Non-Dicke decay in a small spherical sample with radially varying density

Abstract

It is a familiar fact that, in an isolated sphere or ellipsoid of uniform polarization density, the electrostatic field also is uniform. Because of this, the state of uniform polarization in a spherical sample of uniformly distributed two-level atoms is an eigenmode of the coherent decay process in the limit of a small radius compared to the resonant wavelength of a single atom. Consequently, in this special geometry, the Dicke picture of uniform exponential decay should hold. In nonspheroidal geometries or in spherical geometries with nonuniform atomic density, the decay should be more complicated. Here, we find the characteristic equations that determine the eigenmodes of the Lienard-Wiechert interaction for a partly hollowed sphere of identical two-level atoms in two different radial configurations. We show that the Dicke picture for emission from a coherently prepared sample does not correctly describe the system's dynamics even when we take the radius of the sphere to be much smaller than the radiation wavelength.

Electrostatic model of coherent decay in a small spherical sample of two-level atoms of radially varying density

“…We have recently presented [1] a study of coherent radiative emission from a small cloud (radius resonant wavelength) of identical two-level atoms, with spherical symmetry but strong radial variation of density. The purpose of this was to explore the relevance, to a small sample, of the Dicke picture [2] of coherent decay.…”

“…[1] was to show by explicit calculation that this exception no longer holds in a sphere with strongly varying atomic density. We studied two configurations: "shellplus-hollow" consisting of a spherical shell of arbitrary thickness and uniform density surrounding a spherical hollow with no matter, and "shell-plus-core" in which there is an additional spherical core, of the same density as the shell, centered within the hollow.…”

“…[1] are in principle applicable to any value of k 0 R, the numerical algorithms used become unreliable when k 0 R is extremely small. Therefore, we carried out the calculations at k 0 R = 0.05.…”

Effect of atomic distribution on cooperative spontaneous emission

“…The simplest theoretical model is the two-atom system [2][3][4][5], where the dependence of collective decay rate and Lamb shift on the distance is clearly demonstrated. For the N -atom system, several models, such as atomic clouds with spherical, cubic and slab-shaped geometry, or atoms arranged as a straight line, have been studied with different approaches [6][7][8][9][10][11][12]. The manipulations of cooperative spontaneous emission can realize many interesting behaviors and potential applications [13][14][15][16].…”

“…In most of the previous papers on the cooperative spontaneous emission, the details of atomic positions are ignored and an average interatomic distance [11][12][13][14][15][16][17][18] or the continuum approximation [6][7][8][9][10][19][20][21][22][23][24][25][26][27][28][29][30][31] (sums over atoms replaced by integrals, actually, which is equivalent to the distance average) is taken. Furthermore, in most of recent papers about single-excitation cooperative spontaneous emission, the scalar photon theory which ignores the polarization and vector character of the field has been applied [20][21][22][23][24][25][26][27][28][29][30].…”