Scaling theory of decoherence in Dicke superradiance

How does local decoherence—specifically spontaneous emission and dephasing—compete with collective emission to influence the scaling of many-body coherence in Dicke superradiance? The study aims to determine the conditions under which the characteristic N^2 intensity scaling of superradiance is preserved or suppressed as the number of emitters (N) increases.

The authors develop an analytical scaling theory based on the Lindblad master equation for N two-level emitters. By utilizing the permutational symmetry of the system, they map the dynamics onto the 'Dicke triangle' (a representation of total spin states). They derive mean-field equations of motion for the intensive variables in the large-N limit and identify dimensionless scaling variables that govern the transition between different emission regimes.

The study identifies three distinct scaling regimes for the peak intensity: a fully collective regime (I ~ N^2), a partially collective regime (I ~ N^beta, where 1 < beta < 2), and an independent-emitter regime (I ~ N). The transition between these regimes is controlled by two scaling variables: the dephasing rate (g_xi = xi / (N * Gamma)) and the spontaneous emission rate (g_gamma_bar = gamma * ln(N) / (N * Gamma)). Notably, the boundary at beta = 2 represents a continuous phase transition in a transient observable, rather than a steady-state property. The authors show that increasing N does not automatically guarantee N^2 scaling, as the relative influence of local decoherence can grow depending on the specific experimental platform.

This work provides a rigorous framework for interpreting experimental results in quantum optics and many-body physics. It highlights that the thermodynamic limit of open quantum systems is highly sensitive to how local and collective process rates scale with system size. This is crucial for designing quantum technologies, as it demonstrates that simply increasing the number of emitters is insufficient to maintain collective effects if the decoherence environment is not properly managed.