  Quantum fluids of light are an emerging tool employed in quantum many-body
physics. Their amazing properties and versatility allow using them in a wide
variety of fields including gravitation, quantum information and simulation.
However the implications of the quantum nature of light in the nonlinear
optical propagation are still missing many features. We theoretically predict
classical spontaneous squeezing of a photon fluid in a nonlocal nonlinear
medium. By using the so called Gamow vectors, we show that the quadratures of a
coherent state get squeezed and that a maximal squeezing power exists. Our
analysis holds true for temporal and spatial optical propagation in highly
nonlocal regime. These results open a new scenario in quantum photon fluids and
may lead to novel applications in fields like metrology and analogues of
quantum gravity.
