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Journal of Modern Optics

Correlated spontaneous emission on the Danube

Eyob Alebachew Sete, Anatoly A. Svidzinsky, Hichem Eleuch, Zhen Yang, Robert D. Nevels, Marlan O. Scully

Published Mar 1, 2010• 55 citations
Publisher

Abstract

We consider collective spontaneous emission from an ensemble of N identical two-level atoms prepared by absorption of a single photon–a.k.a. single photon Dicke superradiance. We discuss dynamical properties of superradiance for small (R ≪ λ) and large (R ≫ λ) atomic cloud. Moreover, we address the effects of virtual processes on collective decay rate and Lamb shift. It turns out that virtual processes lead to relatively small yet interesting effects on the time evolution of a rapidly decaying state. However, such processes substantially modify the dynamics of trapped states by bringing in new channels of decay.

DOI
10.1080/09500341003605445

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We consider collective spontaneous emission from an ensemble of N identical two-level atoms prepared by absorption of a single photon–a.k.a. single photon Dicke superradiance. We discuss dynamical properties of superradiance for small (R ≪ λ) and large (R ≫ λ) atomic cloud. Moreover, we address the effects of virtual processes on collective decay rate and Lamb shift. It turns out that virtual processes lead to relatively small yet interesting effects on the time evolution of a rapidly decaying state. However, such processes substantially modify the dynamics of trapped states by bringing in new channels of decay.
We consider collective emission of a single photon from a cloud of NNN two-level atoms (one excited, $N\ensuremath{-}1$ ground state). For a dense cloud the problem is reduced to finding eigenfunctions and eigenvalues of an integral equation. We discuss an exact analytical solution of this many-atom problem for a spherically symmetric atomic cloud. Some eigenstates decay much faster then the single atom decay rate, while the others undergo very slow decay. We show that virtual processes yield a small effect on the evolution of rapidly decaying states. However, they change the long time dynamics from exponential decay into a power-law behavior which can be observed experimentally. For trapped states virtual processes are much more important yielding additional decay channels which results in a slow decay of the otherwise trapped states. We also show that quantum mechanical treatment of spontaneous emission of weakly excited atomic ensemble is analogous to emission of NNN classical harmonic oscillators.
We present analytical solutions for the evolution of collective states of N atoms. On the one hand is a (timed) Dicke state prepared by absorption of a single photon and exhibiting superradiant decay. This is in strong contrast to evolution of a symmetric Dicke state which is trapped for large atomic clouds. We show that virtual processes yield a small effect on the evolution of the rapidly decaying timed Dicke state. However, they change the long time dynamics from exponential decay into a power-law behavior which can be observed experimentally. For trapped states virtual processes are much more important and provide new decay channels resulting in a slow decay of the otherwise trapped state.
The collective Lamb shift and associated radiative decay of a large cloud of radius R containing N atoms uniformly excited by one photon of wavelength lambda is analyzed. It is shown that the time evolution of the symmetric state prepared by single photon absorption in the limit R>>lambda is similar to that encountered in the Dicke limit of small sample (R<<lambda) superradiance. The theory includes virtual (counterrotating) terms naturally and thus provides a simple calculation of the collective Lamb shift of a single Dicke state.
We study the correlated spontaneous emission from a dense spherical cloud of N atoms uniformly excited by absorption of a single photon. We find that the decay of such a state depends on the relation between an effective Rabi frequency Omega proportional square root N and the time of photon flight through the cloud R/c. If OmegaR/c<1 the state exponentially decays with rate Omega(2)R/c and the state lifetime is greater than R/c. In the opposite limit OmegaR/c>>1, the coupled atom-radiation system oscillates between the collective Dicke state (with no photons) and the atomic ground state (with one photon) with frequency Omega while decaying at a rate c/R.
The collective nature of light emission by atomic ensembles yields fascinating effects such as superradiance and radiation trapping even at the single-photon level.Light emission is influenced by virtual transitions and the collective Lamb shift which yields peculiar features in temporal evolution of the atomic system.We study how two-dimensional atomic structures collectively emit a single photon.Namely, we consider spherical, cylindrical, and spheroidal shells with two-level atoms continuously distributed on the shell surface and find exact analytical solutions for eigenstates of such systems and their collective decay rates and frequency shifts.We identify states which undergo superradiant decay and states which are trapped and investigate how size and shape of the shell affects collective light emission.Our findings could be useful for quantum information storage and the design of optical switches.
The collective nature of light emission by atomic ensembles yields fascinating effects such as superradiance and radiation trapping even at the single-photon level. Light emission is influenced by virtual transitions and the collective Lamb shift which yields peculiar features in temporal evolution of the atomic system. We study how two-dimensional atomic structures collectively emit a single photon. Namely, we consider spherical, cylindrical, and spheroidal shells with two-level atoms continuously distributed on the shell surface and find exact analytical solutions for eigenstates of such systems and their collective decay rates and frequency shifts. We identify states which undergo superradiant decay and states which are trapped and investigate how size and shape of the shell affects collective light emission. Our findings could be useful for quantum information storage and the design of optical switches.