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Physical Review Letters

Surpassing the Standard Quantum Limit Using an Optical Spring

T. J. Cullen, Ronald Pagano, Scott Aronson, J. Cripe, Safura Sharifi, M. L. Lollie, Henry Cain, Paula Heu, David Follman, Garrett D. Cole, Nancy Aggarwal, T. R. Corbitt

Published Sep 13, 2024• 4 citations
Publisher

Abstract

Quantum mechanics places noise limits and sensitivity restrictions on physical measurements. The balance between unwanted backaction and the precision of optical measurements imposes a standard quantum limit (SQL) on interferometric systems. In order to realize a sensitivity below the SQL, it is necessary to leverage a backaction evading measurement technique, reduce thermal noise to below the level of backaction, and exploit cancellations of any excess noise contributions at the detector. Many proof of principle experiments have been performed, but only recently has an experiment achieved sensitivity below the SQL. In this work, we extend that initial demonstration and realize sub-SQL sensitivity nearly two times better than previous measurements, and with an architecture applicable to interferometric gravitational wave detectors. In fact, this technique is directly applicable to Advanced LIGO, which could observe similar effects with a detuned signal recycling cavity. We measure a total sensitivity below the SQL by 2.8 dB, corresponding to a reduction in the noise power by 72±5.1% below the quantum limit. Through the use of a detuned cavity and the optical spring effect, this noise reduction is tunable, allowing us to choose the desired range of frequencies that fall below the SQL. This result demonstrates access to sensitivities well below the SQL at frequencies applicable to LIGO, with the potential to extend the reach of gravitational wave detectors further into the Universe.

DOI
10.1103/physrevlett.133.113602

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Quantum mechanics places noise limits and sensitivity restrictions on physical measurements. The balance between unwanted backaction and the precision of optical measurements impose a standard quantum limit (SQL) on interferometric systems. In order to realize a sensitivity below the SQL, it is necessary to leverage a back-action evading measurement technique, or else exploit cancellations of any excess noise contributions at the detector. %Many proof of principle experiments have been performed, but only recently has an experiment achieved sensitivity below the SQL. In this work, we extend that initial demonstration and realize sub-SQL measurement sensitivity nearly two times better than previous measurements, and with architecture applicable to interferometric gravitational wave detectors. In fact, this technique is directly applicable to Advanced LIGO, which could observe similar effects with a detuned signal recycling cavity. By exploiting quantum correlations created by an optical spring, we measure a total sensitivity below the SQL by $\textbf{2.8}$ dB, corresponding to a reduction in the noise power by $\textbf{72}\pm\textbf{5.1}$ \% below the quantum limit. Through the use of a detuned optical spring, this noise reduction is tunable, allowing us to choose the desired range of frequencies that fall below the SQL. This result demonstrates access to sensitivities well below the SQL at frequencies ranges applicable to LIGO, with the potential to extend the reach of gravitational wave detectors further into the universe.

