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Physical Review A

Stochastic initiation of superradiance in a cavity: An approximation scheme within quantum trajectory theory

James Clemens, H. J. Carmichael

Published Jan 16, 2002• 21 citations
Publisher

Abstract

We investigate the stochastic initiation of superradiant emission from a collection of excited two-state atoms coupled through a low-Q cavity mode. Noncollective emission into other modes of the electromagnetic field is included, allowing us to describe the transition from predominantly noncollective to collective behavior as the number of atoms is increased. We examine the dependence of the photon statistics on the number of atoms and the ratio of collective to noncollective decay rates. Numerical results for a few to ${10}^{6}$ atoms are obtained using an approximation scheme developed within the framework of quantum trajectory theory. Results are compared with those for a pure collective emission process and an earlier treatment of noncollective effects.

DOI
10.1103/physreva.65.023815

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We investigate the stochastic initiation of superradiant emission from a collection of excited two-state atoms coupled through a low-Q cavity mode. Noncollective emission into other modes of the electromagnetic field is included, allowing us to describe the transition from predominantly noncollective to collective behavior as the number of atoms is increased. We examine the dependence of the photon statistics on the number of atoms and the ratio of collective to noncollective decay rates. Numerical results for a few to 106{10}^{6}106 atoms are obtained using an approximation scheme developed within the framework of quantum trajectory theory. Results are compared with those for a pure collective emission process and an earlier treatment of noncollective effects.
We study superradiance from a fully inverted medium in the presence of two channels for atomic relaxation. Spontaneous emission from individual atoms is included and competes with the collective emission responsible for superradiance. We compare exact results within the quantum trajectory formalism with a previous approximation [J. P. Clemens and H. J. Carmichael, Phys. Rev. A 65, 023815 (2002)] which neglects the reexcitation of an atom after it spontaneously emits. The approximation underestimates the decoherence during the second half of an emitted pulse.
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.
We investigate the emergence of cooperative radiation phenomena in ensembles of two-level atoms coupled to a lossy resonant cavity beyond the Markovian and mean-field approximations. By deriving a complete analytical solution for the two-emitter case and employing a numerically exact method for larger ensembles, we characterize the full transition from Markovian to non-Markovian collective dynamics for systems of up to 10310^3103 emitters. Our results reveal three distinct regimes: a Markovian phase exhibiting the standard superradiant burst, a non-Markovian phase featuring spontaneous superabsorption of the emitted field, and a critical regime marked by pulsed collective emission. We show that the critical spectral width separating these behaviors increases monotonically with the number of emitters, demonstrating that environmental memory effects can be enhanced by cooperativity. Finally, we find that the superradiant scaling of the peak intensity progressively degrades with increasing system size, approaching a subquadratic law in the limit of a perfect cavity. In this regime, spontaneous superabsorption emerges as a distinct manifestation of non-Markovian cooperativity.
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.
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 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 intensity, focusing on pencil- and disc-shaped samples. 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 with shot-to-shot fluctuations occurs for a few hundred to a few thousand atoms.