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arXiv:1206.2393

See-saw protocol for Doppler cooling of multilevel systems with coherent pulse trains

Mahmoud Ahmad, Ekaterina Ilinova, Andrei Derevianko

Published Jun 11, 2012• 0 citations
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Abstract

We consider decelerating and cooling an ensemble of multilevel atoms and molecules with a coherent train of ultrashort laser pulses. In the frequency domain such trains form frequency combs. We propose a novel see-saw scheme of Doppler cooling of multilevel atoms and molecules. In this scheme the teeth of the frequency comb are periodically moved in and out of resonance with the allowed transitions. The see-saw cooling may be carried out in practice by switching carrier-envelope phase offset between predefined values. We study the performance of the see-saw scheme for the simplest prototype three-level $Λ$ system and demonstrate its advantage. For these systems we demonstrate a procedure for determining optimal train parameters, and see-saw switching period. We also illustrate the performance of the protocol by numerically simulating time evolution of velocity distribution.

DOI
10.48550/arxiv.1206.2393

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We consider decelerating and cooling an ensemble of multilevel atoms and molecules with a coherent train of ultrashort laser pulses. In the frequency domain such trains form frequency combs. We propose a novel see-saw scheme of Doppler cooling of multilevel atoms and molecules. In this scheme the teeth of the frequency comb are periodically moved in and out of resonance with the allowed transitions. The see-saw cooling may be carried out in practice by switching carrier-envelope phase offset between predefined values. We study the performance of the see-saw scheme for the simplest prototype three-level ΛΛΛ system and demonstrate its advantage. For these systems we demonstrate a procedure for determining optimal train parameters, and see-saw switching period. We also illustrate the performance of the protocol by numerically simulating time evolution of velocity distribution.
We explore the possibility of decelerating and Doppler cooling an ensemble of two-level atoms by a coherent train of short, nonoverlapping laser pulses. We derive analytical expressions for mechanical force exerted by the train. In frequency space the force pattern reflects the underlying frequency comb structure. The pattern depends strongly on the ratio of the atomic lifetime to the repetition time between the pulses and pulse area. For example, in the limit of short lifetimes, the frequency-space peaks of the optical force wash out. We propose to tune the carrier-envelope offset frequency to follow the Doppler-shifted detuning as atoms decelerate; this leads to compression of atomic velocity distribution about comb teeth and results in a ``velocity comb''---a series of narrow equidistant peaks in the velocity space.
We propose a method of stimulated laser decelerating of diatomic molecules by counter-propagating π -trains of ultrashort laser pulses. The decelerating cycles occur on the rovibrational transitions inside the same ground electronic manifold, thus avoiding the common problem of radiative branching in Doppler cooling of molecules. By matching the frequency comb spectrum of the pulse trains to the spectrum of the R -branch rovibrational transitions we show that stimulated deceleration can be carried out on several rovibrational transitions simultaneously. This enables an increase in the number of cooled molecules with only a single laser source. The exerted optical force does not rely on the decay rates in a system and can be orders of magnitude larger than the typical values of scattering force obtained in conventional Doppler laser cooling schemes.
We propose a method of stimulated laser cooling of diatomic molecules by counter-propagating πππ-trains of ultrashort laser pulses. The cooling cycles occur on the rovibrational transitions inside the same ground electronic manifold, thus avoiding the common problem of radiative branching in Doppler cooling of molecules. By matching the frequency comb spectrum of the pulse trains to spectrum of the R-branch rovibrational transitions we show that stimulated cooling can be carried out on several rovibrational transitions simultaneously, thereby increasing number of cooled molecules. The exerted optical force does not rely on the decay rates in a system and can be orders of magnitude larger than the typical values of scattering force obtained in conventional Doppler laser cooling schemes.
We explore the possibility of decelerating and Doppler cooling an ensemble of three-level $\ensuremath{\Lambda}$-type atoms by a coherent train of short, nonoverlapping laser pulses. We show that $\ensuremath{\Lambda}$ atoms can be Doppler cooled without additional repumping of the population from the intermediate ground state. We derive an analytical expression for the scattering force in the quasi-steady-state regime and analyze its dependence on pulse-train parameters. Based on this analysis we propose a method of choosing pulse-train parameters to optimize the cooling process.
We discuss a possible one-dimensional trapping and cooling of atoms and molecules due to their nonresonant interaction with counterpropagating light pulse trains. The counterpropagating pulses form a one-dimensional trap for atoms and molecules and a properly chosen carrier frequency detuning from the transition frequency of the atoms or molecules keeps the temperature of the atomic or molecular ensemble close to the Doppler cooling limit. The calculation by the Monte Carlo wave-function method is carried out for the two-level and three-level schemes of the atom's and the molecule's interaction with the field, respectively. The models discussed are applicable to atoms and molecules with almost diagonal Frank-Condon factor arrays. Illustrative calculations are carried out for ensemble-averaged characteristics for sodium atoms and SrF molecules in the trap. The potential for the nanoparticle light pulses's trap formed by counterpropagating light pulse trains is also discussed.
Direct frequency-comb spectroscopy is a technique that employs a train of well-stabilized ultrashort pulses to study the spectral properties of atomic or molecular systems. In this way, it opens the possibility of incorporating various coherent-control techniques for such spectral investigations. Here we introduce a theory for the interaction of a multilevel atom with such pulse trains, which is general enough to take into account an arbitrarily shaped frequency comb. We illustrate its application by studying the interaction of 87Rb^{87}\text{R}\text{b}87Rb atoms with trains of pulses of various shapes, resonant with the $5S\text{\ensuremath{-}}5D$ two-photon transition of rubidium. More specifically, we treat the interaction with hyperbolic-secant pulses, chirped pulses, and 0-$\ensuremath{\pi}$ pulses, respectively. The theory is designed to work at an arbitrary perturbation order. For the results presented here, we mostly used a 12th-order perturbation series at the pulse's electric field. Due to the large number of levels involved, such modeling may be quite complex computationally, and an important point of the present work is then to introduce the required numerical approach to treat this problem efficiently.