  We apply the squeezed state formalism to scalar field dark matter (e.g.
axion) perturbations generated during inflation. As for the inflationary
perturbations, the scalar field state becomes highly squeezed as modes exit the
horizon. For as long as $H>m_\phi$ (with $H$ the Hubble rate and $m_\phi$ the
scalar mass) the scalar field field does not interact during reheating, and we
follow its evolution exactly as modes re-enter the horizon. We find that the
quantum state remains squeezed after horizon re-entry during the hot big bang.
This demonstrates a fact well-known in the theory of inflation: cosmological
observables for scalar dark matter are accurately modelled by a classical
stochastic field with a fixed phase. Our calculation covers all modes smaller
than the present-day cosmic de Broglie wavelength. Larger scale modes mix
gravitationally with the environment when $H<m_\phi$, and are thus expected to
decohere.
