Phonons, quantized excitations of vibrational modes in crystals, bear resem- blance to photons, quantized excitations of electromagnetic fields. Both are bosons, and their textbook models have similar Hamiltonians. For harmonic phonons with linear forces, equations of motion are formulated as eigenvalue problems that give dispersions of frequency versus wavevector [1, 2]. Nonlinear forces and anharmonic potentials can be included with many-body perturbation theory [3–5], but the number of dispersions is retained. Exceptions are intrin- sic localized modes (ILM) [6–12], but there are different viewpoints about the experimental evidence for ILMs in crystals [13–15]. In the newer field of optome- chanics, tuning a laser across the resonant frequency of a cavity shows sidebands about the cavity resonance [16–23]. The underlying photon-phonon coupling in optomechanics suggests new features of anharmonic phonon-phonon coupling in crystals. Here we show such features in the phonon spectra of NaBr, using new methods for inelastic neutron scattering on single-crystals, and ab initio computa- tions of anharmonic lattice dynamics. Their physical origin is interpreted with a quantum Langevin model, with parallels to optomechanics. The transverse part of the new feature originates from phonon intermodulation between the trans- verse acoustic (TA) and transverse optical (TO) phonons. Quantum back action from the thermal bath broadens and redistributes the spectral weight of these intermodulation phonon sidebands (IPS). The partner lower sideband proves to be an ILM. These features of quantum anharmonicity offer a new probe of the quantum noise in optical materials. In the new upper sideband, the TA and TO modes should be entangled in the Einstein-Podolsky-Rosen sense.