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Quantum mechanics places noise limits and sensitivity restrictions on physical measurements. The balance between unwanted backaction and the precision of optical measurements imposes a standard quantum limit (SQL) on interferometric systems. In order to realize a sensitivity below the SQL, it is necessary to leverage a backaction evading measurement technique, reduce thermal noise to below the level of backaction, and exploit cancellations of any excess noise contributions at the detector. Many proof of principle experiments have been performed, but only recently has an experiment achieved sensitivity below the SQL. In this work, we extend that initial demonstration and realize sub-SQL sensitivity nearly two times better than previous measurements, and with an architecture applicable to interferometric gravitational wave detectors. In fact, this technique is directly applicable to Advanced LIGO, which could observe similar effects with a detuned signal recycling cavity. We measure a total sensitivity below the SQL by 2.8 dB, corresponding to a reduction in the noise power by 72±5.1% below the quantum limit. Through the use of a detuned cavity and the optical spring effect, this noise reduction is tunable, allowing us to choose the desired range of frequencies that fall below the SQL. This result demonstrates access to sensitivities well below the SQL at frequencies applicable to LIGO, with the potential to extend the reach of gravitational wave detectors further into the Universe.
Quantum mechanics places noise limits and sensitivity restrictions on physical measurements. The balance between unwanted backaction and the precision of optical measurements impose a standard quantum limit (SQL) on interferometric systems. In order to realize a sensitivity below the SQL, it is necessary to leverage a back-action evading measurement technique, or else exploit cancellations of any excess noise contributions at the detector. %Many proof of principle experiments have been performed, but only recently has an experiment achieved sensitivity below the SQL. In this work, we extend that initial demonstration and realize sub-SQL measurement sensitivity nearly two times better than previous measurements, and with architecture applicable to interferometric gravitational wave detectors. In fact, this technique is directly applicable to Advanced LIGO, which could observe similar effects with a detuned signal recycling cavity. By exploiting quantum correlations created by an optical spring, we measure a total sensitivity below the SQL by 2.8\textbf{2.8}2.8 dB, corresponding to a reduction in the noise power by 72±5.1\textbf{72}\pm\textbf{5.1}72±5.1 \% below the quantum limit. Through the use of a detuned optical spring, this noise reduction is tunable, allowing us to choose the desired range of frequencies that fall below the SQL. This result demonstrates access to sensitivities well below the SQL at frequencies ranges applicable to LIGO, with the potential to extend the reach of gravitational wave detectors further into the universe.
The Heisenberg uncertainty principle dictates that the position and momentum of an object cannot be simultaneously measured with arbitrary precision, giving rise to an apparent limitation known as the standard quantum limit (SQL). Gravitational-wave detectors use photons to continuously measure the positions of freely falling mirrors and so are affected by the SQL. We investigated the performance of the Laser Interferometer Gravitational-Wave Observatory (LIGO) after the experimental realization of frequency-dependent squeezing designed to surpass the SQL. For the LIGO Livingston detector, we found that the upgrade reduces quantum noise below the SQL by a maximum of three decibels between 35 and 75 hertz while achieving a broadband sensitivity improvement, increasing the overall detector sensitivity during astrophysical observations.
We report a room-temperature measurement of nanomechanical motion with an imprecision below the standard quantum limit (SQL), using cavity-enhanced optical near fields. Fundamental thermodynamical cavity frequency fluctuation limits the total imprecision to 3dB3 \mathrm{dB}3dB below the SQL at room temperature [corresponding to (530am/Hz)2(530 \mathrm{am}/\sqrt{\mathrm{Hz}}){}^{2}(530am/Hz​)2 in absolute units] and is expected to reduce to negligible values at moderate cryogenic temperatures. Coupling strengths exceeding those required to reach the SQL by more than two orders of magnitude are achieved, allowing a shot-noise limited imprecision more than 10dB10 \mathrm{dB}10dB below the SQL. The transducer, thus, in principle, allows access to the quantum backaction dominated regime, a prerequisite for exploring quantum backaction, measurement-induced squeezing, and obtaining sub-SQL sensitivity using backaction evading techniques.
Quantum backaction (QBA) of a measurement limits the precision of observation of the motion of a free mass. This profound effect, dubbed the "Heisenberg microscope" in the early days of quantum mechanics, leads to the standard quantum limit (SQL) stemming from the balance between the measurement sensitivity and the QBA. We consider the measurement of motion of a free mass performed in a quantum reference frame with an effective negative mass which is not limited by QBA. As a result, the disturbance on the motion of a free mass can be measured beyond the SQL. QBA-limited detection of motion for a free mass is extremely challenging, but there are devices where this effect is expected to play an essential role, namely, gravitational wave detectors (GWDs) such as LIGO and Virgo. Recent reports on the observations of gravitational waves have opened new horizons in cosmology and astrophysics. We present a general idea and a detailed numerical analysis for QBA-evading measurement of the gravitational wave effect on the GWD mirrors, which can be considered free masses under relevant conditions. The measurement is performed by two entangled beams of light, probing the GWD and an auxiliary atomic spin ensemble, respectively. The latter plays the role of a free negative mass. We show that under realistic conditions the sensitivity of the GWD in m/sqrt[Hz] can be increased by 6 dB over the entire frequency band of interest.
Optical interferometry is by far the most sensitive displacement measurement technique available, with sensitivities at the 10(-20) m/square root(Hz) level in the large-scale gravitational-wave interferometers currently in operation. Second-generation interferometers will experience a tenfold improvement in sensitivity and be mainly limited by quantum noise, close to the standard quantum limit (SQL), once considered as the ultimate displacement sensitivity achievable by interferometry. In this Letter, we experimentally demonstrate one of the techniques envisioned to go beyond the SQL: amplification of a signal by radiation-pressure backaction in a detuned cavity.
Interferometers enable ultrasensitive measurement in a wide array of applications from gravitational wave searches to force microscopes. The role of quantum mechanics in the metrological limits of interferometers has a rich history, and a large number of techniques to surpass conventional limits have been proposed. In a typical measurement configuration, the trade-off between the probe’s shot noise (imprecision) and its quantum backaction results in what is known as the standard quantum limit (SQL). In this work, we investigate how quantum correlations accessed by modifying the readout of the interferometer can access physics beyond the SQL and improve displacement sensitivity. Specifically, we use an optical cavity to probe the motion of a silicon nitride membrane off mechanical resonance, as one would do in a broadband displacement or force measurement, and observe sensitivity better than the SQL dictates for our quantum efficiency. Our measurement illustrates the core idea behind a technique known as variational readout, in which the optical readout quadrature is changed as a function of frequency to improve broadband displacement detection. And, more generally, our result is a salient example of how correlations can aid sensing in the presence of backaction.