  Spontaneous vibrational Raman scattering is a ubiquitous form of light-matter
interaction whose description necessitates quantization of the electromagnetic
field. It is usually considered as an incoherent process because the scattered
field lacks any predictable phase relationship with the incoming field. When
probing an ensemble of molecules, the question therefore arises: What quantum
state should be used to describe the molecular ensemble following spontaneous
Stokes scattering? We experimentally address this question by measuring
time-resolved Stokes--anti-Stokes two-photon coincidences on a molecular liquid
consisting of several sub-ensembles with slightly different vibrational
frequencies. When spontaneously scattered Stokes photons and subsequent
anti-Stokes photons are detected into a single spatiotemporal mode, the
observed dynamics is inconsistent with a statistical mixture of individually
excited molecules. Instead, we show that the data are reproduced if
Stokes--anti-Stokes correlations are mediated by a collective vibrational
quantum, i.e. a coherent superposition of all molecules interacting with light.
Our results demonstrate that the degree of coherence in the vibrational state
of the liquid is not an intrinsic property of the material system, but rather
depends on the optical excitation and detection geometry.
