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Improving Broadband Displacement Detection with Quantum Correlations

N. S. Kampel, Robert W. Peterson, Ran Fischer, Yu, P.-L., Katarina Cicak, Raymond W. Simmonds, Konrad W. Lehnert, Cindy A. Regal

Published Apr 18, 2017• 36 citations
OpenAlex

Abstract

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.

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Improving Broadband Displacement Detection with Quantum Correlations

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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.
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.
Optical atomic magnetometry is a powerful tool for continuous sensing applications, yet, in the absence of quantum correlations, its sensitivity is limited by the standard quantum limit (SQL) stemming from a trade-off between optical probe imprecision and quantum measurement backaction. Beyond-SQL sensitivity requires quantum correlations that modify these measurement noise sources. Here we demonstrate such sensitivity by using entangled state of the probe light and by engineering correlations between measurement imprecision and backaction. Having first explored SQL in a broad range of frequencies, we demonstrate overcoming the limit by combining variational readout with coupling the magnetometer to one mode of a bipartite entangled light state and conditioning the results on the other entangled mode. Tuning the detected light quadratures and combining the signals from the two measurement channels, we achieve sensitivity beyond the SQL in a broad range of acoustic frequencies which has so far remained inaccessible to quantum-noise-limited optical magnetometry.
We propose an ultrasensitive displacement measurement scheme to overcome the standard quantum limit (SQL) in the unresolved sideband cavity optomechanical system with nonlinear optomechanical coupling and squeezed light injection. By introducing the optimized quantum correlation, which is enabled by suitable choices of the squeezing angle, squeezing level, power of the probe light, and measurement angle of homodyne detection, the off-resonant displacement sensitivity reaches 6 dB below the SQL in linear optomechanical coupling. In contrast, displacement sensitivities with a coherent probe plus variational readout and squeezed probe plus fixed measurement angle (phase quadrature) are 2.6 dB and 4.6 dB below the SQL, respectively. By combining linear and quadratic optomechanical coupling, we show that the displacement sensitivity can be further improved to 9.6 dB below the SQL. Our results have potential applications in gravitational-wave detectors, quantum metrology, and the search for dark matter.
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.
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.