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arXiv:2105.08554 · Journal of the Optical Society of America B

Radiation pressure on single atoms: generalization of an exact analytical approach to multilevel atoms

L. Podlecki, John Martin, Thierry Bastin

Published Sep 3, 2021• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1364/josab.433090

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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.
The mechanical action of light on atoms is nowadays a tool used ubiquitously in cold atom physics. In the semiclassical regime where the atomic motion is treated classically, the computation of the mean force acting on a two-level atom requires in the most general case numerical approaches. Here we show that this problem can be tackled in a pure analytical way. We provide an analytical yet simple expression of the mean force that holds in the most general case where the atom is simultaneously exposed to an arbitrary number of lasers with arbitrary intensities, wave vectors, and phases. This yields a novel tool for engineering the mechanical action of light on single atoms.
In recent years interest has significantly quickened in investigation of nonlinear optical and spectroscopic phenomena in such unique objects as Rydberg atoms (the atoms in the energy states near the ionization limit) and van der Waals complexes (dimers). These objects are characterized, in particular, by that their energy states are strongly degenerate due to a large value of angular (rotational) momentum. Here, the problem arises of adequate theoretical description of experimental results, especially when polarization peculiarities of nonlinear radiation processes are considered. The problem is caused by the existence of a huge number of quantum magnetic sublevels of energy states, which are, in the general case, coherently coupled to each other and take part in the radiation processes. Figure 1 gives a vivid presentation of the problem arising even in such a seemingly simple case when one need describe the radiation transitions caused by a strong monochromatic field between two energy levels with large values of the angular momentum J. If the field polarization is arbitrary, the whole set of the magnetic sublevels turn out to be coupled by radiative transitions. Formally, the problem becomes essentially multilevel. In this case not only the hope fades of solving it analytically using the traditional quantum-mechanical approach, but the problems of numerical solution grow abruptly with increasing quantum number J as well. On the other hand, as is often the case, every cloud has a silver lining. With large J we approach the situation when the rotational motion of particles can be described classically. It turns out that the transition from the quantum description of orientation states of the angular momentum to the classical one simplifies the problem radically: it reduces to the problem of radiation processes in the simplest model of nondegenerate states. In this case the rotational motion manifests itself in a dependence of the density matrix elements on orientation angles of the angular momentum as on a parameter.
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.
In describing the nonlinear interaction of radiation with matter it is well known that the perturbation expansion technique is used to calculate the atomic wave functions and the transitions between the states of a system. However the technique, though involving all states of the system, is valid only in the limit of weak interaction fields and non-resonant interactions. For strong fields and resonant interactions, density matrix or dressed atom formulisms are commonly used though these exact treatments are restricted to simple two level schemes or approximations of these; their application to general resonant-near resonant multilevel interactions being prohibitively complex.
A general theory of the motion of a two-level atom in a resonant or near-resonant electromagnetic wave of arbitrary amplitude and phase, including effects of radiative relaxation due to interaction with the quantized vacuum field, is developed from first principles. Particular emphasis is placed on the effects of quantum-mechanical fluctuations of the radiation force and on the associated diffusion of atomic momentum due to spontaneous and induced absorption and emission processes. Analytic results and numerical examples are presented for (1) the lower bound on the temperature achievable by radiation cooling in a standing wave tuned below resonance, (2) the heating rate in a strong resonant standing wave, (3) the maximum confinement time for an atom in a Gaussian radiation trap, (4) the deflection and spreading of an atomic beam transversely illuminated by a strong resonant running wave, and (5) the transverse cooling of an atomic beam by a strong running wave tuned below resonance.
Depending on the spatial and temporal structure of light field, its strength and wavelength, the radiation force may be a very complex function of the atoms position and velocity. But, since all the known studies on the application of the radiation forces have been carried out mainly using three types of light fields, namely, a plane traveling light field, a Gaussian laser beam and a standing light wave, or their combination, this chapter restricts to qualitative consideration of these types of fields only. At low radiation intensity and for a two level atom the radiation force in the standing wave is determined by the sum of the forces from each traveling waves. In the presence of static magnetic field the radiative forces acting on a multilevel atom in a laser field may acquire new properties. Of particular interest for the creation of new types of atomic traps is a confining potential — like character of the radiation force.