Nonclassicality of axion-like dark matter through gravitational
  self-interactions
  Axion-like particles (ALPs) are promising dark matter candidates. A classical
field description is typically employed, motivated by large phase space
occupation numbers. Here we show that such a description is accompanied by a
quantum effect: squeezing due to gravitational self-interactions. For a typical
QCD axion today, the onset of squeezing is reached on microsecond-scales and
grows over millennia. Thus within the usual models based on the classical
Schr\"odinger-Poisson equation, a type of Gross-Pitaevskii equation, any viable
ALP is nonclassical. We also show that squeezing may be relevant on scales of
axion haloscopes, or within galactic solitonic cores. Conversely, our results
highlight the incompleteness and limitations of the typically employed
classical single field description of ALPs.
