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Physical Review A

Resonance interaction between two atomic dipoles separated by the surface of a dielectric nanosphere

В. В. Климов, Vladilen S Letokhov

Published Oct 1, 1998• 25 citations
Publisher

Abstract

Studied within the framework of both classical and quantum-mechanical approaches is the resonance interaction between two atomic dipoles one of which is located inside a dielectric microsphere and the other near its outer surface. The dispersion equation of this system is found. The analysis of this equation in a quasistatic approximation has shown that the behavior of the eigenfrequencies depends in a complex manner on the parameters of the system, and that exact resonance can be achieved, provided the parameters are suitably selected. Based on the solutions of the above equation, relationships are found between the energy-transfer rate and the system parameters. It is demonstrated that as the inside atom approaches the surface of the microsphere, resonance excitation transfer from one atom to the other can take place. Similar results are obtained when using the quantum-mechanical density matrix to define the atomic interaction. The results obtained can be of use in implementing selective microscopy with a nanometer-high spatial resolution.

DOI
10.1103/physreva.58.3235

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Studied within the framework of both classical and quantum-mechanical approaches is the resonance interaction between two atomic dipoles one of which is located inside a dielectric microsphere and the other near its outer surface. The dispersion equation of this system is found. The analysis of this equation in a quasistatic approximation has shown that the behavior of the eigenfrequencies depends in a complex manner on the parameters of the system, and that exact resonance can be achieved, provided the parameters are suitably selected. Based on the solutions of the above equation, relationships are found between the energy-transfer rate and the system parameters. It is demonstrated that as the inside atom approaches the surface of the microsphere, resonance excitation transfer from one atom to the other can take place. Similar results are obtained when using the quantum-mechanical density matrix to define the atomic interaction. The results obtained can be of use in implementing selective microscopy with a nanometer-high spatial resolution.
A solution is found of the dispersion equation for a classical oscillator in the vicinity of a dielectric microsphere in the case of strong electromagnetic coupling. The solution obtained agrees with the corresponding quantum-mechanical solution obtained within the framework of the dressed states approach and presents a clear signature of the vacuum Rabi splitting of the energy levels in real systems. Based on this solution, a qualitative expression is found for the intensity of the resultant line doublet.
van der Waals interactions between atoms and dielectric surfaces are reinvestigated. To describe the nonretarded interaction potential between a dispersive dielectric surface and an atom in an arbitrary internal energy state, we derive a general expression in terms of an integral, over real frequency, of the combined atom and surface polarizabilities. It is shown that, for excited atoms, the expression is equivalent to the one obtained by Wylie and Sipe [Phys. Rev. A 32, 2030 (1985)]. We thus demonstrate how to extend this approach to excited atoms interacting with birefringent dielectrics. For isotropic dielectrics, a method of integration in closed form allows us to derive an approximate formula for the van der Waals interaction constant in terms of resonance frequencies and oscillator strengths of both the atom and the dielectric. Frequency-dependent ``dielectric reflection'' coefficients are introduced for virtual atomic dipole couplings either in absorption or in emission. In absorption, the reflection coefficient is always positive and smaller than unity. In emission, it may take arbitrary values, positive or negative (corresponding to van der Waals repulsion). Such a behavior is shown to be related to resonant excitation exchange between the atomic system and the dielectric medium, when an atomic transition frequency gets in resonance with a dielectric absorption band. Numerical calculations performed for the cesium-sapphire system are shown to be in good agreement with data obtained by selective-reflection spectroscopy. Finally, experimental tests of the birefringent character of the sapphire response are discussed.
A strong resonant interaction of a two-level atom with a dielectric microsphere is studied on the basis of quantum electrodynamics. The initial condition considered is one in which the atom is initially excited and the resonant mode of the microsphere has been excited by a single photon. The spectrum of two emitted photons depends strongly on the method used to excite the microsphere, i.e., on the spatial distribution of the photon energy. The most characteristic feature of the two-photon fluorescence spectrum is a strong energy correlation of the emitted photons. This correlation is expressed in the fact that the energies of the emitted photons are related by the equation of an ellipse (ω+ω 2−2ω vA )2+3(ω 1−ω 2)2= 4Ω Rabi 2 . The relation between the results obtained and the predictions of the theory of dressed states is discussed.
Abstract An effective Hamiltonian and equations of motion for treating both the resonant dipole‐dipole interaction between two‐level atoms and the resonant atom‐field interaction are derived, which can suitably be used for studying the influence of arbitrary dispersing and absorbing material surroundings on these interactions. It is shown that the dipole‐dipole interaction and the atom‐field interaction, respectively, are closely related to the real part and the imaginary part of the (classical) Green tensor. The theory is applied to the study of the transient behavior of two atoms that initially share a single excitation, with special emphasis on the role of the two competing processes of virtual and real photon exchange in the energy transfer between the atoms. To illustrate the powerfulness of the theory, specific results for the case of the atoms being near a dispersing and absorbing microsphere are presented. In particular, the regimes of weak and strong atom‐field coupling are addressed.
The lifetime of an excited atom near an absorbing dielectric surface is calculated from an exact solution of a microscopic Hamiltonian model, which includes the effects of dispersion, local-field correction, and near-field Coulomb interaction. Results for the total decay rate are shown to be in excellent agreement with those based on classical electromagnetic theory and to yield the well-known result for the rate of nonradiative energy transfer in the limit of very small distance from the surface. \textcopyright{} 1996 The American Physical Society.
The strong resonance interaction of a two-level atom with the continuum of quantized electromagnetic modes falling within the contour of a resonance mode of a dielectric microsphere is considered within the framework of quantum electrodynamics. Analytical solutions are derived. As an initial condition, we consider the case when, at time t = 0, the atom is excited and the resonance modes of the microsphere contain a single-photon wavepacket. It is shown that the properties of the emitted photon pair depend crucially on space-time properties of the photon wavepacket contained in the resonator. When the mean square of the electric field of the photon wavepacket at the initial instant of time at the atom position is close to the vacuum value, the radiation of an atom is similar to a spontaneous one and the emitted photon pair has no correlations. On the contrary, if the mean square of the electric field of the photon wavepacket at the initial instant of time at the atom position is substantially greater than the vacuum value, the radiation of an atom has a stimulated nature and the emitted photon pair has very complicated strong correlations. The relationship between the results obtained and the predictions of the dressed states theory are briefly discussed. The results obtained are of a general character and can be applied to the description of the resonant interaction of an excited atom and an excited resonator of an arbitrary shape.