  We study the far-from-equilibrium dynamical regimes of a many-body spin boson
model with disordered couplings relevant for cavity QED and trapped ions
experiments, using the discrete truncated Wigner approximation (DTWA). We focus
on the dynamics of spin observables upon varying the disorder strength and the
frequency of the photons, finding that the latter can considerably alter the
structure of the system's dynamical responses. When the photons evolve at a
similar rate as the spins, they can induce qualitatively distinct frustrated
dynamics characterized by either logarithmic or algebraically slow relaxation.
The latter illustrates resilience of glassy-like dynamics in the presence of
active photonic degrees of freedom, suggesting that disordered quantum many
body systems with resonant photons or phonons can display a rich diagram of
non-equilibrium responses, with near future applications for quantum
information science.
