Cooperative spontaneous emission of N atoms: Many-body eigenstates, the effect of virtual Lamb shift processes, and analogy with radiation of N classical oscillators

We consider collective emission of a single photon from a cloud of N two-level atoms (one excited, N-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 sp...

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2010-05, Vol.81 (5), Article 053821
Main Authors: Svidzinsky, Anatoly A., Chang, Jun-Tao, Scully, Marlan O.
Format: Article
Language:English
Subjects:
ANALYTICAL SOLUTION
ATOMIC AND MOLECULAR PHYSICS
ATOMS
BOSONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
EIGENFUNCTIONS
EIGENSTATES
EIGENVALUES
ELECTRONIC EQUIPMENT
ELEMENTARY PARTICLES
EMISSION
ENERGY LEVELS
ENERGY-LEVEL TRANSITIONS
EQUATIONS
EVOLUTION
FUNCTIONS
GROUND STATES
HARMONIC OSCILLATORS
INTEGRAL EQUATIONS
LAMB SHIFT
MANY-BODY PROBLEM
MASSLESS PARTICLES
MATHEMATICAL SOLUTIONS
MECHANICS
OSCILLATORS
PHOTON EMISSION
PHOTONS
QUANTUM MECHANICS
SPECTRAL SHIFT
STIMULATED EMISSION
SUPERRADIANCE
SYMMETRY
TRAPPING
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Summary:We consider collective emission of a single photon from a cloud of N two-level atoms (one excited, N-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 N classical harmonic oscillators.
ISSN:1050-2947
1094-1622
DOI:10.1103/PhysRevA.81.053821