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Nonlinear Optics

Nonlinear Optics with Ultracold Cesium Atoms

Philippe Verkerk, Brahim Lounis, Robert W. Boyd, Ch Salomon, G. Grynberg

Published Jan 1, 1992• 0 citations
Publisher

Abstract

Recently, great progress has been made in the cooling and trapping of atoms. It is now possible to create a collection of atoms with a number density in excess of 1011cm-3 and a kinetic temperature of the order of 10 μK. At such low temperatures the mean atomic velocity is of the order of 10cm/sec and the resulting Doppler width of the atomic transition is much lower than the homogeneous width. Furthermore, it has been shown that a substantial fraction of the atoms are localized inside wavelength-scale potential wells due to light-shifts[1]. Such a collection of essentially stationary atoms provide a reasonably large nonlinear susceptibility that can be exploited for the study of various nonlinear optical interactions [2].

DOI
10.1364/nlo.1992.tua4

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Recently, great progress has been made in the cooling and trapping of atoms. It is now possible to create a collection of atoms with a number density in excess of 1011cm-3 and a kinetic temperature of the order of 10 μK. At such low temperatures the mean atomic velocity is of the order of 10cm/sec and the resulting Doppler width of the atomic transition is much lower than the homogeneous width. Furthermore, it has been shown that a substantial fraction of the atoms are localized inside wavelength-scale potential wells due to light-shifts[1]. Such a collection of essentially stationary atoms provide a reasonably large nonlinear susceptibility that can be exploited for the study of various nonlinear optical interactions [2].
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.
Abstract This paper presents a calculation of the third‐order nonlinear susceptibility for the frequency upconversion of 10‐μm atmospheric window to the visible band. The following cases are compared. Two‐photon resonance 1 at 6 d 2D3/2, and 2 at 6 d 2D5/2 of cesium to generate difference frequency. 3 Two‐photon resonance at 7 s 2S1/2 of cesium to generate sum frequency. 4 Two‐photon resonance at 3 d 2D5/2 of sodium to generate sum frequency. Density matrix is used in the calculation, and the spinorbit coupling and the Doppler effect are considered. The major results are the following. In 1, a large nonlinear susceptibility and large number density is obtained at relatively low temperature. The nonlinear susceptibility has the maximum at the wavelength of 12.1 μm. In 2, a large nonlinear susceptibility and large number density are obtained at relatively low temperature. The nonlinear susceptibility increases with the increase of infrared wavelength. In 3, a system free from polarization property can be constructed, but the temperature must be raised by more than 100°C, compared with the forementioned two cases. In 4 the largest nonlinear susceptibility is obtained for the wavelength of 9.1 μm. However, the temperature must be raised by several hundreds degree compared with the cases of 1 and 2.