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arXiv:1607.06831 · Physical Review X

Improving Broadband Displacement Detection with Quantum Correlations

N. S. Kampel, R. W. Peterson, R. Fischer, P.-L. Yu, K. Cicak, R. W. Simmonds, K. W. Lehnert, C. A. Regal

Published Apr 18, 2017• 65 citations
arXivHTMLPDF

Abstract

Ultraprecise measurements of displacement and force can run into a limit on precision due to random forces imparted by the photons used for the measurement. An investigation into a technique for modifying the readout of an interferometer to avoid these limits demonstrates sensitivity improvements.
DOI
10.1103/physrevx.7.021008

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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.
The standard quantum limit (SQL) of a classical mechanical force detection results from quantum backaction impinged by the meter on a probe mechanical transducer perturbed by the force of interest. In this paper we introduce a technique of continuous broadband backaction, avoiding measurements for the case of a resonant signal force acting on a linear mechanical oscillator supporting one of the mirrors of an optical Michelson-Sagnac interferometer (MSI). The interferometer with the movable mirror is an optomechanical transducer able to support the polychromatic probe field. The method involves a dichromatic optical probe resonant with the MSI modes and having frequency separation equal to the mechanical frequency. We show that analyzing each of the harmonics of the probe reflected from the mechanical system separately and postprocessing the measurement results allows excluding the backaction in a broad frequency band and measuring the force with sensitivity better than the SQL.