We demonstrate how recent protocols developed for the stabilization of Gottesman-Kitaev-Preskill states can be used for the estimation of two-quadrature displacement sensing, with sensitivities approaching the multivariate quantum Cramer-Rao bound. Thanks to the stabilization, this sensor is backaction evading and can function continuously without reset, making it well suited for the detection of itinerant signals. Additionally, we provide numerical simulations showing that the protocol can unconditionally surpass the Gaussian limit of displacement sensing with prior information, even in the presence of realistic noise. Our work shows how reservoir engineering in bosonic systems can be leveraged for quantum metrology, with potential applications in force sensing, waveform estimation, and quantum channel learning.We demonstrate how recent protocols developed for the stabilization of Gottesman-Kitaev-Preskill states can be used for the estimation of two-quadrature displacement sensing, with sensitivities approaching the multivariate quantum Cramer-Rao bound. Thanks to the stabilization, this sensor is backaction evading and can function continuously without reset, making it well suited for the detection of itinerant signals. Additionally, we provide numerical simulations showing that the protocol can unconditionally surpass the Gaussian limit of displacement sensing with prior information, even in the presence of realistic noise. Our work shows how reservoir engineering in bosonic systems can be leveraged for quantum metrology, with potential applications in force sensing, waveform estimation, and quantum channel learning.

arXiv:2506.20627PRX QuantumMar 5, 20263 citations

Displacement Sensing using Quantum Mechanical Interference

Hiroshi Yamaguchi, S. Miyashita, Y. Hirayama

International Conference on Solid State Devices and Materials (SSDM)Sep 18, 20030 citations

Harnessing quantum correlations for physics beyond the standard quantum limit in broadband displacement detection

N. S. Kampel, Robert W. Peterson, Ran Fischer +5 more

When one seeks knowledge of the full dynamics of the displacement of a harmonic oscillator, non-commutation of the two mechanical quadratures requires a minimum added noise equal to the mechanical resonator's zero point motion. This fundamental quantum limit (QL) is a distinct bound from the standard quantum limit (SQL) that is often considered in interferometric displacement measurement. The SQL is a consequence of the non-commutation of the probe's quadratures in a specific measurement configuration and is characterized by a tradeoff between shot noise (SN) imprecision and quantum backaction that are uncorrelated. The QL and SQL reach the same limit when probing at the peak mechanical response, but the QL can be a significantly lower bound off resonance. In studies of micro-mechanical motion, there has been great interest in observing quantum backaction and approaching the SQL on mechanical resonance. However, much of what historically motivates SQL research is displacement monitoring over a wide frequency band, such as gravitational wave searches. One long-standing concept for surpassing the SQL is to introduce correlations by changing the readout quadrature as a function of frequency in a technique known as variational readout. Here we harness quantum correlations in the measurement of a macroscopic resonator by modifying the readout quadrature of an optical interferometer. By using an optomechanical device thermalized to a dilution refrigerator, we measure quantum noise far off resonance where we improve upon the off-resonance SQL for our quantum efficiency.When one seeks knowledge of the full dynamics of the displacement of a harmonic oscillator, non-commutation of the two mechanical quadratures requires a minimum added noise equal to the mechanical resonator's zero point motion. This fundamental quantum limit (QL) is a distinct bound from the standard quantum limit (SQL) that is often considered in interferometric displacement measurement. The SQL is a consequence of the non-commutation of the probe's quadratures in a specific measurement configuration and is characterized by a tradeoff between shot noise (SN) imprecision and quantum backaction that are uncorrelated. The QL and SQL reach the same limit when probing at the peak mechanical response, but the QL can be a significantly lower bound off resonance. In studies of micro-mechanical motion, there has been great interest in observing quantum backaction and approaching the SQL on mechanical resonance. However, much of what historically motivates SQL research is displacement monitoring over a wide frequency band, such as gravitational wave searches. One long-standing concept for surpassing the SQL is to introduce correlations by changing the readout quadrature as a function of frequency in a technique known as variational readout. Here we harness quantum correlations in the measurement of a macroscopic resonator by modifying the readout quadrature of an optical interferometer. By using an optomechanical device thermalized to a dilution refrigerator, we measure quantum noise far off resonance where we improve upon the off-resonance SQL for our quantum efficiency.

