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Physical Review A

Large swings in the forward-backward super-radiant emission direction from a nearly inverted ensemble of a three-level cascade system

Jamal T. Manassah

Published Feb 16, 2016• 1 citation
Publisher

Abstract

I show unambiguously that, in a slab geometry, the direction of emission of the super-radiant pulse from the lower two levels' transition in an ensemble of a three-level cascade homogeneously broadened atomic system, which was initially prepared in a nearly fully inverted coherent state, exhibits high sensitivity to the value of the initial atomic population for the case that the slab thickness is equal to $n{\ensuremath{\lambda}}_{0}/2$ ($n$ is an integer and ${\ensuremath{\lambda}}_{0}$ is the wavelength of the atomic transition). Specifically, I compute, in this regime, the swings in the ratio of the forward over backward fluxes for both transitions as a function of the initial population of the highest energy level.

DOI
10.1103/physreva.93.023820

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I show unambiguously that, in a slab geometry, the direction of emission of the super-radiant pulse from the lower two levels' transition in an ensemble of a three-level cascade homogeneously broadened atomic system, which was initially prepared in a nearly fully inverted coherent state, exhibits high sensitivity to the value of the initial atomic population for the case that the slab thickness is equal to n\ensuremathλ0/2n{\ensuremath{\lambda}}_{0}/2n\ensuremathλ0​/2 (nnn is an integer and \ensuremathλ0{\ensuremath{\lambda}}_{0}\ensuremathλ0​ is the wavelength of the atomic transition). Specifically, I compute, in this regime, the swings in the ratio of the forward over backward fluxes for both transitions as a function of the initial population of the highest energy level.
Using eigenmode analysis I calculate in the linear regime the emission characteristics from a slab of two-level resonant atoms excited by a delta-pulse propagating normal to the surface of the slab. I show that the qualitative features of the emitted spectra in the forward and backward directions to be different from each other; I also find the effects of the total linewidth of the resonance line and of the deviation in the spatial periodicity of the initial atomic polarization from k 0, where k 0 = ω0/c and ω0 is the two level resonant frequency, on the spectra. The dominant spatial mode of the system is identified as the key parameter for determining the forward emission spectral width.
Previous numerical work on the spatiotemporal distributions of the atomic polarization and of the difference in levels population of a one-dimensional system of two-level atoms initially inverted strongly suggested that the dynamics of the slab atomic ensemble in the linear regime of superradiance may best be treated by an eigenmode analysis. This method proved effective in obtaining both the time dependence of the atomic polarization and the spectral distribution of the emitted radiation from the slab in a number of physically interesting problems in the linear regime. In the present paper, I use the eigenfunction expansion technique to reduce the Maxwell-Bloch system of partial differential equations into a system of coupled first-order ordinary differential equations whose solutions clearly detail the contributions of the different modes to the system dynamics in the nonlinear regime of superradiant emission. I compute also the delay in time of the peak of the superradiant burst and its magnitude as functions of the ratio of the longitudinal decay rate to the transverse decay rate of the system.
We present a theory of cascade emission from an array of NNN fixed, ``three-level'' atoms. The total angular momentum of the ground state of each atom is J=0J=0J=0, that of the intermediate state is J=1J=1J=1, and that of the upper state is J=0J=0J=0. The atoms are prepared in a spatially phased superposition of their ground and upper states, collectively sharing a single excitation. We calculate the time-integrated, joint probability distribution for radiation to be emitted in a given direction with a given polarization on each transition and use this joint probability distribution to calculate the time-integrated intensity emitted on each transition. The dipole-dipole interaction between the atoms is taken into account. Analytic expressions are obtained for two atoms and the calculation is then extended formally to an ensemble of NNN atoms at arbitrary positions. As expected, the radiation emitted on the upper transition is unpolarized and isotropic. However, somewhat surprisingly, we find that for excitation by counterpropagating fields and for nearly equal ground to intermediate and intermediate to upper level transition frequencies, the radiation on the lower transition is also isotropic and unpolarized, provided the atoms are prepared in a fully symmetric state. We also establish conditions for which there can be a phase-matched enhancement of the joint probability density for specific directions of emissions on the upper and lower transitions.
We analyze the temporal development of a seed signal propagating in an ensemble of three-level atoms initially pumped by a two- photon excitation pulse. In an incoherently prepared system, the medium acts as a two-level system. Such a system is scale- invariant and therefore its dynamics are uniquely determined by the value of (alpha) L. On the other hand, a coherently prepared system is not scale invariant, leading to more complicated dynamics. We show that at low optical gain the amplification is reduced when the pumping is coherent. We further show that at high inversion there is an exponential increase in the radiation emitted from the lower transition in an initially prepared coherent system.
The coherent coupling of atomic levels under the action of driving electromagnetic fields is known to create unusual and interesting effects, such as the well-known population trapping phenomenon and subnatural line narrowing. In this paper we discuss two alternative configurations of three-level atoms, the cascade model and the inverted-V (lambda) model, in an effort to provide alternative options for experimental tests. In both cases we focus on the fluorescent emission spectrum of atom driven by two resonant fields and on the absorption spectrum of a weak probe passing through a gas in such a driven system. Subnatural line narrowing can be obtained from the cascade system but not from the lambda system. The lambda system, however, is characterized by strong population trapping so that it is not suitable for fluorescence studies (except out of resonance) because of its strongly reduced emission rate. The absorption spectrum of a weak probe displays gain features under high field conditions which suggest that useful amplification of a probe or laser-like emission should be possible over appropriate frequency ranges. We give a physical interpretation of the origin of the gain and explain why that in the case of a lambda system, but not a cascade system, steady-state population inversion can be obtained between both excited states relative to the lowest state of the atom. We also discuss the effect of Doppler broadening on the predicted emission and absorption lineshapes.
The effect of resonance reabsorption of fluorescent radiation on the spectral distribution has been considered as early as 1913 by Laudenburg and Reivhe [1]. Schein [2] and Zemansky [3] recognized that the reabsorption causes a broadening of the light emitted by resonance lamps. \n \nIn this note we report an experimental and theoretical study of the complementary effect, i.e., of resonance radiation originating in a system in which the population of the upper level of the resonance transition is made to exceed that of the lower one (inverted population system).