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Frontiers in Optics

A numerical study of optical dipole force on three level atoms by few-cycle-pulse laser fields

Parvendra Kumar, Amarendra K. Sarma

Published Jan 1, 2012• 0 citations
Publisher

Abstract

It is shown that under non-resonant excitation, the optical dipole force induced by the trains of few-cycle-pulses may be used for focusing and defocusing of atoms in an atomic beam by numerically solving the density matrix equations and force equation beyond the so-called rotating wave approximation.
DOI
10.1364/fio.2012.fth2e.4

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We report a study on light force on a beam of neutral two-level atoms superimposed upon a few-cycle-pulse Gaussian laser field under both resonant and off-resonant conditions. The phenomena of focusing, defocusing, and steering of the neutral atoms in the laser field are analyzed by solving the optical Bloch equation beyond the rotating-wave approximation and the force equation self-consistently. We find that two-level atoms in an atomic beam can be focused and defocused for large, positively and negatively detuned interactions even in the regime of extreme nonlinear optics. The so-called optical potential may be used for stable trapping of the neutral two-level atoms for large positively detuned interaction. This work successfully reproduces some of the features reported in recent experimental and theoretical works.
The optical forces on neutral two-level atoms by the subcycle pulsed focused vector field are investigated by numerically solving the density-matrix equations without the rotating-wave approximation. The phenomena of focusing or defocusing of the neutral atom are analyzed. For the transverse optical force, an acceleration of an atom that is 10 orders of magnitude higher than the Earth's gravitational acceleration ggg can be obtained. The optical force can change from a focusing force to a defocusing force depending on the initial state of the atom. The optical potential may be used to trap the neutral two-level atoms in the experiment of cold atoms.
We theoretically show how the effective focusing and defocusing of a diverging atomic beam can be realized using an appropriate sequence of linearly chirped few-cycle pulsed laser fields. First, we investigate and show that the time averaged optical dipole force induced by the sequence of either positively or negatively chirped pulses vanishes due to the periodic oscillations of the phases of in-phase components of atomic dipole moments. Then, we demonstrate that this issue could be overcome by utilizing a sequence of alternatively chirped pulses instead of either positively or negatively chirped pulses. It is shown that for such a sequence of pulses, the phases of in-phase components of atomic dipole moments does not oscillate periodically and in fact remain constant at either 0 or $\ensuremath{\pi}$ depending on the chirping direction of the initial pulse, resulting in either an effective focusing or defocusing optical dipole force. The trajectory of atoms under an optical dipole force is also investigated to actually show the focusing and defocusing. Finally, the role of beam shape on the proposed scheme is investigated and it turns out that a super-Gaussian pulse of order m=2m=2m=2 shows more efficacy compared to the normal Gaussian pulse.
We calculate analytically the error introduced by the rotating-wave approximation (RWA) to the description of a two-level-atom response to a resonant sufficiently intense femtosecond optical pulse of a few-cycle duration and any envelope. The analytically calculated non-RWA refinements to the RWA response are of the lowest order, i.e., linear in the small ratio of the Rabi to optical frequencies. One type of such refinements is small-amplitude rapid oscillations at nearly twice the optical frequency superimposed on the standard RWA population-inversion evolution. The other refinement is an extension of the spectrum of the induced atomic dipole moment in which the third harmonic of the transition frequency appears. The spectrum of this harmonic has an internal structure dependent on both strength and duration of the pulse. The analytically found non-RWA corrections are in qualitative agreement with the recent results of different numerical approaches by other authors and a recent experiment.
Abstract Developing an analytical theory for atomic coherence driven by ultrashort laser pulses has proved to be challenging due to the breakdown of the rotating wave approximation (RWA). In this paper, we present an approximate analytical solution that describes a two-level atom under the excitation of a far-off-resonance, few-cycle pulse of arbitrary shape without invoking the RWA. As an example of its applicability, a closed-form solution for Gaussian pulses is explicitly given, and the result is used to analyse the impact of carrier envelope phase on atomic population ratios. Comparisons with numerical solutions validate the accuracy our solution within the scope of the approximation. Finally, we outline an alternative approach that can lead to a more accurate solution by capturing the nonlinear behaviors of the system. The work lays out feasible theoretical paths toward analytically describing two-level atoms driven by ultrashort pulses.