The choice of the wrong kernel for describing the cooperative effects in an ensemble of identical atoms, in most instances, leads to wrong predictions for the system's dynamics whether the system initially was excited weakly or nearly was inverted. In this Brief Report, using previously derived theoretical expressions, I compare the numerical values for the emission amplitude as a function of time for the complex exponential and the sine kernels for different-size spheres. The deviations found in the respective results show that, in general, the two kernels are not, as often claimed, up to a frequency shift in their spectra, interchangeable.The choice of the wrong kernel for describing the cooperative effects in an ensemble of identical atoms, in most instances, leads to wrong predictions for the system's dynamics whether the system initially was excited weakly or nearly was inverted. In this Brief Report, using previously derived theoretical expressions, I compare the numerical values for the emission amplitude as a function of time for the complex exponential and the sine kernels for different-size spheres. The deviations found in the respective results show that, in general, the two kernels are not, as often claimed, up to a frequency shift in their spectra, interchangeable.

Physical Review AJan 4, 20123 citations

Two-Level Atoms and Spontaneous Emission

H. J. Carmichael

Springer eBooksJan 1, 19994 citations

Superradiance from a cylindrically shaped cloud of N two-level atoms

Jamal T. Manassah

Using the eigenmodes of the scalar-photon kernel of interacting $N$ two-level atoms in a cylindrical configuration, I obtain the time dependence of the superradiant emission for this geometry in two cases of interest. In particular, I consider first the case when one or two eigenmodes dominate the system's dynamics for an inverted system which has been initially prepared in an isotropic state and show that for certain values of the radius of the cylinder ($r=m\ensuremath{\lambda},m \mathrm{integer}$) one obtains temporal modulation in the state function. In the second case of interest, I show that the angular distribution of the state function of a system initially prepared in a phased state appears to be chaotic; however, I show that this behavior is due to the high multiplicity of modes having close values for their amplification coefficients.Using the eigenmodes of the scalar-photon kernel of interacting $N$ two-level atoms in a cylindrical configuration, I obtain the time dependence of the superradiant emission for this geometry in two cases of interest. In particular, I consider first the case when one or two eigenmodes dominate the system's dynamics for an inverted system which has been initially prepared in an isotropic state and show that for certain values of the radius of the cylinder ($r=m\ensuremath{\lambda},m \mathrm{integer}$) one obtains temporal modulation in the state function. In the second case of interest, I show that the angular distribution of the state function of a system initially prepared in a phased state appears to be chaotic; however, I show that this behavior is due to the high multiplicity of modes having close values for their amplification coefficients.

Physical Review ANov 15, 20107 citations

Collective collapses and revivals in spontaneous emission of a partially inverted system of two-level atoms: Analytical solution

M. Kozierowski, S. M. Chumakov, J. ŚwiatłLowski +1 more

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.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.

Physical Review ADec 1, 199229 citations

Using the eigenmodes of the scalar-photon kernel of interacting

N

two-level atoms in a cylindrical configuration, I obtain the time dependence of the superradiant emission for this geometry in two cases of interest. In particular, I consider first the case when one or two eigenmodes dominate the system's dynamics for an inverted system which has been initially prepared in an isotropic state and show that for certain values of the radius of the cylinder ($r=m\ensuremath{\lambda},m \mathrm{integer}$) one obtains temporal modulation in the state function. In the second case of interest, I show that the angular distribution of the state function of a system initially prepared in a phased state appears to be chaotic; however, I show that this behavior is due to the high multiplicity of modes having close values for their amplification coefficients.