits the highest robustness to very high internal losses. We finally apply this framework to a ubiquitous $|α,0\rangle$ input two-mode coherent probe state. This approach permits the comparison of different strategies and the optimization of the interferometer performance in the presence of losses. In particular, we determine which amplification and detection configurations provide the best performance, depending on the level of losses. This exemplifies how this general analytical approach provides a powerful tool to design quantum-enhanced interferometers and achieve optimal sensitivity with selected probe states and homodyne detection.

quant-pharXiv:2605.22029•May 22, 2026•0 citations
We present experimental and theoretical results on a new interferometer topology that nests a SU(2) interferometer, e.g., a Mach-Zehnder or Michelson interferometer, inside a SU(1,1) interferometer, i.e., a Mach-Zehnder interferometer with parametric amplifiers in place of beam splitters. This SU(2)-in-SU(1,1) nested interferometer (SISNI) simultaneously achieves a high signal-to-noise ratio (SNR), sensitivity beyond the standard quantum limit (SQL) and tolerance to photon losses external to the interferometer, e.g., in detectors. We implement a SISNI using parametric amplification by four-wave mixing (FWM) in Rb vapor and a laser-fed Mach-Zehnder SU(2) interferometer. We observe path-length sensitivity with SNR 2.2 dB beyond the SQL at power levels (and thus SNR) 2 orders of magnitude beyond those of previous loss-tolerant interferometers. We find experimentally the optimal FWM gains and find agreement with a minimal quantum noise model for the FWM process. The results suggest ways to boost the in-practice sensitivity of high-power interferometers, e.g., gravitational wave interferometers, and may enable high-sensitivity, quantum-enhanced interferometry at wavelengths for which efficient detectors are not available.
The use of squeezing and entanglement allows advanced interferometers to detect signals that would otherwise be buried in quantum mechanical noise. High sensitivity instruments including magnetometers and gravitational wave detectors have shown enhanced signal-to-noise ratio (SNR) by injecting single-mode squeezed light into SU(2) interferometers, e.g. the Mach-Zehnder or Michelson topologies. The quantum enhancement in this approach is sensitive to losses, which break the fragile quantum correlations in the squeezed state. In contrast, SU(1,1) interferometers achieve quantum enhancement by noiseless amplification; they noiselessly increase the signal rather than reducing the quantum noise. Prior work on SU(1,1) interferometers has shown quantum-enhanced SNR11 and insensitivity to losses but to date has been limited to low powers and thus low SNR. Here we introduce a new interferometer topology, the SU(2)-in-SU(1,1) nested interferometer, that combines quantum enhancement, the high SNR possible with a SU(2) interferometer, and the loss tolerance of the SU(1,1) approach. We implement this interferometer using four-wave mixing in a hot atomic vapor and demonstrate 2:2(5) dB of quantum SNR enhancement, in a system with a phase variance nearly two orders of magnitude below that of any previous loss-tolerant enhancement scheme. The new interferometer enables new possibilities such as beyond-shot-noise sensing with wavelengths for which efficient detectors are not available.
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.
Quantum-enhanced precision measurements have emerged as one of the most useful applications of quantum optics. Exploiting quantum states of light and quantum processes, classical measurement limits can be surpassed, leading to improvements in areas including clocks, spectroscopy, magnetometry, and imaging. One measurement where straightforward quantum enhancements are possible is phase sensing with an interferometer. One can inject squeezed vacuum states into the dark port of the beamsplitter in a traditional interferometer to reduce the quantum noise and reach phase sensitivities beyond the shot noise limit. An alternate approach is to replace the beamsplitters of an interferometer with nonlinear parametric amplifiers, which produce nonclassical states of light that can be used to surpass classical performance. This so called SU(1,1) interferometer can theoretically approach sensitivities that scale as 1/n, the Heisenberg limit where n is the interior phase sensing photon number, compared to the shot noise limit of 1/ √ n for a traditional interferometer [1]. I will present our group’s experimental progress in testing a Mach-Zender SU(1,1) interferometer using four-wave mixers (4WMs) in hot Rb atoms as the parametric beamsplitters. The 4WM process generates entangled twin beams which serve as the two arms of the interferometer, and are then recombined in a second 4WM cell, resulting in a phase-sensitive output. We will extend the work done on this interferometer [2, 3] by performing a detailed analysis of the output signal to noise through homodyne measurements, and will attempt to observe the better-than-shot-noise scaling of the sensitivity. We will also consider the various difficulties of this optical interferometer such as the susceptibility to loss and imperfect mode-matching within the interferometer. Our group is also considering an analogous SU(1,1) interferometer in a cold atom system. Collisions in a spinor Bose-Einstein condensate of sodium atoms give rise to a 4WM process that produces spin states of the atoms which are entangled in atom number. These interactions can be controlled to set up an SU(1,1) atom interferometer, where the relevant measurements are now atomic population differences rather than photon intensities. These enhancements can lead to drastic improvements in atomic spin interferometry [3, 4].
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.
With the help of quantum entanglement, quantum dense metrology (QDM) is a technique that can make joint estimates of two conjugate quantities such as phase and amplitude modulations of an optical field, with an accuracy beating the standard quantum limit simultaneously. SU(1,1) interferometers (SUIs) can realize QDM with detection loss tolerance but is limited in absolute sensitivity. Here, we present a QDM scheme with a linear or SU(2) interferometer nested inside an SUI. By using a degenerate SUI and controlling the phase angle of the phase-sensitive amplifiers in the SUI, we can achieve the optimum quantum enhancement in the measurement precision of an arbitrary mixture of phase and amplitude modulation.
We provide a general theoretical derivation of the phase sensitivity achieved by SU(1,1) interferometers under homodyne detection. The general expressions obtained accommodate arbitrary input states and include internal and external losses. In this systematic review, both full SU(1,1) interferometers with two parametric amplifiers and the truncated interferometers with only one parametric amplifier are examined. We investigate scenarios involving both single-output ports and joint homodyne detection, and consider parametric amplifiers with equal gains or with a boosted gain second amplifier. Our analytical formulation provides physical insight and understanding of the improvements in the sensitivity, which are shown to originate from noise reduction and/or signal amplification, depending on the configurations and practical implementations. Surprisingly, the configuration with single-output mode detection and parametric amplifiers with equal gains exhibits the highest robustness to very high internal losses. We finally apply this framework to a ubiquitous ∣α,0⟩|α,0\rangle∣α,0⟩ input two-mode coherent probe state. This approach permits the comparison of different strategies and the optimization of the interferometer performance in the presence of losses. In particular, we determine which amplification and detection configurations provide the best performance, depending on the level of losses. This exemplifies how this general analytical approach provides a powerful tool to design quantum-enhanced interferometers and achieve optimal sensitivity with selected probe states and homodyne detection.