  As one of the central topics in quantum optics, collective spontaneous
emission such as superradiance has been realized in a variety of systems. This
work proposes an innovative scheme to coherently control collective emission
rates via a self-interference mechanism in a nonlinear waveguide setting. The
self-interference is made possible by photon backward scattering incurred by
quantum scatterers in a waveguide working as quantum switches. Whether the
interference is constructive or destructive is found to depend strongly on the
distance between the scatterers and the emitters. The interference between two
propagation pathways of the same photon leads to controllable superradiance and
subradiance, with their collective decay rates much enhanced or suppressed
(also leading to hyperradiance or population trapping). Furthermore, the
self-interference mechanism is manifested by an abrupt change in the emission
rates in real time. An experimental setup based on superconducting transmission
line resonators and transmon qubits is further proposed to realize controllable
collective emission rates.
