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We consider using spontaneous light scattering by terahertz-frequency phonon polaritons as a source of quantum-correlated pairs of optical and terahertz photons. Frequency-angular distributions of the optical Stokes and anti-Stokes signal photons are measured in the wide range of the nonlinear crystal temperatures, 4 K - 300 K, and analyzed using the nonlinear Kirchhoff law. It is shown that cryogenic cooling enables to suppress contributions from thermal field fluctuations and to detect pure contributions from the quantum zero vacuum field fluctuations.