  We investigate the creation and control of emergent collective behavior and
quantum correlations using feedback in an emitter-waveguide system using a
minimal model. Employing homodyne detection of photons emitted from a
laser-driven emitter ensemble into the modes of a waveguide allows to generate
intricate dynamical phases. In particular, we show the emergence of a
time-crystal phase, the transition to which is controlled by the feedback
strength. Feedback enables furthermore the control of many-body quantum
correlations, which become manifest in spin squeezing in the emitter ensemble.
Developing a theory for the dynamics of fluctuation operators we discuss how
the feedback strength controls the squeezing and investigate its temporal
dynamics and dependence on system size. The largely analytical results allow to
quantify spin squeezing and fluctuations in the limit of large number of
emitters, revealing critical scaling of the squeezing close to the transition
to the time-crystal. Our study corroborates the potential of integrated
emitter-waveguide systems -- which feature highly controllable photon emission
channels -- for the exploration of collective quantum phenomena and the
generation of resources, such as squeezed states, for quantum enhanced
metrology.
