Quantum fluctuations induce collective multi-phonons in finite Fermi liquids

We show that collective multi-phonon states in atomic nuclei emerge at high excitation energies when quantum fluctuations are included beyond the independent particle approximation. The quadrupole response of a nucleus is studied using an extension of the nuclear time-dependent density functional theory that mixes several many-body trajectories. While a single trajectory can account for the excitation of the first collective quantum, the second and the third quanta emerge due to the interference between trajectories. The collective spectrum, found as nearly harmonic, is in excellent agreement with the experimentally observed three quanta of the isoscalar giant quadrupole resonance in $^{40}$Ca. This study offers guidance for multi-phonon searches in other self-bound systems and demonstrates the resistance to internal excitation of finite Fermi liquids.