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arXiv:1104.3325 · Physical Review A

Numerical studies of the interaction of an atomic sample with the electromagnetic field in two dimensions

Maxim Sukharev, Abraham Nitzan

Published Oct 3, 2011• 81 citations
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Abstract

We consider the interaction of electromagnetic radiation of arbitrary polarization with multilevel atoms in a self-consistent manner, taking into account both spatial and temporal dependencies of local fields. This is done by numerically solving the corresponding system of coupled Maxwell-Liouville equations for various geometries. In particular, we scrutinize linear optical properties of nanoscale atomic clusters, demonstrating the significant role played by collective effects and dephasing. It is shown that subwavelength atomic clusters exhibit two resonant modes, one of which is localized slightly below the atomic transition frequency of an individual atom, while the other is positioned considerably above it. As an initial exploration of future applications of this approach, the optical response of core-shell nanostructures, with a core consisting of silver and a shell composed of resonant atoms, is examined.

DOI
10.1103/physreva.84.043802

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We consider the interaction of electromagnetic radiation of arbitrary polarization with multilevel atoms in a self-consistent manner, taking into account both spatial and temporal dependencies of local fields. This is done by numerically solving the corresponding system of coupled Maxwell-Liouville equations for various geometries. In particular, we scrutinize linear optical properties of nanoscale atomic clusters, demonstrating the significant role played by collective effects and dephasing. It is shown that subwavelength atomic clusters exhibit two resonant modes, one of which is localized slightly below the atomic transition frequency of an individual atom, while the other is positioned considerably above it. As an initial exploration of future applications of this approach, the optical response of core-shell nanostructures, with a core consisting of silver and a shell composed of resonant atoms, is examined.
Optical properties of ensembles of coupled three-level quantum emitters are investigated in linear and non-linear regimes. The model of the Maxwell–Liouville von Neumann equations is implemented to explore the reflection, transmission, and absorption of a thin layer of atom-like emitters at low and high densities. The stimulated Raman adiabatic passage is analysed in systems of coupled quantum emitters of various densities. It is shown that coupling via local electromagnetic fields shifts the energy levels and modifies propagating fields leading to a mixed final population distribution and appearance of new absorption resonances. Strong femtosecond pulses induce population inversion in emitters leading to optical gain.
Optical properties of ensembles of coupled three-level quantum emitters are investigated in linear and non-linear regimes. The model of the Maxwell–Liouville von Neumann equations is implemented to explore the reflection, transmission, and absorption of a thin layer of atom-like emitters at low and high densities. The stimulated Raman adiabatic passage is analysed in systems of coupled quantum emitters of various densities. It is shown that coupling via local electromagnetic fields shifts the energy levels and modifies propagating fields leading to a mixed final population distribution and appearance of new absorption resonances. Strong femtosecond pulses induce population inversion in emitters leading to optical gain.
We propose and develop a method for theoretical description of circularly (elliptically) polarized optical pulse resonant coherent interactions with two-level atoms. The method is based on the time-evolution equations of a two-level quantum system in the presence of a time-dependent dipole perturbation for electric dipole transitions between states with total angular-momentum projection difference $(\ensuremath{\Delta}{J}_{z}=\ifmmode\pm\else\textpm\fi{}1)$ excited by a circularly polarized electromagnetic field [Feynman et al., J. Appl. Phys. 28, 49 (1957)]. The adopted real-vector representation approach allows for coupling with the vectorial Maxwell's equations for the optical wave propagation and thus the resulting Maxwell pseudospin equations can be numerically solved in the time domain without any approximations. The model permits a more exact study of the ultrafast coherent pulse propagation effects taking into account the vector nature of the electromagnetic field and hence the polarization state of the optical excitation. We demonstrate self-induced transparency effects and formation of polarized solitons. The model represents a qualitative extension of the well-known optical Maxwell-Bloch equations valid for linearly polarized light and a tool for studying coherent quantum control mechanisms.
The existence of optical size resonances in atomic nanostructures is proved. The properties of optical size resonances strongly depend on the interatomic distances and on the polarization of an external radiation field. The properties of linear and nonlinear size resonances are considered in the case of two-dimensional nanostructures. The linear optical size resonances are described based on a closed system of equations for dipole oscillators and nonlocal field equations taking into account the dipole-dipole interactions of atoms in the radiation field. Using a stationary solution to these equations, it is demonstrated that two isotropic atoms with definite intrinsic frequencies form an anisotropic system in the radiation field, possessing two or four size resonances depending on whether the component atoms are identical or different. The nanostructure composed of two different atoms possesses two size resonances with positive dispersion and two other resonances with negative dispersion. The frequencies of the size resonances significantly differ from the intrinsic frequencies of isolated atoms entering into the nanostructure. By changing the angle of incidence of the external wave, it is possible to excite various size resonances. The properties of nonlinear optical size resonances excited by an intense radiation field were theoretically and numerically studied using the modified Bloch equations and nonlocal field equations. Dispersion relationships for the nonlinear resonances were derived and the inversion properties of atoms in the nanostructure were studied for various polarizations of the external optical wave.
We have developed the quantum theory of the interaction of ultracold atomic ensemble with the electromagnetic field of vacuum and laser photons. The main attention is paid to the consistent consideration of dynamical dipole-dipole interactions in the case of the second quantized matter. We show that the retardation effects significantly influence the behavior of atomic ensemble in the radiation field. We have derived the general system of equations, which can be used for the investigation of various linear and nonlinear phenomena in atom optics. As an example, we have considered the diffraction of ultracold atomic beam by the standard laser wave. We show that with the increase of the initial density of the intensities of diffractions modes decrease. We also show that the angles of diffraction for different modes depend on the density.
The theory of interaction of intense bichromatic field of laser radiation with multilevel atomic system in the external magnetic field is considered. The magnitudes of interaction are much larger than the width of atomic levels. The vector-potential of radiation field consisting of two monochromatic components with the frequencies resonant to adjacent transitions is taken in electric dipole approximation. The eigenvalues and eigenstates of the Hamiltonian, including spin-orbit interaction and interactions with laser radiation and external magnetic fields, are found without perturbation theory using resonant approximation. When the effects of resonantly excited radiation are considered the Hamiltonian of interaction with the weak field of scattered radiation is included also. Its eigenfunctions are found with the help of perturbation theory. We consider tow types of effects: polarization effects and effects of resonantly excited radiation. As the atomic system is multilevel we use the numerical methods. The influence of the magnetic field on coherent population trapping effect for multilevel systems is considered. Some of our theoretical results coincide with known experimental ones.