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.With the advent of lasers, the mechanical action of light has become an extraordinary tool for controlling the motion of atoms. The first evidence of this control with laser light was demonstrated in the early seventies with the deflection of an atomic beam by resonant laser radiation pressure [1]. One of the most remarkable achievements was made a decade later when the first cold atomic cloud in a magneto-optical trap was observed [2]. These initial experiments gave birth to the vast array of cold atom physics experiments with each more spectacular than the last. Regimes that were thought to forever remain in the realm of Gedankenexperiments became reality in labs, for example Bose-Einstein condensation [3].As long as the atomic motion can be treated classically, i.e., in regimes where the atomic wavepackets are sufficiently localized in space, the resonant laser radiation acts mechanically as a force on the atomic center-ofmass. In a standard two-level approximation and modeling the laser electromagnetic field as a plane wave, the mean force F exerted by a single laser, averaged over its optical period, reaches shortly after establishment of the laser action a stationary regime where it takes the well-known simple expression [4]Here, Γ is the rate of spontaneous decay from the upper level of the transition, k is the laser photon momentum, and s = (|Ω| 2 /2)/(δ 2 + Γ 2 /4) is the saturation parameter, where Ω is the Rabi frequency and δ = ω − ω 0 is the detuning between the laser and the atomic transition angular frequencies, ω and ω 0 , respectively. The maximal force the laser can exert on the atom is (Γ/2) k.The question naturally arises of how Eq. (1) generalizes when several lasers of arbitrary intensities, wave vectors and phases are acting simultaneously on the atom. Surprisingly, to date no general exact analytical expression of the resulting force can be found in the scientific literature and one is often reduced to using numerical approaches [5][6][7]. In the low intensity regime a generalized version of Eq. (1) provides an approximation of the incoherent action of each laser field. Each individual laser j (j = 1, . . . , N with N the total number of lasers) is characterized by an individual detuning δ j , a photon momentum k j , a Rabi frequency Ω j , and an individual saturation parameter s j = (|Ω j | 2 /2)/(δ 2 j + Γ 2 /4). When ...

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)JOBPDE0740-322410.1364/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.

In a recent work, we provided a standardized and exact analytical formalism for computing in the semiclassical 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, 127-132 (2018)]. 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.