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 tradeoff 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 \textit{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.
Highlights
When one seeks knowledge of the full dynamics of the displacement of a harmonic oscillator, noncommutation of the two mechanical quadratures requires a minimum added noise equal to the mechanical resonator’s zero point motion [1,2]
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 standard quantum limit (SQL) dictates for our quantum efficiency
This fundamental quantum limit (QL) is a distinct bound from the standard quantum limit (SQL) that is often considered in interferometric displacement measurement [3,4,5]
Summary
Langevin equations for the probe light operator u, based on the Hamiltonian given above. We write the solution to the Heisenberg-. Langevin equations of motion of our optomechanical system [33,43,45,46]. In subsequent sections we convert the solutions to the units used in our final equations.
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