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Conference on Lasers and Electro-Optics

Quantum Measurement of a Mechanical Resonator at and Below the Standard Quantum Limit

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

Published May 1, 2019• 0 citations
Publisher

Abstract

We measure mechanical displacements within 35% of the Heisenberg limit. By exploiting quantum correlations in an optomechanical system, we achieve for the first time a total sensitivity below the standard quantum limit by 1.5 dB. © 2019 The Author(s)
DOI
10.23919/cleo.2019.8749319

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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.
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.
Interferometers operating at or close to quantum limits of precision have found wide application in tabletop searches for physics beyond the standard model, the study of fundamental forces and symmetries of nature and foundational tests of quantum mechanics. The limits imposed by quantum fluctuations and measurement backaction on conventional interferometers (δϕ∼1/Nδϕ\sim 1/\sqrt{N}δϕ∼1/N​) have spurred the development of schemes to circumvent these limits through quantum interference, multiparticle interactions and entanglement. A prominent example of such schemes, the so-called SU(1,1)SU(1,1)SU(1,1) interferometer, has been shown to be particularly robust against particle loss and inefficient detection, and has been demonstrated with photons and ultracold atoms. Here, we realize a SU(1,1)SU(1,1)SU(1,1) interferometer in a fundamentally new platform in which the interfering arms are distinct flexural modes of a millimeter-scale mechanical resonator. We realize up to 15.4(3) dB of noise squeezing and demonstrate the Heisenberg scaling of interferometric sensitivity (δϕ∼1/Nδϕ\sim 1/Nδϕ∼1/N), corresponding to a 6-fold improvement in measurement precision over a conventional interferometer. Our work extends the optomechanical toolbox for the quantum manipulation of macroscopic mechanical motion and presents new avenues for studies of optomechanical sensing and the nonequilibrium dynamics of multimode optomechanical systems.
The motion of a macroscopic mechanical oscillator – a glass nanostring – has been measured, using a cavity-enhanced optical interferometer, with a sensitivity that is 40 dB below that at the standard quantum limit, forming the most precise measurement of the zero-point motion of a mechanical oscillator yet. The resulting back-action due to the measurement has been observed. A quantum feedback protocol is used to cancel 20 dB of back-action, in a first instance of quantum feedback applied on a mechanical oscillator. Quantum correlations developed between the oscillator and the measuring instrument – light – has been observed. The role of these correlations in quantum-enhanced metrology of weak forces is illustrated, and feedback is used to manipulate and enhance the same correlations.