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Physical Review A

Spontaneous emission by a system ofNtwo-level atoms in terms of the SU(2)-group representations

M. Kozierowski, A. A. Mamedov, S. M. Chumakov

Published Aug 1, 1990• 41 citations
Publisher

Abstract

We consider cooperative spontaneous emission by an assembly of N two-level atoms immersed in a high-Q single-mode cavity, when s (s\ensuremath{\ll}N) atoms are initially excited. The atoms are noninteracting with each other except via the action of the electromagnetic field. The eigenvalues of the system and the time development of the mean energy of the atomic subsystem are presented in the form of power series in the parameter \ensuremath{\epsilon}=(N-s/2+1/2${)}^{\mathrm{\ensuremath{-}}1}$ using the SU(2)-group-representation technique.

DOI
10.1103/physreva.42.1762

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We consider cooperative spontaneous emission by an assembly of N two-level atoms immersed in a high-Q single-mode cavity, when s (s\ensuremath{\ll}N) atoms are initially excited. The atoms are noninteracting with each other except via the action of the electromagnetic field. The eigenvalues of the system and the time development of the mean energy of the atomic subsystem are presented in the form of power series in the parameter \ensuremath{\epsilon}=(N-s/2+1/2)\ensuremath−1{)}^{\mathrm{\ensuremath{-}}1})\ensuremath−1 using the SU(2)-group-representation technique.
Applying a perturbation method, constructed in terms of SU(2) group representations, we study spontaneous emission of a system of N identical two-level atoms immersed in a single-mode ideal cavity with s atoms initially inverted. For the cases s\ensuremath{\ge}3, characterized by nonequidistant spectra of the eigenvalues of the Hamiltonian, the phenomenon of collective collapses and revivals manifests itself. For s=3 the approximate solution is compared with the exact one and the limit of good applicability of our method is established.
The problem of a single two level atom in its excited state, placed in a cavity in which no photons are present initially, and interacting with N modes of the electromagnetic field is solved exactly in the electric dipole, rotating wave approximation. Expressions for the energy eigenvalues and eigenvectors are derived, and an exact representation for the time dependent wavefunction of the system is given. These quantities are evaluated analytically for N=1,2 and 3, and the time dependent properties of the system for these values of N are investigated and discussed.
NNN two-level "atoms" are considered in interaction with a single-mode resonant electromagnetic field. The exact solution is given nonrelativistically for all times for the case of spontaneous emission, when only one atom is initially excited. The solution is given for the general case of the NNN atoms in inequivalent mode positions.
We investigate (non-relativistic) atomic systems interacting with quantum electromagnetic field (QEF). The resulting model describes spontaneous emission of light from a two-level atom surrounded by various initial states of the QEF. We assume that the quantum field interacts with the atom via the standard, minimal-coupling Hamiltonian, with the A2 term neglected. We also assume that there will appear at most single excitations (photons). By conducting the analysis on a general level we allow for an arbitrary initial state of the QEF (which can be for instance: the vacuum, the ground state in a cavity, or the squeezed state). We derive a Volterra-type equation which governs the time evolution of the amplitude of the excited state. The two-point function of the initial state of the QEF, integrated with a combination of atomic wavefunctions, forms the kernel of this equation.