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Coupled 'Ihmsitions in Superradiance

A. Crubellier, Catherine Bréchignac, Ph. Cahuzac, P. Pillet

Published Jan 1, 1979• 0 citations
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Abstract

In the theoretical stuqy of superradiance, the atoms or molecules are generally considered as two-level systems. However in many experimental situations, this simple assumption is not valid. It is the case, for example, in all experiments exhibiting superradiant beats [1-3]. Moreover, these beats are sometimes due to a specific property of superradiance : the existence of interferences between different atoms. Other examples of multilevel superradiance are encountered each time one observes several superradiant transitions sharing a common level [3,4]. In addition, superradiance is generally observed between degenerate levels, and it has been alreaqy shown experimentally that the level-degeneracy influences the properties of the superradiant light, in particular its polarization characteristics [5].

Related papers

Superradiance and subradiance. II. Atomic systems with degenerate transitions

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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.

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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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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 in spin- j particles: Effects of multiple levels

Guin-Dar Lin, Susanne F. Yelin

We study the superradiance dynamics in a dense system of atoms each of which can be generally a spin-$j$ particle, with $j$ an arbitrary half-integer. We generalize Dicke's superradiance point of view to multiple-level systems and compare the results based on a novel approach we developed previously [Lin and Yelin, Adv. Atom. Mol. Opt. Phys. 61, in press (2012)]. Using this formalism we derive an effective two-body description that shows cooperative and collective effects for spin-$j$ particles, taking into account the coherence of transitions between different atomic levels. We find that superradiance, which is well known as a many-body phenomenon, can also be modified by multiple-level effects. We also discuss the feasibility and propose that our approach can be applied to polar molecules, for their vibrational states have a multilevel structure which is partially harmonic.

arXiv:1112.1975•Physical Review A•Mar 26, 2012•26 citations
In the theoretical stuqy of superradiance, the atoms or molecules are generally considered as two-level systems. However in many experimental situations, this simple assumption is not valid. It is the case, for example, in all experiments exhibiting superradiant beats [1-3]. Moreover, these beats are sometimes due to a specific property of superradiance : the existence of interferences between different atoms. Other examples of multilevel superradiance are encountered each time one observes several superradiant transitions sharing a common level [3,4]. In addition, superradiance is generally observed between degenerate levels, and it has been alreaqy shown experimentally that the level-degeneracy influences the properties of the superradiant light, in particular its polarization characteristics [5].
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.
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.
This article reviews the present status of superradiance in atoms and molecules. The introductory section describes the important physical properties of superradiant emission, and presents the important experimental features. A simple theoretical formulation, based on the coupled Maxwell-Schrödinger equations, is described. Simple expressions for observable output parameters are given, valid in experimentally relevant regimes. These results are compared with superradiance experiments performed at a wide range of wavelengths in numerous laboratories since 1973. While the principal features of superradiance are generally agreed upon, details of the initiation of the radiation process and of the observed ringing are still under study.
In order to check theoretical results obtained recently in the treatment of the superradiant emission of atoms when taking the level degeneracy into account explicitly, an experiment has been performed using a special "multiple beam" of Rb atoms. A careful study of the polarization characteristics of the emitted light has shown us several features which appear to be quite different in the superradiant emission and in the ordinary spontaneous one. An analysis is given for the few typical cases which have been observed and reported.
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.
We study the superradiance dynamics in a dense system of atoms each of which can be generally a spin-jjj particle, with jjj an arbitrary half-integer. We generalize Dicke's superradiance point of view to multiple-level systems and compare the results based on a novel approach we developed previously [Lin and Yelin, Adv. Atom. Mol. Opt. Phys. 61, in press (2012)]. Using this formalism we derive an effective two-body description that shows cooperative and collective effects for spin-jjj particles, taking into account the coherence of transitions between different atomic levels. We find that superradiance, which is well known as a many-body phenomenon, can also be modified by multiple-level effects. We also discuss the feasibility and propose that our approach can be applied to polar molecules, for their vibrational states have a multilevel structure which is partially harmonic.