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Journal of Physics B Atomic and Molecular Physics

Superradiance theory and random polarisation

A. Crubellier, Sylvain Liberman, P. Pillet

Published Sep 28, 1986• 19 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/19/18/025

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Level-degeneracy effects in superradiance theory

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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 $j$ 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.

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Superradiance and subradiance. IV. Atomic cascades between degenerate levels

A. Crubellier, D Pavolini

For pt.III see ibid., vol.20, p.971 (1987). This paper is the fourth in a series devoted to the theoretical study of subradiance, i.e. of the cooperative inhibition of spontaneous emission. It first describes how the main results of the first paper have been developed in the general case of j to j' transitions between degenerate levels. In particular, the link between statistical mixing and symmetry properties is now derived in the general case of n-level atoms. The authors also explain how these results have allowed them to conceive the experiment which has recently provided the first evidence for the subradiance phenomenon, in the case of the 3 / 2 to 1 / 2 to 1 / 2 cascade of atomic gallium. The specific influence of the degenerate transitions which are associated with the Zeeman transitions of same polarisation is then discussed in a simplified example. Numerical simulations corresponding to the case of the experiment and to similar cases are finally presented and analysed.

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Superradiance and subradiance. II. Atomic systems with degenerate transitions

A. Crubellier, D Pavolini

For pt.I see ibid., vol.18, p.3811 (1985). This paper is the second of a theoretical study of subradiance, i.e. of the cooperative inhibition of spontaneous emission by a destructive interatomic interference, a phenomenon which has recently been observed. It is devoted to the particular case of atomic systems with degenerate transitions, i.e. with several transitions of the same frequency and the same polarisation. The interatomic interference which then occurs between the different transitions is responsible, when destructive, for a new sort of subradiance. The phenomenon is studied for a few typical level configurations, using both quantum mechanical and semiclassical models. The first example concerns a four-level configuration with two transitions of the same frequency and polarisation. The other examples concern three-level configurations with a degenerate transition; in the case of the 'degenerate' cascade, new superradiant beats and subradiance effects are predicted.

Journal of Physics B Atomic and Molecular Physics•Jul 28, 1986•29 citations
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.
The authors report on an experimental study of intensity and delay fluctuations for a two-level system by analysing stochastic distribution of the polarisation of superradiant pulses emitted on the transition 6p 2 P 1 /2 to 6s 2 S 1/2 of rubidium atoms. They develop a theoretical interpretation of their results. Finally, use of these properties of polarisation fluctuations has permitted one to study the very beginning of the superradiant emission and to give a new estimate of the so-called 'tipping angle'.
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.
For pt.III see ibid., vol.20, p.971 (1987). This paper is the fourth in a series devoted to the theoretical study of subradiance, i.e. of the cooperative inhibition of spontaneous emission. It first describes how the main results of the first paper have been developed in the general case of j to j' transitions between degenerate levels. In particular, the link between statistical mixing and symmetry properties is now derived in the general case of n-level atoms. The authors also explain how these results have allowed them to conceive the experiment which has recently provided the first evidence for the subradiance phenomenon, in the case of the 3 / 2 to 1 / 2 to 1 / 2 cascade of atomic gallium. The specific influence of the degenerate transitions which are associated with the Zeeman transitions of same polarisation is then discussed in a simplified example. Numerical simulations corresponding to the case of the experiment and to similar cases are finally presented and analysed.
For pt.I see ibid., vol.18, p.3811 (1985). This paper is the second of a theoretical study of subradiance, i.e. of the cooperative inhibition of spontaneous emission by a destructive interatomic interference, a phenomenon which has recently been observed. It is devoted to the particular case of atomic systems with degenerate transitions, i.e. with several transitions of the same frequency and the same polarisation. The interatomic interference which then occurs between the different transitions is responsible, when destructive, for a new sort of subradiance. The phenomenon is studied for a few typical level configurations, using both quantum mechanical and semiclassical models. The first example concerns a four-level configuration with two transitions of the same frequency and polarisation. The other examples concern three-level configurations with a degenerate transition; in the case of the 'degenerate' cascade, new superradiant beats and subradiance effects are predicted.