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:1512.01497 · Physical Review A

Quantum-enhanced metrology with the single-mode coherent states of an optical cavity inside a quantum feedback loop

Lewis A. Clark, Adam Stokes, Almut Beige

Published Aug 23, 2016• 18 citations
arXivHTMLPDF

Abstract

In this paper, we use the nonlinear generator of dynamics of the individual quantum trajectories of an optical cavity inside an instantaneous quantum feedback loop to measure the phase shift between two pathways of light with a precision above the standard quantum limit. The feedback laser provides a reference frame and constantly increases the dependence of the state of the resonator on the unknown phase. Since our quantum metrology scheme can be implemented with current technology and does not require highly efficient single photon detectors, it should be of practical interest until highly entangled many-photon states become more readily available.

DOI
10.1103/physreva.94.023840

Related papers

Quantum-enhanced metrology with single-mode coherent states

Lewis A. Clark, Adam Stokes, Almut Beige

In this paper, we use the temporal quantum correlations in the photon statistics of an optical cavity inside an instantaneous quantum feedback loop to measure the phase shift between two pathways of light with an accuracy above the standard quantum limit. The feedback laser provides a reference frame and constantly increases the phase space volume occupied by the resonator field, thereby increasing the dependence of its final state on the measured phase. Since our quantum metrology scheme can be implemented with current technology and does not require highly-efficient single photon detectors, it should be of practical interest until technologies for the generation of highly-entangled many-photon states become more readily available.

•Dec 4, 2015•0 citations

Quantum-enhanced Metrology without Entanglement based on Optical Cavities with Feedback

Lewis A. Clark, Adam Stokes, Muhammad Mubashir Khan +2 more

There are a number of different strategies to measure the phase shift between two pathways of light more efficiently than suggested by the standard quantum limit. One way is to use highly entangled photons. Another way is to expose photons to a non-linear or interacting Hamiltonian. This paper emphasises that the conditional dynamics of open quantum systems provides an interesting additional tool for quantum-enhanced metrology. As a concrete example, we review a recent scheme which exploits the conditional dynamics of a laser-driven optical cavity with spontaneous photon emission inside a quantum feedback loop. Deducing information from second-order photon correlation measurements requires neither optical non-linearities nor entangled photons and should therefore be of immediate practical interest.

arXiv:1609.02412•International Conference on Photonics, Optics and Laser Technology•Jan 1, 2017•0 citations

Quantum jump metrology in a two-cavity network

Kawthar Al Rasbi, Almut Beige, Lewis A. Clark

Quantum metrology enhances measurement precision by utilizing the properties of quantum physics. In interferometry, this is typically achieved by evolving highly entangled quantum states before performing single-shot measurements to reveal information about an unknown parameter. While this is often the optimum approach, implementation with all but the smallest states is still extremely challenging. An alternative approach is quantum jump metrology [L. A. Clark et al., Phys. Rev. A 99, 022102 (2019)], which deduces information by continuously monitoring an open quantum system while inducing phase-dependent temporal correlations with the help of quantum feedback. Taking this approach here, we analyze measurements of a relative phase in an optical network of two cavities with quantum feedback in the form of laser pulses. It is shown that the proposed approach can exceed the standard quantum limit without the need for complex quantum states while being scalable and more practical than previous related schemes.

arXiv:2201.04412•Physical Review A•Dec 27, 2022•3 citations

Quantum-enhanced interferometry with cavity QED-generated non-classical light

Karol Gietka, Tomasz Wasak, Jan Chwedeńczuk +2 more

We propose an enhanced optical interferometer based on tailored non-classical light generated by nonlinear dynamics and projective measurements in a three-level atom cavity QED system. A coherent state in the cavity becomes dynamically entangled with two ground states of the atom and is transformed to a macroscopic superposition state via a projective measurement on the atom. We show that the resulting highly non-classical state can improve interferometric precision measurements well beyond the shot-noise limit once combined with a classical laser pulse at the input of a Mach–Zehnder interferometer. For a practical implementation, we identify an efficient phase shift estimation scheme based on the counting of photons at the interferometer output. Photon losses and photon-counting errors deteriorate the interferometer sensitivity, but we demonstrate that it still can be significantly better than the shot-noise limit under realistic conditions.

