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We study temporal oscillations, known as dynamical beats, developed by a propagating pulse due to its interaction with a near-resonant collective medium of $^{133}$Cs atoms randomly captured by a nanofiber-based optical lattice. A phenomenological theory provides an intuitive explanation and quantitative predictions, which are improved by an input-output theory considering multiple-scattering between the atoms. The results deepen our understanding of light propagation in waveguide QED, essential in time-frequency analysis and light engineering for probing, manipulating, and exploiting many-body quantum systems.

The many-body decay of extended collections of two-level systems remains an open problem. Here, we investigate whether an array of emitters coupled to a one-dimensional bath undergoes Dicke superradiance, a process whereby a completely inverted system synchronizes as it decays, generating correlations between emitters via dissipation. This leads to the release of all the energy in the form of a rapid photon burst. We derive the minimal conditions for the burst to happen as a function of the number of emitters, the chirality of the waveguide, and the single-emitter optical depth, both for ordered and disordered ensembles. Many-body superradiance occurs because the initial fluctuation that triggers the emission is amplified throughout the decay process. We show that this avalanche-like behavior leads to a dynamical spontaneous symmetry breaking, where most photons are emitted into either the left- or the right-propagating optical modes, giving rise to an emergent chirality. Superradiant bursts may be a smoking gun for the generation of correlated photon states of exotic quantum statistics. This physics can be explored in diverse setups, ranging from atoms close to nanofibers to superconducting qubits coupled to transmission lines., Comment: 13 pages, 7 figures