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arXiv:1105.0665 · Physical Review A

Doppler cooling with coherent trains of laser pulses and a tunable velocity comb

Ekaterina Ilinova, Mahmoud Ahmad, Andrei Derevianko

Published Sep 26, 2011• 25 citations
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Abstract

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.

DOI
10.1103/physreva.84.033421

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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 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 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 study Doppler cooling of atoms using a frequency comb and develop a theory to quantitatively describe the process by investigating the interaction of two-level atoms with two counterpropagating pulse trains. We derive the radiative force on atoms and show that each comb mode effectively acts as a cooling laser, thereby indicating that simultaneous laser cooling in multiple cooling channels can be achieved using a single-frequency comb source. Possible experimental applications involving alkali-metal atoms are illustrated.
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.
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#.
We investigate coherent accumulation processes in three-level atoms excited by a train of ultrashort pulses in the case where the atomic relaxation times are greater than the laser repetition period. In this situation the resonances of the laser field with the atomic system are determined by the laser frequency comb rather than by the spectrum of a single pulse. Using the density matrix formalism, we develop a perturbative theory that is valid for arbitrary pulse shapes. The excitation of a Doppler-broadened atomic vapor by hyperbolic-secant pulses and $0\ensuremath{\pi}$ pulses is analyzed. It is shown that pulse shape has a great influence on the accumulation process and can change the spectral periodicity of the pattern impressed on the Doppler profile of the medium due to the two-photon absorption process. The effect of interpulse phases is also investigated, and we show that the atomic populations can vary by more than one order of magnitude with small variations of the laser repetition rate, while being insensitive to variations of the laser offset. Finally, the theory is adapted for the temporal-coherent-control technique, and its results are compared with previously reported experimental data.