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Quantum Information and Measurement (QIM)

Measuring Motion Below the Standard Quantum Limit by Strong Optomechanical Quantum Correlations

Junxin Chen, David Mason, Massimiliano Rossi, Yeghishe Tsaturyan, Albert Schließer

Published Jan 1, 2019• 0 citations
Publisher

Abstract

In interferometric displacement and force measurement, the tradeoff between imprecision noise and quantum backaction sets the standard quantum limit (SQL). By exploiting quantum correlations in an optomechanical system, we demonstrate the first sub-SQL interferometric measurement.
DOI
10.1364/qim.2019.s3c.5

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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.
Interferometrie techniques to measure mechanical displacement are subject to constraints ultimately governed by quantum mechanics. In a "standard" measurement of a mechanically induced optical phase shift, there exists a trade-off between measurement imprecision and motion disturbance, known as standard quantum limit (SQL) [1]. For a mechanical resonator with susceptibility χm(Ω), this limit is SSQL(Ω) = ħ|χm(Ω)| (ħ reduced Planck constant), at any frequency Ω. In the last half-century, a number of systems, including advanced LIGO and ultracold atoms have progressed towards this limit, but excess sources of noise have yet prevented fully reaching the SQL. Here, we show measurements of an ultracoherent mechanical resonator performed at the SQL within 33% [2] and, for the first time, below the SQL by 1.5 dB[3]. The latter has been possible by a non-standard measurement scheme that explois quantum correlations between optical quadratures induced in the optomechanical device.
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.
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.
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.