Influence of dipole-dipole interactions on superradiance

Superradiance, known as the cooperative spontaneous emission of a
directional light pulse by excited atoms placed in vacuum, has recently
regained attention in the context of photon localization [1] and single
photon cooperative emission [2]. The dissipative dynamics of the atoms
is known to depend dramatically on the ratio between the typical inter-
atomic distance and the atomic transition wavelength, notably because
of dipole-dipole interactions [3]. In this work, we study the effects of
these interactions on superradiance as in [4] by solving numerically the
corresponding master equation. In particular, by averaging over many
realizations of the randomly distributed atomic positions, we show that
the decay of the radiated energy pulse height with the intensity of the
dipolar coupling follows a power law.
[1] E. Ackermans, A. Gero & R. Kaiser, Phys. Rev. Lett. 101, 103602
(2008).
[2] R. Friedberg & J. T. Manassah, J. Phys. B 43, 035501 (2010).
[3] M. Gross & S. Haroche, Physics reports 93, 301-396 (1982).
[4] B. Coffey & R. Friedberg, Phys. Rev. A 17, 1033 (1978).