Abstract
Quantum mechanics imposes a limit on the precision of a continuous position measurement of a harmonic oscillator, due to backaction arising from quantum fluctuations in the measurement field. This standard quantum limit can be surpassed by monitoring only one of the two non-commuting quadratures of the motion, known as backaction-evading measurement. This technique has not been implemented using optical interferometers to date. Here we demonstrate, in a cavity optomechanical system operating in the optical domain, a continuous two-tone backaction-evading measurement of a localized gigahertz-frequency mechanical mode of a photonic-crystal nanobeam cryogenically and optomechanically cooled close to the ground state. Employing quantum-limited optical heterodyne detection, we explicitly show the transition from conventional to backaction-evading measurement. We observe up to 0.67 dB (14%) reduction of total measurement noise, thereby demonstrating the viability of backaction-evading measurements in nanomechanical resonators for optical ultrasensitive measurements of motion and force.
Highlights
Quantum mechanics imposes a limit on the precision of a continuous position measurement of a harmonic oscillator, due to backaction arising from quantum fluctuations in the measurement field
For an interferometric position measurement, in which a mechanical oscillator is parametrically coupled to a cavity, the trade-off arising from measurement imprecision and quantum backaction (QBA) force noise on the mechanical oscillator, dictates a minimum added noipse ffiffieffiffiqffiffiffiuffiffiiffivffiffiffiaffiffilffieffiffint to the oscillator’s zero-point fluctuations, xzpf 1⁄4 h=2mΩm, referred to as the standard quantum limit (SQL), originally studied in the context of gravitational wave detection[1,3]
Recent advances in the field of cavity optomechanics[4], which utilizes a nano- or micromechanical oscillator coupled to an optical or superconducting microwave cavity, have allowed reaching the regime where the QBA arising from radiation pressure quantum fluctuations becomes relevant
Summary
Quantum mechanics imposes a limit on the precision of a continuous position measurement of a harmonic oscillator, due to backaction arising from quantum fluctuations in the measurement field This standard quantum limit can be surpassed by monitoring only one of the two non-commuting quadratures of the motion, known as backaction-evading measurement. One technique to surpass the SQL, applicable to measurements far from the mechanical resonance frequency Ωm, utilizes quantum correlations in the probe (due to ponderomotive squeezing16–19), known as “variational readout”[20,21] This technique has recently been demonstrated in a cryogenic micromechanical oscillator coupled to an optical cavity[22] and in a room-temperature nano-optomechanical system for quantum-enhanced force measurements[23]. By exclusively measuring X^, e.g., all QBA is diverted to Y^
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