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Journal of the Optical Society of America B

Quantum trajectory theory of superradiant emission from randomly distributed atomic samples

Ryan Nowak, James Clemens

Published Mar 24, 2008• 6 citations
Publisher

Abstract

We consider the directed superradiant emission from a collection of N two-state atoms with arbitrary spatial locations within the framework of quantum trajectory theory and without a single-mode assumption. The formalism is developed around an unravelling of the master equation in terms of source mode quantum jumps. A modified boson approximation is made to treat the many-atom case, where it is found that strong directional superradiance occurs for a few thousand atoms, even with randomized atomic positions.

DOI
10.1364/josab.25.000564

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We consider the directed superradiant emission from a collection of N two-state atoms with arbitrary spatial locations within the framework of quantum trajectory theory and without a single-mode assumption. The formalism is developed around an unravelling of the master equation in terms of source mode quantum jumps. A modified boson approximation is made to treat the many-atom case, where it is found that strong directional superradiance occurs for a few thousand atoms, even with randomized atomic positions.
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We study collective spontaneous emission from arbitrary distributions of N two-state atoms using quantum trajectory theory and without an a priori single-mode assumption. Assuming a fully excited initial state, we calculate the angular distribution of the average integrated intensity. We investigate the dependence of the angular distribution of emission on the geometry of the atomic distribution. The formalism is developed around an unravelling of the master equation in terms of source mode quantum jumps. A modified boson approximation is made to treat the many-atom case, where it is found that strong directional superradiance occurs for a few hundred to a few thousand atoms. In order to illustrate important differences between our model and single-mode models we consider shot-to-shot intensity fluctuations and angular correlations in the emitted intensity.
We study collective spontaneous emission from a linear array of N two-state atoms using quantum trajectory theory and without an a priori single-mode assumption. Assuming a fully excited initial state, we calculate the angular distribution of the kthk\mathrm{th}kth emitted photon, k=1,…,N.k=1,\dots{},N.k=1,…,N. We investigate the evolution of the distribution from a dipole radiation pattern for the first photon emission to a distribution characteristic of directional superradiance. The formalism is developed around an unravelling of the master equation in terms of source-mode quantum jumps. Exact calculations for 11 and fewer atoms do not show directional superradiance, but are characterized by delayed (subradiant) photon emissions directed along the axis of the linear array. A modified boson approximation is made to treat the many-atom case, where it is found that strong directional superradiance occurs for a few hundred atoms; the decay of subradiant excitations is preserved in the tail of the superradiant pulse.
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The cooperative spontaneous emission from a system of NNN identical two-level atoms, excited arbitrarily and interacting with a single mode of radiation, is studied by using the Bonifacio-Schwendimann-Haake approach. The evolution of the probability distribution of the atomic system is considered as a Markov process described by a time-evolution matrix (TEM). The exact analytic expressions for the elements of this TEM are obtained by solving the superradiance master equation. It is proved that the TEM satisfies the normalization condition and the Chapman-Kolmogorov equation as required. The exact general formulas for the expectation values of various physical observables, expressed in terms of an arbitrary initial distribution, are obtained. Finally, these results are applied to a specific example, the superradiant initial state.