At absolute zero (0 degrees Kelvin, -273 degrees Celsius
or -460 degrees Fahrenheit), atoms lose all thermal energy
and have only their quantum motion.

Once the objects get cold enough, quantum effects such
as squeezed state generation, quantum information storage
and quantum entanglement between the light and the mirror
should be observable, Mavalvala said.

The Newtonian physics says that at T=0K the motion of particles
is stoped. And this is correct. The Quantum physics says that
at T=0K there is some kind of particles motion . And this is correct too.
Is one part of physics contradicts with the other one? Is here a paradox?
No, here is not paradox. How then is it possible to understand situation?
My opinion.
Newtonian physics and Quantum physics are two different parts of
one whole Physics.
These two parts of Physics explain behavior of two different particles.
Newtonian physics says about particles which have mass and energy
and speed : c<1.
Quantum physics says about particles which have mass/energy
and speed : c=1 and c>1.
As a result of this situation QED tries clearly and logical to explain
the interaction between Newtonian and Quantum particles.