Exact Analytical Treatment of Collectively Pumped Dicke Superradiant Systems

Solving the dynamics of many-body open systems is usually intractable due to the exponential scaling of the Hilbert space. An important exception is the case of Dicke superradiance, in which the full permutational symmetry of the system leads to a significant reduction in complexity, thus admitting an exact solution. In this work, we present an analytical framework to describe the dynamics of an ensemble of collectively pumped two-level emitters undergoing Dicke superradiance. We use a quantum jump unraveling of the Lindblad master equation to derive exact expressions for the system's time evolution, without resorting to mean-field or other approximate methods. This work establishes rigorous mathematical tools to analytically model superradiant lasing. Our solution suggests the possibility of fully analytical solutions for a broader class of open quantum system dynamics problems.