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Journal of Modern Optics

Analysis of transient effects of two-level atom in laser light

Smail B. Bougouffa, S. Al‐Awfi

Published Feb 1, 2008• 12 citations
Publisher

Abstract

We are concerned with an analytic separation approach of the optical Bloch equations in the case of the two-level atom interacting with a classical light. The conditions that permit a complete separation of these equations are extracted in a natural manner and the exact solutions are obtained. A theoretical comparison with Torrey method is given. In this context, we find that the transient regime, valid from the instant of the application of the laser on atom, is significant for the evolution of forces and the dynamics before the steady-state regime will be reached. The case of Eu3 + ion moving in plane-light wave and standing-wave is treated with some details. The implications of the results for operating atoms and ions using laser light are discussed.

DOI
10.1080/09500340701485522

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We are concerned with an analytic separation approach of the optical Bloch equations in the case of the two-level atom interacting with a classical light. The conditions that permit a complete separation of these equations are extracted in a natural manner and the exact solutions are obtained. A theoretical comparison with Torrey method is given. In this context, we find that the transient regime, valid from the instant of the application of the laser on atom, is significant for the evolution of forces and the dynamics before the steady-state regime will be reached. The case of Eu3 + ion moving in plane-light wave and standing-wave is treated with some details. The implications of the results for operating atoms and ions using laser light are discussed.
The time evolution of the radiation pressure forces due to the action of a laser light on two-level atom moving inside a long hollow cylinder with a rectangular cross-section of sub-wavelength dimensions a × b is presented.This evolution is considered when the frequency of the light is comparable to a dipole allowed transition frequency.In this limit, the decay emission Γ is possible only via a very small number of modes.From the solutions of the Bloch equations in the dynamic regime, we nd that the transient regime, applicable from the instant the laser is switched on.This is important for the gross motion, provided that the upper-state lifetime Γ -1 is relatively long while the steady-state regime, formally such that t Γ -1 , is appropriate for the evaluation of the forces and the dynamics for large Γ .Signicant variations of the characteristics of the system are emphasized.These features are illustrated using typical parameters for the case of Eu 3+ that has a particularly small Γ .
The time evolution of the radiation pressure forces due to the action of laser light on matter in the form of neutral molecules, atoms, and ions is considered when the frequency of the light is comparable to a dipole-allowed transition frequency. We find that the transient regime, applicable from the instant the laser is switched on, is important for the gross motion, provided that the upper-state lifetime ${\ensuremath{\Gamma}}^{\ensuremath{-}1}$ is relatively long, while the steady-state regime, formally such that $t⪢{\ensuremath{\Gamma}}^{\ensuremath{-}1}$, is appropriate for the evaluation of the forces and the dynamics for large $\ensuremath{\Gamma}$. With a focus on the orbital-angular-momentum-endowed laser light, the light-induced time-dependent forces and torques are determined and their full time dependence utilized to determine trajectories. Marked differences are found in both translational and rotational features in comparison with the results emerging when the steady-state forces are assumed from the outset. Intricate and detailed atom trajectories are plotted for Laguerre-Gaussian light at near resonance for a transition of Eu3+{\mathrm{Eu}}^{3+}Eu3+ that has a particularly small $\ensuremath{\Gamma}$. The implications of the results for trapping and manipulating atoms and ions using laser light are pointed out and discussed.
This work presents an analytical calculation of the time-dependent radiation forces on a two-level atom interacting with a single-mode laser field. Such a closed and compact expression of the radiation forces is derived by solving the optical Bloch equations analytically. It is confirmed, in particular, that the radiation force consists of reactive as well as dissipative components, whose explicit analytical forms of the temporal solutions can be explicitly obtained. The succinct analytical solutions of the radiation forces may be helpful for a convenient and intuitive description of the complex atomic dynamics such as interaction with various laser fields.
Splitting of the atomic wave packet in velocity space due to the action of ultrashort laser pulses in the coherent regime of interaction was obtained in @2,9,10#. The transient regime of cooling by a sequence of short laser pulses of the narrowband traveling-wave field under the condition that the atoms decay completely between pulses was investigated in @11# .I t was shown in @12# that more deceleration of neutral atoms may be achieved with the train of ultrashort p pulses separated by a few radiative lifetimes than would be achived with the same average intensity used for cw generation. Laser cooling on transitions with a linewidth narrower than the recoil shift was studied by the Monte Carlo method using broadband excitation in @13#. The force of the stimulated light pressure on an atom arising from the action of two near-resonant standing waves with different frequencies modeling two counterpropagating waves with modulated in time amplitudes was studied in @14#.
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.
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.