The interplay of measurement imprecision and quantum backac
tion limits the sensitivity with which the position of an oscillator can b
e continuously monitored\, to be at best equal to the oscillator’s zero-
point fluctuations. However\, any single quadrature of the motion can\, in
principle\, be measured without limit\, provided that the measurement bac
kaction is shunted to the orthogonal quadrature. Such backaction evading (
BAE) measurements\, which are examples of quantum nondemolition measuremen
ts\, can be achieved by appropriately synchronizing the measurement with t
he oscillator’s intrinsic motion. In our work\, we study the collective
modes of two uncoupled mechanical oscillators\, each independently coupled
to a microwave cavity. The oscillators are realized as aluminum drumheads
. We carry out a mechanical two-mode BAE measurement of the collective qua
dratures\, and achieve an evasion of quantum backaction\, caused by microw
ave shot noise\, below the backaction arising in a continuous position mea
surement. The canonically conjugate quadrature is heated predominantly by
the quantum backaction. On top of this\, the work realizes the concept of
quantum-mechanics-free subsystem. By perturbing the measurement slightly (
i.e.\, reservoir engineering)\, such measurements can be used to generate
stabilized entanglement between two macroscopic mechanical oscillators. Th
is prepares a canonical entangled state known as the two-mode squeezed sta
te. It corresponds to the variances of collective position and momentum qu
adratures being reduced below the quantum zero-point fluctuations level. W
e carry out such a measurement\, and infer the existence of entanglement i
n the steady state by combining measurements of correlated mechanical fluc
tuations with an analysis of the microwaves emitted from the cavity.

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