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Optics Communications

Light pressure forces on multi-level atoms in intense polychromatic light fields: a continued fraction approach

Tianwu Cai, N. P. Bigelow

Published Dec 1, 1993• 12 citations
Publisher

Abstract

Abstract Described is the application of a matrix form of the continued fraction technique to the calculation of the velocity dependent force experienced by a multi-level atom interacting with a complex optical field. Unlike other techniques, this approach provides a solution which is valid for a wide range of optical field configurations and atomoc velocities and which includes the effects of both single and multi-photon processes. As a specific example of this technique the force experienced by a three-level atom (V) in a bichromatic light field is calculated.

DOI
10.1016/0030-4018(93)90126-p

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Abstract Described is the application of a matrix form of the continued fraction technique to the calculation of the velocity dependent force experienced by a multi-level atom interacting with a complex optical field. Unlike other techniques, this approach provides a solution which is valid for a wide range of optical field configurations and atomoc velocities and which includes the effects of both single and multi-photon processes. As a specific example of this technique the force experienced by a three-level atom (V) in a bichromatic light field is calculated.
Stimulated optical forces offer a simple and efficient method for providing optical forces far in excess of the saturated radiative force. The bichromatic force, using a counterpropagating pair of two-color beams, has so far been the most effective of these stimulated forces for deflecting and slowing atomic beams. We have numerically studied the evolution of a two-level system under several different bichromatic and polychromatic light fields, while retaining the overall geometry of the bichromatic force. New insights are gained by studying the time-dependent trajectory of the Bloch vector, including a better understanding of the remarkable robustness of bi- and polychromatic forces with imbalanced beam intensities. We show that a four-color polychromatic force exhibits great promise. By adding new frequency components at the third harmonic of the original bichromatic detuning, the force is increased by nearly 50% and its velocity range is extended by a factor of 3, while the required laser power is increased by only 33%. The excited-state fraction, crucial to possible application to molecules, is reduced from 41% to 24%. We also discuss some important differences between polychromatic forces and pulse trains from a high-repetition-rate laser.
The interaction of a beam of two level atoms with a standing wave laser field has been the subject of extensive investigation in recent times. A standing wave perpendicular to an atomic beam allows the manipulation of the transverse velocity distribution. The interaction of an atomic beam with a strong standing wave laser field has been systematically investigated by both theoretical simulation and experiment in this thesis. We have developed a numerical model based on a continued fraction solution for the light pressure forces to simulate the near perpendicular interaction of an atomic beam with a strong standing wave laser field. The reshaping of the transverse spatial profile of an atomic beam by a perpendicular, near resonant, standing wave laser field is investigated for red detunings using a longitudinal velocity selective detection system. The experimental dependence of the reshaped profile on the longitudinal and transverse atomic velocities agrees well with a continued fraction solution for the light force. In particular, a regime is found where channelling of the atoms near the antinodes of the standing wave produces a central peak in the spatial distribution of the atomic beam in the far field which have also been observed elsewhere.
This dissertation describes calculations and simulations which extend the optical bichromatic force (BCF), which has previously been examined primarily in the context of two-level systems, to more complex polychromatic fields and to multilevel systems. Through detailed examination of various simple multilevel systems, I develop prescriptions for the application of the BCF to general multilevel systems. I apply these prescriptions to simulations of the molecular systems CaF and SrOH and provide BCF parameters for each that will guide future experiments. The design of an experiment to measure BCF deflection of a molecular beam of CaF is discussed. I close with discussion of prospects for extending this work to a molecular decelerator which can be used as the first stage of a molecular trap.
We investigate the force on a two-level atom interacting with intense monochromatic laser fields which are combinations of standing and traveling waves. We present a continued-fraction solution to the optical Bloch equations. Using this solution to calculate the force on an atom, we have examined the slowing and cooling of a thermal Na atomic beam. We find that the addition of a traveling wave to an intense standing wave can significantly improve the slowing rate and simultaneously decrease the final velocity of the cooled beam.
In a recent work, we provided a standardized and exact analytical formalism for computing in the semiclassical and asymptotic regime, the radiation force experienced by a two-level atom interacting with any number of plane waves with arbitrary intensities, frequencies, phases, and propagation directions [ J. Opt. Soc. Am. B 35 , 127 ( 2018 ) JOBPDE 0740-3224 10.1364/JOSAB.35.000127 ]. Here, we extend this treatment to the multilevel atom case, where degeneracy of the atomic levels is considered and polarization of light enters into play. A matrix formalism is developed to this aim.
We have recently begun to explore the very strong optical forces that can be exerted on atoms by polychromatic light. Unlike the radiative force that is limited to be less than ℏkγ/2 in monochromatic light or the dipole force that alternates on a wavelength scale in a monochromatic standing wave, limiting its utility, these new forces have very attractive features. Not only is their strength far greater than Frad, but also their velocity range is far greater than γ/k, so that beam slowing can be accomplished without Doppler compensation in distances measured in millimeters instead of meters. These forces have been implemented by modulation of a single-frequency laser or by combination of the light of two different single-frequency lasers.