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Journal of Physics B Atomic and Molecular Physics

Superradiance and subradiance. III. Small samples

A. Crubellier

Published Mar 14, 1987• 17 citations
Publisher

Abstract

For pt.II see ibid., vol.19, p.2109 (1986). This paper is the third in a theoretical study of subradiance, i.e. the cooperative inhibition of spontaneous emission by a destructive interatomic interference, a phenomenon which has recently been observed. The paper is devoted to the problem of the cooperative spontaneous emission of atomic samples with linear dimensions much smaller than the wavelength of the emitted light. The treatment, which is based on a fully quantum mechanical description of the problem, corroborates the results obtained in a semiclassical treatment by Friedberg and Hartmann (1974). Starting from a master equation describing both the cooperative spontaneous emission and the dipole-dipole interaction, a statistical treatment of the latter is introduced and the corresponding symmetry relaxation is studied. The evolution of the atoms is described in three typical cases that correspond to different sample geometries and/or atomic distributions. In one of these cases, in particular, the symmetry is first conserved and the atoms follow Dicke's predictions for a time. A 'retarded' symmetry breaking then occurs suddenly, near the zero value of the collective energy, as in Friedberg and Hartmann's calculations for a small sphere. With regard to the further evolution of the atoms in this case, which cannot be studied in a semiclassical model, it is shown that the decay rate quickly becomes much smaller than the incoherent decay rate. An unquestionable subradiance phenomenon is thus predicted in this case.

DOI
10.1088/0022-3700/20/5/017

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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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For pt.II see ibid., vol.19, p.2109 (1986). This paper is the third in a theoretical study of subradiance, i.e. the cooperative inhibition of spontaneous emission by a destructive interatomic interference, a phenomenon which has recently been observed. The paper is devoted to the problem of the cooperative spontaneous emission of atomic samples with linear dimensions much smaller than the wavelength of the emitted light. The treatment, which is based on a fully quantum mechanical description of the problem, corroborates the results obtained in a semiclassical treatment by Friedberg and Hartmann (1974). Starting from a master equation describing both the cooperative spontaneous emission and the dipole-dipole interaction, a statistical treatment of the latter is introduced and the corresponding symmetry relaxation is studied. The evolution of the atoms is described in three typical cases that correspond to different sample geometries and/or atomic distributions. In one of these cases, in particular, the symmetry is first conserved and the atoms follow Dicke's predictions for a time. A 'retarded' symmetry breaking then occurs suddenly, near the zero value of the collective energy, as in Friedberg and Hartmann's calculations for a small sphere. With regard to the further evolution of the atoms in this case, which cannot be studied in a semiclassical model, it is shown that the decay rate quickly becomes much smaller than the incoherent decay rate. An unquestionable subradiance phenomenon is thus predicted in this case.
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.
This paper is the first of a sequence of four papers devoted to the theoretical study of subradiance, i.e. of the cooperative inhibition of spontaneous emission, a phenomenon which has been recently observed. It is shown, in the typical example of a pencil-shaped sample of three-level atoms in the 'V' configuration (two transitions sharing a common lower level), that the system can spontaneously reach a state in which the emission in the so-called 'end-fire' superradiant field modes is cooperatively inhibited; this occurs for initially uncorrelated atoms when the initial state is a statistical mixing of the two upper states. The whole study is centered on the concept of destructive interatomic interference and it is therefore based on the symmetry properties of the collective atomic state with respect to the permutations of locally indistinguishable atoms. Semiclassical and fully quantum-mechanical models are used in turn. The obstacles to the interatomic interference and thus to subradiance are finally discussed.
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.
Fully-excited two-level atoms separated by less than the transition wavelength cooperatively emit light in a short burst, a phenomenon called superradiance by R. Dicke in 1954. The burst is characterized by a maximum intensity scaling with the square of the number of atoms NNN and a temporal width reduced by NNN compared to the single atom spontaneous decay time. Both effects are usually attributed to a synchronization of the electric dipole moments of the atoms occurring during the process of light emission. Contrary to this explanation, it was recently shown by use of a quantum path description that the peak intensity results from the quantum correlations among the atoms when occupying symmetric Dicke states. Here we investigate from this perspective the temporal evolution of the ensemble, starting in the small sample limit, i.e., when the atoms have mutual separations much smaller than the transition wavelength λλλ and pass down the ladder of symmetric Dicke states. In addition, we explore the temporal evolution for the case of non-interacting atoms with mutual separations much larger than λλλ. We show that in this case a similar superradiant burst of the emitted radiation is observed if the quantum correlations of the atoms are generated by conditional photon measurements retaining the atomic ensemble within or close to the symmetric subspace.
Fully excited two-level atoms separated by less than the transition wavelength cooperatively emit light in a short burst, a phenomenon called superradiance by R. Dicke in 1954 [Phys. Rev. 93, 99 (1954)]. The burst is characterized by a maximum intensity scaling with the square of the number of atoms NNN and a temporal width reduced by NNN compared to the single atom spontaneous decay time. Both effects are usually attributed to a synchronization of the electric dipole moments of the atoms occurring during the process of light emission. Contrary to this explanation, it was recently shown by use of a quantum path description that the peak intensity results from the quantum correlations among the atoms when occupying symmetric Dicke states. Here we investigate from this perspective the temporal evolution of the ensemble, starting in the small sample limit, i.e., when the atoms have mutual separations much smaller than the transition wavelength $\ensuremath{\lambda}$ and pass down the ladder of symmetric Dicke states. In addition, we explore the temporal evolution for the case of distant noninteracting atoms with mutual separations much larger than $\ensuremath{\lambda}$. We show that in this case a similar superradiant burst of the emitted radiation is observed if the quantum correlations of the atoms are generated by conditional photon measurements retaining the atomic ensemble within or close to the symmetric subspace.
When atoms are coupled to a common electromagnetic environment, the exchange of photons through dipole-dipole interactions leads to the emergence of cooperative effects. As a particular example, superradiance arises from spontaneous emission when this exchange leads to constructive interference of the emitted photons. Here, we introduce an integrated method for studying cooperative radiation in many-body systems. This method, which allows to study extended systems with arbitrarily large number of particles, can be formulated by an effective, nonlinear, two-atom master equation that describes the dynamics using a closed form which treats single- and many-body terms on an equal footing. We apply this method to a homogeneous gas of initially inverted two-level atoms, and demonstrate the appearance of both superradiance and subradiance, identifying a many-body coherence term as the source of these cooperative effects. We describe the many-body induced broadening -- which is analytically found to scale with the optical depth of the system -- and light shifts, and distinguish spontaneous effects from induced ones. In addition, we theoretically predict the time-dependence of subradiance, and the phase change of the radiated field during the cooperative decay.