Jul 22, 20162 citations

Ultimate Quantum Limits In The Measurement Of Very Small Displacements in Optical Images

Claude Fabre, Agnès Maître, Matthias Vaupel

European Quantum Electronics Conference (EQEC)Aug 24, 20050 citations

Estimating IF shifts based on SU(1,1) interferometer

Chen Yuetao, Chen Gaiqing, Luo MengMeng +2 more

IF (Imbert--Fedorov) shifts which refers to a transverse micro-displacement occurs at the interface between two media. The estimation of such micro-displacement enables a deeper understanding of light-matter interactions. In this paper, we propose a theoretical scheme to investigate the IF shifts and incident angle sensitivity by introducing SPR sensor into the SU(1,1) interferometer. By injecting two coherent states in the SU(1,1) interferometer, we obtain the sensitivity of the IF shifts and incident angle based on the homodyne detection. Our results demonstrate that it is possible to get the maximal IF shift and the optimal IF shifts sensitivity simultaneously. Meanwhile, the orbit angular momentum carried by Laguerre-Gauss (LG) beam is unfavorable for improving the IF shift sensitivity. Furthermore, we have investigated the sensitivity of the incident angle in our scheme and found that it is capable of surpassing the sensitivity limit of $(6\times 10^{-6}){{}^\circ}$ . This allows us to achieve a more precise IF shifts sensitivity than the traditional weak measurement method used for IF shift detection, which typically has a rotation precision limit of 0.04 ${{}^\circ}$ [Journal of Optics, 19(10), 105611]. More importantly, both the sensitivity of IF shifts and incident angle can breakthrough the (shot noise limit) SNL, even approaching the Cramér-Rao bound (QCRB) at the incident angle $θ=43.6208{{}^\circ}$ and $θ=43.6407{{}^\circ}$ . We also discover that increasing the coherent amplitude is beneficial for improving the sensitivity of both the IF shifts and incident angle. Our findings shall offer a novel scheme for measuring micro-displacement in SPR sensor. These results can be helpful in the development of more precise quantum-based sensors for studying light-matter interactions.IF (Imbert--Fedorov) shifts which refers to a transverse micro-displacement occurs at the interface between two media. The estimation of such micro-displacement enables a deeper understanding of light-matter interactions. In this paper, we propose a theoretical scheme to investigate the IF shifts and incident angle sensitivity by introducing SPR sensor into the SU(1,1) interferometer. By injecting two coherent states in the SU(1,1) interferometer, we obtain the sensitivity of the IF shifts and incident angle based on the homodyne detection. Our results demonstrate that it is possible to get the maximal IF shift and the optimal IF shifts sensitivity simultaneously. Meanwhile, the orbit angular momentum carried by Laguerre-Gauss (LG) beam is unfavorable for improving the IF shift sensitivity. Furthermore, we have investigated the sensitivity of the incident angle in our scheme and found that it is capable of surpassing the sensitivity limit of $(6\times 10^{-6}){{}^\circ}$. This allows us to achieve a more precise IF shifts sensitivity than the traditional weak measurement method used for IF shift detection, which typically has a rotation precision limit of 0.04${{}^\circ}$ [Journal of Optics, 19(10), 105611]. More importantly, both the sensitivity of IF shifts and incident angle can breakthrough the (shot noise limit) SNL, even approaching the Cramér-Rao bound (QCRB) at the incident angle $θ=43.6208{{}^\circ}$ and $θ=43.6407{{}^\circ}$. We also discover that increasing the coherent amplitude is beneficial for improving the sensitivity of both the IF shifts and incident angle. Our findings shall offer a novel scheme for measuring micro-displacement in SPR sensor. These results can be helpful in the development of more precise quantum-based sensors for studying light-matter interactions.

arXiv:2307.00291Jul 1, 20230 citations

(6\times 10^{-6}){{}^\circ}

. This allows us to achieve a more precise IF shifts sensitivity than the traditional weak measurement method used for IF shift detection, which typically has a rotation precision limit of 0.04

{{}^\circ}

[Journal of Optics, 19(10), 105611]. More importantly, both the sensitivity of IF shifts and incident angle can breakthrough the (shot noise limit) SNL, even approaching the Cramér-Rao bound (QCRB) at the incident angle

θ=43.6208{{}^\circ}

and

θ=43.6407{{}^\circ}

. We also discover that increasing the coherent amplitude is beneficial for improving the sensitivity of both the IF shifts and incident angle. Our findings shall offer a novel scheme for measuring micro-displacement in SPR sensor. These results can be helpful in the development of more precise quantum-based sensors for studying light-matter interactions.