Angular Momentum Fluctuations in the Phonon Vacuum of Symmetric Crystals

Although time-reversal and inversion symmetry constrain the angular momentum of each phonon mode to vanish, we show that the vacuum state of crystals with such symmetries can, nevertheless, exhibit finite angular momentum fluctuations, which persist at finite temperature. These fluctuations arise from quantum coherence between nondegenerate modes with noncollinear polarizations and are encoded in the off-diagonal components of the angular momentum operator. Their origin lies in the noncommutativity between the phonon Hamiltonian and angular momentum, which enables time-dependent rotational dynamics even in symmetric vacua. Using a minimal model, we provide an intuitive picture of this phenomenon in terms of beating between linearly polarized modes, which generates a finite instantaneous angular momentum while remaining symmetry forbidden in the mean. We further show that these vacuum fluctuations give rise to distinct finite-frequency spectral signatures and outline a concrete route for their detection using time-resolved spectroscopic probes sensitive to lattice polarization and symmetry. Our results identify a previously unexplored regime of lattice dynamics, revealing that even the symmetric phonon vacuum can harbor structured, dynamical angular-momentum correlations.