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Journal of Experimental and Theoretical Physics

Atom-photon cluster as an elementary emitter

Ashat M. Basharov

Published Jun 1, 2010• 18 citations
Publisher

Abstract

The interaction of an atomic ensemble localized in a microcavity with external electromagnetic fields under Raman resonance conditions with an optically forbidden atomic transition involving photons of the microcavity mode has been described in terms of third-order polynomial algebra. It has been shown that atoms and photons localized in the microcavity under these conditions form a united object, an atom-photon cluster, on the states of which the irreducible representations of polynomial algebra are implemented. Classical coherent and quantum broadband electromagnetic fields are considered as external fields. The effective Hamiltonian, effective dipole moment operator, and relaxation operator of the atom-photon cluster are expressed in terms of the generators of polynomial algebra, which is the algebra of the dynamical symmetry of the problem. The developed mathematical technique has been applied to describe the main radiative processes—spontaneous emission and nutation effect—on atom-photon clusters. All of these effects are peculiar and differ from similar phenomena on two-level atoms, but only simple cases of the mentioned radiative processes have been considered.

DOI
10.1134/s106377611006004x

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Physical Review A•Feb 14, 2000•118 citations
The interaction of an atomic ensemble localized in a microcavity with external electromagnetic fields under Raman resonance conditions with an optically forbidden atomic transition involving photons of the microcavity mode has been described in terms of third-order polynomial algebra. It has been shown that atoms and photons localized in the microcavity under these conditions form a united object, an atom-photon cluster, on the states of which the irreducible representations of polynomial algebra are implemented. Classical coherent and quantum broadband electromagnetic fields are considered as external fields. The effective Hamiltonian, effective dipole moment operator, and relaxation operator of the atom-photon cluster are expressed in terms of the generators of polynomial algebra, which is the algebra of the dynamical symmetry of the problem. The developed mathematical technique has been applied to describe the main radiative processes—spontaneous emission and nutation effect—on atom-photon clusters. All of these effects are peculiar and differ from similar phenomena on two-level atoms, but only simple cases of the mentioned radiative processes have been considered.
It is shown that our description of the dynamics of interaction between atoms with microcavity mode quanta and an external electromagnetic field under conditions of two-photon resonance follows from a simple theory of one-photon resonance interaction between two-level atoms and the same external electromagnetic field, if we substitute su (2) algebra elements of the one-photon resonance theory for third-order elements of polynomial algebra. Commutation relations of polynomial algebra determine the features of processes with the participation of a single object, i.e. an atom-photon cluster localized in a microcavity. Its states are the basis for irreducible representations of this polynomial algebra.
The spontaneous emission from an atomic ensemble localized in a microcavity with the participation of microcavity photons and an external broadband quantized electromagnetic field at the Raman resonance of photons with an optically forbidden (two-photon) atomic transition has been studied. The average spontaneous decay intensity has been calculated for simple cases. It is shown that the dynamics of spontaneous emission from this atomic ensemble differs generally from the conventional superradiance (spontaneous emission of an atomic ensemble at a one-photon optically allowed transition from excited to the ground state. When the atomic ensemble is strongly excited, the delay times and the emission pulse shape differ significantly. The parameter ranges where the spontaneous emission from the atomic ensemble under consideration at a two-photon Raman transition can be described as conventional superradiance with renormalized parameters are found. In the case of single excitation the photon emission probability depends on the number of photons and atoms in the microcavity.
Abstract Models of radiative quantum systems were constructed as analogs of multiphoton and Raman resonances of classical field quanta on an atomic system with the participation of cavity mode quanta. A distinctive feature of the models is the description of an atomic ensemble and quanta using either the generators of polynomial algebra or the two-mode Jordan–Schwinger representation of the su(2) algebra, so that one can talk about an atom–photon and/or photon clusters. The arising algebras are mathematically unsolvable, in contrast to the Heisenberg–Weyl algebra. This makes it possible to implement and observe fundamental effects of coherent nonlinear optics, such as photon echo, optical nutation, and superradiance, in ensembles of the described clusters.
We described the constructed models of radiative quantum systems analogous of multiphoton and Raman resonances of classical field quanta on an atomic system with the participation of resonator mode quanta. A distinctive feature of the models is the possibility to describe an atomic ensemble and quanta using either the generators of polynomial algebra or the two-mode Jordan-Schwinger representation of the su(2) algebra, that could point to atomic-photon and/or photon clusters. The algebras are arising that are mathematically insoluble, in contrast to the Heisenberg — Weyl algebra, which makes it possible to implement and observe fundamental effects of coherent nonlinear optics, such as photon echo, optical nutation, and superradiance in ensembles of the described clusters.
In the effective Hamiltonian representation, we have obtained a quantum stochastic differential equation of a generalized Langevin type for the evolution operator of an atomic ensemble in a microcavity in an external broadband quantized field and in a nonresonant field of the microcavity. We show that, depending on the number of particles in the atomic ensemble, its dynamics demonstrates both the Langevin and the generalized Langevin types of the two-photon spontaneous decay. In this case, one photon is emitted into the cavity mode, whereas the other photon is emitted into the external broadband electromagnetic field. The Langevin type is determined by a considerable Stark interaction of the atomic ensemble with the broadband photon-free quantized field. We show that, here, the Stark interaction is represented by a quantized Poisson process and, depending on its magnitude (at certain numbers of atoms in the ensemble), the two-photon collective spontaneous emission of microcavity atoms can be completely suppressed. In this case, the two-photon spontaneous emission of the singly excited atomic ensemble is described by the two-level model, while the atom-photon cluster of the microcavity under the described conditions is an artificial two-level quantum particle with a strong Stark interaction.
Starting from a quantum Maxwell equation for the vector potential operator, we study the spontaneous emission properties of a two-level atom interacting with the electromagnetic field in a lossless and inhomogeneous dielectric structure and express the spontaneous emission rate, the external quantum efficiency, and the spontaneous emission factor in terms of the classical Green function of the dielectric structure. Comparing these results with the corresponding classical results, we show that the above quantities can be calculated from the radiation field of a classical dipole. Based on this correspondence, a numerical algorithm is developed to calculate the modification of spontaneous emission in microcavities. The line shape of the emission spectrum of the light source and the decay of the cavity resonant modes are automatically taken into account in this algorithm. The approximate expressions for the spontaneous emission rate and the spontaneous emission factor are discussed.