Here we present an approach to superradiance in dense atomic samples in the presence of dipole-dipole interactions. We have considered all-to-all interactions as a first step toward understanding the more complicated position-dependent interactions. In addition, we combine the Holstein-Primakoff and mean-field approximations, from which we derive master equations for both the strong- and weak-coupling regimes between the sample and the reservoir. We find that, in both cases, the emitted radiation exhibits striking features, with characteristic emission times much shorter and intensities much higher than those of Dicke superradiance. In particular, in the strong sample-reservoir coupling regime, a comb of superpulses emerges within an envelope whose characteristic emission time is significantly reduced and whose intensity is substantially enhanced relative to Dicke superradiance.

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• Quantum optics
• Atomic ensemble
• Dicke model
• Schroedinger equation
• Semiclassical methods
• Two-level models