Superradiance in dynamically modulated Tavis-Cumming model with spectral disorder

Superradiance is a cooperative phenomenon in quantum optical systems wherein the emission of photons from a quantum emitter is enhanced due to other quantum emitters coupling to the same electromagnetic mode. However, disorder in the resonant frequencies of the quantum emitters can perturb this effect. In this work, we study the interplay between superradiance, spectral disorder and dynamical modulation in a Tavis-Cumming model wherein all the emitters couple to a single resonant electromagnetic mode. As a consequence of the all-to-all coupling between the emitters, the presence of spectral disorder never prohibits the formation of a superradiant state over an extensive number of emitters. Furthermore, in such disordered systems, we show that a quantum control protocol modulating the resonant frequency of the optical mode leads to a multiplicative enhancement in the superradiance even in the limit of large number of emitters. Our results are relevant to experimental demonstration and application of superradiant effects in solid-state quantum optical systems such as color centers or rare-earth ions.