Superradiance and subradiance in extended atomic ensembles

Superradiance is central to studies of collective behaviour in areas of quantum optics, cavity quantum electrodynamics, laser physics and Bose-Einstein condensation. Superradiance and subradiance are manifestations of coherent quantum phenomena for large ensembles of sources. We have studied the angular dependence and time-resolved build-up of superradiance without the commonly used priori single-mode assumption by unravelling of the master equation in terms of source-mode quantum jumps. We have shown that the development of directional emission arises from the competition between many collective source-modes. Starting from an inverted system, the first emitted photon on average follows the dipole emission pattern, but in subsequent emissions the modes with the highest emission rates begin to dominate via the process of stimulated emission. This process continue until complete energy depletion occur with some trapped energy in subradiant modes decaying in the long time limit (in the tail of the emission pulse). Superradiant pulse develops provided that there is enough energy in the system to feed the mode competition. Therefore, together with the energy content, the rates and directionality of collective source-modes are determine the characteristics of superradiant and subradiant emissions. To aid the analysis of superradiant dynamics, we have characterised the rates and directionality of collective source-modes for many extended systems deriving fundamental relationships between discrete and continuous extended sources with a well defined polarisation.

1. J. P. Clemens, L. Horvath, B. C. Sanders, and H. J. Carmichael, Journal of Optics B: Quantum and Semiclassical Optics, 6 (8), S736 (2004).
2. J. P. Clemens, L. Horvath, B. C. Sanders, and H. J. Carmichael, Physical Review A, 68, 023809 (2003).
3. L. Horvath, J. P. Clemens, B. C. Sanders, and H. J. Carmichael, Superradiant Emission Modes for Extended Finite Sources, unpublished.

The animation shows the development of superradiance pulse from an ensemble of identical two-level sources arranged in a rectangular lattice (9x9x162). In this lattice, the separation between next neighbours is set to the third of the resonance wavelength and all the dipole moments of the sources aligned perpendicular to the major (or longest) axis of the lattice. Starting from an inverted system, vacuum fluctuations initiate the decay process. Initially, the sources are uncorrelated and the emission of the first photon follows on average the dipole emission pattern. As the decay continues, the competition between collective emission modes breaks this pattern because more energy is channeled into modes that have high decay rates via the process of stimulated emission. The dipole pattern develops into two emission cones with holes (along the major axis of the lattice) in their centre as shown by the animation. These holes indicate the directionality of subradiant modes which fire along the major axis of the lattice. The emission process continues until all the stored energy from the system is depleted, returning the system to its ground energy state.