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arXiv:1203.1963 · Physical Review A

Doppler cooling of three-level Λ systems by coherent pulse trains

Ekaterina Ilinova, Andrei Derevianko

Published Aug 27, 2012• 5 citations
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Abstract

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.

DOI
10.1103/physreva.86.023417

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We explore the possibility of decelerating and Doppler cooling an ensemble of three-level \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type atoms by a coherent train of short, nonoverlapping laser pulses. We show that \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ 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 study the dynamics of three-level $\ensuremath{\Lambda}$-type atoms driven by a coherent train of short, nonoverlapping laser pulses. We derive analytical nonperturbative expressions for the density matrix by approximating the pulses by a $\ensuremath{\delta}$ function. We demonstrate that, depending on the train parameters, several scenarios of system dynamics can be realized. We show the possibility of driving Raman transitions between the two ground states of the $\ensuremath{\Lambda}$ system, avoiding populating excited states by using pulses with effective area equal to $2\ensuremath{\pi}$. The number of $2\ensuremath{\pi}$ pulses needed to transfer the entire population from one ground state to another depends on the ratio between the Rabi frequencies of two allowed transitions. In the case of equal Rabi frequencies, the system can be transferred from one ground state to another with a single $2\ensuremath{\pi}$ pulse. When the total pulse area differs from $2\ensuremath{\pi}$ and the two-photon resonance condition is fulfilled, the system evolves into a ``dark'' state and becomes transparent to subsequent pulses. The third possible scenario is the quasi-steady-state regime when neither the total single-pulse area is equal to $2\ensuremath{\pi}$ nor is the two-photon resonance condition fulfilled. In this regime the radiative-decay-induced drop in the population following a given pulse is fully restored by the subsequent pulse. We derive an analytical expression for the density matrix in the quasi-steady-state regime. We analyze the dependence of the postpulse excited-state population in the quasi-steady-state regime on the train parameters. We find the optimal values for the train parameters corresponding to the maximum of the excited-state population. The maximum of the excited-state population in the steady-state regime is reached at an effective single-pulse area equal to $\ensuremath{\pi}$ and is equal to 2/32/32/3 in the limiting case when its radiative lifetime is much shorter than the pulse repetition period.
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 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.
Analogous to the extension of laser cooling techniques from two-level to three-level atoms, Doppler cooling of molecules with an intermediate electronic state is considered. In particular, we use a rate-equation approach to simulate cooling of SiO+{\mathrm{SiO}}^{+}SiO+, in which population buildup in the intermediate state is prevented by its short lifetime. We determine that Doppler cooling of SiO+{\mathrm{SiO}}^{+}SiO+ can be accomplished without optically repumping from the intermediate state, at the cost of causing undesirable parity flips and rotational diffusion. Since the necessary repumping would require a large number of continuous-wave lasers, optical pulse shaping of a femtosecond laser is proposed as an attractive alternative. Other candidate three-electron-level molecules are also discussed.
We examine the laser cooling of three-level (Lambda) -atoms in the field of two standing waves when frequency detunings are considerably greater than natural width of the excited state as well as the Rabi frequencies in the system. It is shown that at the difference of frequency detunings is small when compared to the Rabi frequencies sub-Doppler cooling of the (Lambda) -atom is possible. We present the dependence of the light pressure force on the atoms velocity and dependence of cooled atoms temperature on the parameters of the exciting waves.
A theoretical study is made of the dissipative force and Doppler cooling of a ladder-type three-level atom coupled to a travelling coherent light beam. The dependence of the force on parameters such as detunings, Rabi frequencies, spontaneous decay and coherence transfer rates is calculated numerically and shown graphically. Analytical expressions for the force are obtained for special parameter values. It is shown that for suitable choices of parameter values, it is possible to cool three-level atoms to temperatures down below the Doppler limit.