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Journal of Physics B Atomic Molecular and Optical Physics

Polarization properties of superradiance from levels with hyperfine structure

Решетов Владимир Александрович

Published May 14, 1995• 1 citation
Publisher

Abstract

The equations describing the evolution during the linear-emission period of the electric field of superradiance formed by transitions with partially or totally resolved hyperfine structure are obtained in a semiclassical approximation in the case of arbitrary values of electronic angular momenta of the levels and nuclear spin. These equations are used to analyse the polarization properties of superradiance from the levels initially excited from the ground state by the ultra-short linearly polarized laser pulses with small area.

DOI
10.1088/0953-4075/28/9/024

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The equations describing the evolution during the linear-emission period of the electric field of superradiance formed by transitions with partially or totally resolved hyperfine structure are obtained in a semiclassical approximation in the case of arbitrary values of electronic angular momenta of the levels and nuclear spin. These equations are used to analyse the polarization properties of superradiance from the levels initially excited from the ground state by the ultra-short linearly polarized laser pulses with small area.
The polarization properties and the temporal shapes of the super-radiance pulses formed on degenerate levels are studied theoretically in a semiclassical approximation. The dependence of the super-radiance pulse polarization on the values of the total angular momenta of resonant levels and on the polarization and area of the pumping pulse is examined in detail. Non-linear equations describing the temporal shapes of the super-radiance pulses with different polarizations are obtained. Some examples with low values of angular momenta of the levels are discussed. It is shown that, in general, the temporal shape of the super-radiance pulse differs from hyperbolic secant.
The two approaches to the description of superradiance polarization properties - semiclassical and quantum - are compared. It is shown that both approaches predict the same polarization of the superradiance pulse, except for the case of the initially symmetric state of the atomic system. In this latter case the superradiance is expected to be fully unpolarized in a quantum approach and fully polarized with the polarization vector varying randomly from pulse to pulse - in a semiclassical approach. So, the experimental study of polarization of superradiance from the atomic (molecular) level with zero total angular momentum (which ensures the symmetry of the atomic state regardless of the pumping process) will provide support to one of the two approaches.
Up to now, the problem of the influence of level degeneracy on superradiance has been neglected. We describe here a first approach to this problem, in the frame of "small system" quantum model, generalized to the case of a collection of atoms with two degenerate levels of angular momenta jjj and ${j}^{\ensuremath{'}}$ connected by an electric or magnetic dipole transition. The differences between this case and the well-known case of two (nondegenerate) level atoms are of two types. The first type is due to the competition between different transitions sharing a common state: superradiant emission on a transition inhibits or initiates superradiance on transitions with smaller transition probability, depending upon which state, upper or lower, is the common one. This effect does not come from the equality of the different wavelengths and would also appear with the same states even if the degeneracy were removed; its qualitative influence on the features of the superradiant pulse can be easily estimated. The second type of differences is quite specific to level degeneracy and consists in interferences between the transitions of the collective system having the same frequency and polarization. In analogy with the description of collections of two-level atoms as spin-\textonehalf{} systems, a group-theoretical description of the considered collection of atoms is found suitable; the problem of the determination of a basis of collective states and its group-theoretical implications are discussed; in particular, it is found that the isotropic character of spontaneous emission allows us to use tensorial formalism and simplifies the formal description of the problem.
A density-matrix approach is developed to provide a theoretical description of the intensity, angular distribution, and polarization of superradiative emission from an ensemble of many-electron atomic systems. The many-electron atomic systems are described as cooperatively interacting by means of forces that can be long range. Particular emphasis is given to the coherent excitation of the collective atomic-ensemble states, which may be produced by incident laser radiation. The initial excitation and spontaneous emission processes may be described as independent. Both frequency-domain and time-domain formulations of the density-matrix approach are developed. The collective atomic-ensemble states are specified in a detailed hyperfine representation, corresponding to successively coupling the individual hyperfine angular momenta F pertaining to the many-electron atoms. A less detailed fine-structure angular-momentum representation may also be used. In the density-operator approach, account can be taken of the coherent excitation of a particular subspace of the initial atomic-ensemble states. For a comprehensive and unified development of time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations, a reduced-density-matrix (quantum-open-systems) approach is introduced. The non-equilibrium atomic-ensemble-state kinetics and the homogeneous spectral-line shapes can thereby be systematically and self-consistently determined. The collective atomic-ensemble states may be obtained using a variety of different methods. These states can be determined using a dressed-state approach, in which the required states are calculated in the presence of an electromagnetic field.
The problem of superradiant emission from a small atomic system is treated under conditions in which the effects of inhomogeneous broadening are important, as in a solid. The treatment is semiclassical, with the assumption that all atoms see the same electromagnetic field. A set of coupled integrodifferential equations is obtained characterizing the state of each atom of resonant frequency \ensuremath{\omega} at time ttt. It is found that, in general, atoms of different frequencies evolve differently in time, whether or not they start from the same initial state. The effect of the inhomogeneous broadening is generally to delay the onset and to reduce the amplitude of the superradiant pulse. Some effects of inhomogeneous broadening are manifest even when the inhomogeneous lifetime is much longer than the usual superradiance time. When the atomic system starts in the ground state and is then exposed to a coherent excitation pulse, superradiant effects can appear even when the inhomogeneous lifetime is very short compared with the usual superradiance time.