  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.
