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Journal of Physics B Atomic Molecular and Optical Physics

On the superradiance polarization: semiclassical and quantum approaches

Решетов Владимир Александрович

Published Jun 14, 1997• 0 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/30/11/005

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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.
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.
Describes a theoretical study of the polarisation properties of the superradiant light emitted on a j to j' transition between degenerate levels. Two specific orthogonal polarisation vectors are associated with each set of initial conditions and the corresponding field components are shown to evolve independently during the whole linear-emission period. Due to a quenching effect, the polarisation of the emitted light is predicted to be identical to one of the two specific polarisations of the superradiant system if the intensities of the two field components are not equal during this period. If, on the other hand, the two intensities remain equal, a spontaneous symmetry breaking is expected to occur and consequently the polarisation of the superradiant light is expected to vary randomly from pulse to pulse.
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.
Two-atom superradiance is studied for atoms having a J=0 ground state and a J=1 excited state. The atoms lie on the x-axis and are excited by a σ_{+}-polarized laser pulse propagating in the z-direction. We use two, complementary approaches to obtain the final angular momentum in the field, a source-field approach and a Schrodinger picture approach. Both approaches give identical answers, but it is necessary to include terms in both calculations that, at first glance, might not be expected to contribute. We show that, owing to an exchange between a state in which atom 1 is in its m=1 excited state and atom 2 is in its ground state to one in which atom 2 is in its m=-1 excited state and atom 1 in its ground state, the final angular momentum in the field is not necessarily equal to the initial angular momentum in the two-atom system. The missing angular momentum appears as orbital angular momentum of the two atoms.
A generalized master equation previously proposed to describe oscillatory superfluorescence is numerically solved in the case of strong ringing. When the atomic system is fully excited, anomalous fluctuations and large atom-field correlations make the time evolution of the mean quantities (e.g., number of photons, total population inversion) quantitatively different from those found in the semiclassical treatment. In particular, because of fluctuations, the minima of the radiation output are notably larger than zero. On the contrary, when the atomic system exhibits a sizable initial macroscopic polarization (superradiance), we find a remarkable non-Markoffian effect consisting of a sizable delay in the radiation emission. However, in such conditions all quantum effects disappear, as in the case of pure superradiance.
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.