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Springer eBooks

Nonlinear optical and atomic systems : at the interface of physics and mathematics

Christophe Besse, Jean Claude Garreau

Published Jan 1, 2015• 14 citations
Publisher
DOI
10.1007/978-3-319-19015-0

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Optical nonlinearities at the single-photon level are key features to build efficient photon-photon gates and to implement quantum networks. Such optical nonlinearities can be obtained using an ideal two-level system such as a single atom coupled to an optical cavity. While efficient, such atom-photon interface however presents a fixed bandwidth, determined by the spontaneous emission time and thus the spectral width of the cavity-enhanced two-level transition, preventing an efficient transmission to bandwidth-mismatched atomic systems in a single quantum network. In the present work, we propose a tunable atom-photon interface making use of the direct dipole-dipole coupling of two slightly different atomic systems. We show that, when weakly coupled to a cavity mode and directly coupled through dipole-dipole interaction, the subradiant mode of two slightly detuned atomic systems is optically addressable and presents a widely tunable bandwidth and single-photon nonlinearity.
We introduce a versatile platform for studying nonlinear out-of-equilibrium physics. The platform is based on a slow light setup where an optical waveguide is interfaced with cold atoms to realize the driven nonlinear Schrödinger equation with a potential. We compare the proposed setup with similar setups using Bose-Einstein condensates and investigate the system's response under coherent driving for a lattice potential. The slow light setup provides novel angles in the study of nonlinear dynamics due to its advantages in introducing and modulating the driving, the extra tunability over the sign and strength of the available nonlinearities, and the possibility to electromagnetically carve out the underlying potential on demand.
Nonlinear magneto-optical processes are a rich source of interesting and useful phenomena, with both practical and fundamental-physics applications. Theoretical modeling is helpful for understanding and visualizing the mechanisms for nonlinear magneto-optical effects (NMOE), and for analyzing and optimizing devices based on these effects. Part I of this Thesis describes Bloch-equation methods and visualization techniques that can be used to model a wide variety of NMOE in atomic vapors. Part II presents several applications of the methods, including the investigation and visualization of a specific effect involving radio-frequency fields, a study of the general consequences of hyperfine structure on NMOE, and modeling and optimization of systems for laser guide stars. Appendices present additional mathematical material and describe a Mathematica package used for density-matrix calculations.