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Optics and Spectroscopy

Simple cases of spontaneous emission from an atom-photon cluster localized in a microcavity

Ashat M. Basharov

Published Jul 1, 2010• 0 citations
Publisher

Abstract

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.

DOI
10.1134/s0030400x10070088

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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.
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.
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.
We study the cooperative two-photon spontaneous decay of an excited atomic system in a microcavity whose size is of the order of several wavelengths of atomic radiation. We show that a thermalized electromagnetic field in the microcavity strongly affects the two-photon cooperative spontaneous emission of radiation. The increase in the rate of spontaneous cooperative decay is due to the presence of a small number of thermalized photons in a microcavity mode. At low temperatures, the two-photon absorption probability is found to be a linear function of the two-photon flux, and photon superbunching is observed.
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.
Dynamics of the spontaneous emission from a two-level atom embedded in a bisphere microcavity is analyzed theoretically. A bisphere supports a morphology-dependent resonance having such a high quality factor with local field enhancement that the strong coupling between the atom and the cavity can be realized. By taking full account of the photon degree of freedom, we derive theoretically the coupling constant between the atom and the cavity as well as the radiation damping constants, which are used in the conventional cavity QED approach. In addition, we show that the power spectrum of the spontaneous emission at a local observation point is strongly affected by the photon Green function.