  An entangled quantum state of two or more particles or objects exhibits some
of the most peculiar features of quantum mechanics. Entangled systems cannot be
described independently of each other even though they may have an arbitrarily
large spatial separation. Reconciling this property with the inherent
uncertainty in quantum states is at the heart of some of the most famous
debates in the development of quantum theory. Nonetheless, entanglement
nowadays has a solid theoretical and experimental foundation, and it is the
crucial resource behind many emerging quantum technologies. Entanglement has
been demonstrated for microscopic systems, such as with photons, ions, and
electron spins, and more recently in microwave and electromechanical devices.
For macroscopic objects, however, entanglement becomes exceedingly fragile
towards environmental disturbances. A major outstanding goal has been to create
and verify the entanglement between the motional states of slowly-moving
massive objects. Here, we carry out such an experimental demonstration, with
the moving bodies realized as two micromechanical oscillators coupled to a
microwave-frequency electromagnetic cavity that is used to create and stabilise
the entanglement of the centre-of-mass motion of the oscillators. We infer the
existence of entanglement in the steady state by combining measurement of
correlated mechanical fluctuations with an analysis of the microwaves emitted
from the cavity. Our work qualitatively extends the range of entangled physical
systems, with implications in quantum information processing, precision
measurement, and tests of the limits of quantum mechanics.
