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Quantum Electronics

The influence of the spatial inhomogeneity of the field on the nonlinear-optical response of an atom

Anatolii V Andreev, Alexander B. Kozlov

Published Nov 30, 2000• 1 citation
Publisher

Abstract

The theory of the interaction of a centrosymmetric atom with a superstrong spatially inhomogeneous laser field is developed. This theory employs the two-level approximation to describe the dynamics of spatially nonlocal interactions related to variations in the populations of the levels. We propose a model that includes spatially nonlocal interactions, such as magnetic-dipole and quadrupole interactions and interactions due to the gradient of the ponderomotive potential of the field. We consider the interaction of a homogeneous medium of centrosymmetric atoms with a superstrong laser field, which is represented as a superposition of two plane-wave ultrashort pulses propagating at some angle with respect to each other. Perturbation theory, which is valid for the fields of moderate intensity, is developed for the atomic response. The results of numerical simulations are compared with the predictions of this perturbation theory. The specific features of the nonlinear-optical response of an atom in a superstrong field are investigated. The angular distribution of the second- and third-harmonic emission is calculated in the constant-field approximation for different polarisations of the incident field.

DOI
10.1070/qe2000v030n11abeh001848

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The theory of the interaction of a centrosymmetric atom with a superstrong spatially inhomogeneous laser field is developed. This theory employs the two-level approximation to describe the dynamics of spatially nonlocal interactions related to variations in the populations of the levels. We propose a model that includes spatially nonlocal interactions, such as magnetic-dipole and quadrupole interactions and interactions due to the gradient of the ponderomotive potential of the field. We consider the interaction of a homogeneous medium of centrosymmetric atoms with a superstrong laser field, which is represented as a superposition of two plane-wave ultrashort pulses propagating at some angle with respect to each other. Perturbation theory, which is valid for the fields of moderate intensity, is developed for the atomic response. The results of numerical simulations are compared with the predictions of this perturbation theory. The specific features of the nonlinear-optical response of an atom in a superstrong field are investigated. The angular distribution of the second- and third-harmonic emission is calculated in the constant-field approximation for different polarisations of the incident field.
There is a broad interest in enhancing the strength of light-atom interactions to the point where injecting a single photon induces a nonlinear material response. Here we show theoretically that sub-Doppler-cooled two-level atoms that are spatially organized by weak optical fields give rise to a nonlinear material response that is greatly enhanced beyond that attainable in a homogeneous gas. Specifically, in the regime where the intensity of the applied optical fields is much less than the off-resonance saturation intensity, we show that the third-order nonlinear susceptibility scales inversely with atomic temperature and, due to this scaling, can be two orders of magnitude larger than that of a homogeneous gas for typical experimental parameters. As a result, we predict that spatially bunched two-level atoms can exhibit single-photon nonlinearities. Our model is valid for all regimes of atomic bunching and simultaneously accounts for the backaction of the atoms on the optical fields. Our results agree with previous theoretical and experimental results for light-atom interactions that have considered only limited regimes of atomic bunching. For lattice beams tuned to the low-frequency side of the atomic transition, we find that the nonlinearity transitions from a self-focusing type to a self-defocusing type at a critical intensity. We also show that higher than third-order nonlinear optical susceptibilities are significant in the regime where the dipole potential energy is on the order of the atomic thermal energy. We therefore find that it is crucial to retain high-order nonlinearities to accurately predict interactions of laser fields with spatially organized ultracold atoms. The model presented here is a foundation for modeling low-light-level nonlinear optical processes for ultracold atoms in optical lattices.
The interaction of intense laser fields with matter is accompanied by a multitude of phenomena, ranging from the generation of coherent radiation across various spectral ranges (from terahertz to soft X-rays) to the creation of beams of accelerated charged particles and micromodification of the volume and surface of various samples.To describe this diversity of phenomena, several theoretical approaches have been developed to date.These approaches utilize different approximations to address this complex nonlinear problem, allowing for the explanation of specific aspects of such interactions.The developed theoretical frameworks consider the interaction at both microscopic and macroscopic levels; at the microscopic level, they investigate the characteristics of single atoms interacting with laser fields, while at the macroscopic level, they analyze nonlinear susceptibilities that describe the nonlinear polarization of the medium during the propagation of laser radiation through it.This work presents an overview of methods describing some of the most commonly employed theoretical approaches to model the response of a medium at a microscopic (quantum-mechanical) level, as well as various methods for controlling the properties of generated coherent radiation.A model for the gas medium is described that accounts for both the response characteristics of individual atoms and allows for consideration of phase and quasiphase matching effects during radiation generation.The influence of medium parameters on the efficiency of generation and polarization properties of generated radiation is analyzed under both phase and quasi-phase matching conditions.A detailed description of an analytical method for calculating the nonlinear susceptibility of a gas medium is provided.The obtained values of nonlinear susceptibility for arbitrary orders may be useful in numerical calculations concerning the propagation of laser radiation in matter.Various channels for radiation generation are analyzed as parameters of the laser field are varied.
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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.
The formalism of Maker, Terhune, and Savage [Phys. Rev. Lett. 12, 507 (1964)] for third-order nonlinear susceptibilities is extended to account for nonlocal response. In the case of counterpropagating beams, we show that five constants instead of two are required in general to describe the nonlinearity. In the particular case of optical pumping nonlinearities, which we study extensively, we show that four constants, which describe the magnetization and electric-quadrupole moment of the medium induced by the forward and backward beams, are sufficient. We evaluate these constants for various values of the angular momenta of the atomic levels connected by the incident field. We finally show how this formalism can be applied to several problems such as induced focusing, four-wave-mixing generation, optical instability, and polarization properties of phase-conjugate and phase-contrast mirrors.