arXiv:1703.03651•The European Physical Journal D•Nov 1, 2017•7 citations

Quantum metrology in a nonlinear interferometer with feedback

Shivani Singh, Craig S. Hamilton, Igor Jex

In this paper, we propose a nonlinear interferometer with feedback loops and explore its efficiency for phase estimation. We analyse two feedback schemes, one where both modes of the interferometer are fed-back into the device and another where only one mode is fed-back. The quantum Fisher information (QFI) for phase estimation in each feedback scheme increases with each feedback loop, and similar to the standard SU(1,1) nonlinear interferometer, phase estimation in this scheme is sensitive to photon loss when the inputs are vacuum state. In terms of resources, we show that, in the low-loss regime, our scheme performs better than standard nonlinear interferometer. The feedback scheme provides the minimum phase variance when the unknown phase is small. We have also provided a special case where feedback scheme provided enhanced QFI even for large phase values. This is achieved by switching between squeezing and anti-squeezing operators after every few loops.

arXiv:2507.17160•Physical Review A•Jul 15, 2025•0 citations

Enhanced Phase Estimation via Photon-Added Two-Mode Squeezed States and Kerr Nonlinearity

Zekun Zhao, Qingqian Kang, Teng Zhao +3 more

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.

quant-pharXiv:2602.00700•Feb 3, 2026•0 citations
In this paper, we use the nonlinear generator of dynamics of the individual quantum trajectories of an optical cavity inside an instantaneous quantum feedback loop to measure the phase shift between two pathways of light with a precision above the standard quantum limit. The feedback laser provides a reference frame and constantly increases the dependence of the state of the resonator on the unknown phase. Since our quantum metrology scheme can be implemented with current technology and does not require highly efficient single photon detectors, it should be of practical interest until highly entangled many-photon states become more readily available.
In this paper, we use the temporal quantum correlations in the photon statistics of an optical cavity inside an instantaneous quantum feedback loop to measure the phase shift between two pathways of light with an accuracy above the standard quantum limit. The feedback laser provides a reference frame and constantly increases the phase space volume occupied by the resonator field, thereby increasing the dependence of its final state on the measured phase. Since our quantum metrology scheme can be implemented with current technology and does not require highly-efficient single photon detectors, it should be of practical interest until technologies for the generation of highly-entangled many-photon states become more readily available.
There are a number of different strategies to measure the phase shift between two pathways of light more efficiently than suggested by the standard quantum limit. One way is to use highly entangled photons. Another way is to expose photons to a non-linear or interacting Hamiltonian. This paper emphasises that the conditional dynamics of open quantum systems provides an interesting additional tool for quantum-enhanced metrology. As a concrete example, we review a recent scheme which exploits the conditional dynamics of a laser-driven optical cavity with spontaneous photon emission inside a quantum feedback loop. Deducing information from second-order photon correlation measurements requires neither optical non-linearities nor entangled photons and should therefore be of immediate practical interest.
Quantum metrology enhances measurement precision by utilizing the properties of quantum physics. In interferometry, this is typically achieved by evolving highly entangled quantum states before performing single-shot measurements to reveal information about an unknown parameter. While this is often the optimum approach, implementation with all but the smallest states is still extremely challenging. An alternative approach is quantum jump metrology [L. A. Clark et al., Phys. Rev. A 99, 022102 (2019)], which deduces information by continuously monitoring an open quantum system while inducing phase-dependent temporal correlations with the help of quantum feedback. Taking this approach here, we analyze measurements of a relative phase in an optical network of two cavities with quantum feedback in the form of laser pulses. It is shown that the proposed approach can exceed the standard quantum limit without the need for complex quantum states while being scalable and more practical than previous related schemes.
We propose an enhanced optical interferometer based on tailored non-classical light generated by nonlinear dynamics and projective measurements in a three-level atom cavity QED system. A coherent state in the cavity becomes dynamically entangled with two ground states of the atom and is transformed to a macroscopic superposition state via a projective measurement on the atom. We show that the resulting highly non-classical state can improve interferometric precision measurements well beyond the shot-noise limit once combined with a classical laser pulse at the input of a Mach–Zehnder interferometer. For a practical implementation, we identify an efficient phase shift estimation scheme based on the counting of photons at the interferometer output. Photon losses and photon-counting errors deteriorate the interferometer sensitivity, but we demonstrate that it still can be significantly better than the shot-noise limit under realistic conditions.
In this paper, we propose a nonlinear interferometer with feedback loops and explore its efficiency for phase estimation. We analyse two feedback schemes, one where both modes of the interferometer are fed-back into the device and another where only one mode is fed-back. The quantum Fisher information (QFI) for phase estimation in each feedback scheme increases with each feedback loop, and similar to the standard SU(1,1) nonlinear interferometer, phase estimation in this scheme is sensitive to photon loss when the inputs are vacuum state. In terms of resources, we show that, in the low-loss regime, our scheme performs better than standard nonlinear interferometer. The feedback scheme provides the minimum phase variance when the unknown phase is small. We have also provided a special case where feedback scheme provided enhanced QFI even for large phase values. This is achieved by switching between squeezing and anti-squeezing operators after every few loops.
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.