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AIP conference proceedings

On the optical cooling of trapped ions

P. E. Toschek

Published Jan 1, 1991• 0 citations
Publisher

Abstract

Limits for the laser cooling of a trapped ion and some experimental observations are summarized. The final temperature is low when a dipole‐forbidden line is two‐photon excited, e.g. by way of an electronic Raman process. Now, the two light modes also support dispersive interaction by stimulated Raman‐like scattering. A simplified model in terms of the vibrational Raman effect identifies processes analogous to those known from atoms in a standing light wave, and it reveals novel parametric interaction of ion vibration and light. In the diabatic limit, when dephasing by spontaneous decay is small, the ion approaches the dynamics of an electron in a free‐electron laser.

DOI
10.1063/1.41005

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Bulletin of the American Physical Society•May 1, 1993•0 citations
Limits for the laser cooling of a trapped ion and some experimental observations are summarized. The final temperature is low when a dipole‐forbidden line is two‐photon excited, e.g. by way of an electronic Raman process. Now, the two light modes also support dispersive interaction by stimulated Raman‐like scattering. A simplified model in terms of the vibrational Raman effect identifies processes analogous to those known from atoms in a standing light wave, and it reveals novel parametric interaction of ion vibration and light. In the diabatic limit, when dephasing by spontaneous decay is small, the ion approaches the dynamics of an electron in a free‐electron laser.
The results of a recent experiment on the mechanical interaction of a bichromatic light beam with a single three-level ion serve to redefine laser cooling of ions in a trap and of atoms in standing light waves. Novel variants of light forces are demonstrated. They are caused by stimulated Raman-type two-photon transitions combined with spontaneous Raman scattering and by all-stimulated parametric interaction. These efficient processes parallel the generation of a stimulated light force in a standing wave and the operation of a free-electron laser, respectively. The latter force imposes no natural limit on the residual excitation energy of trapped particles.
We study cooling of the collective vibrational motion of two 138Ba+{}^{138}{\mathrm{Ba}}^{+}138Ba+ ions confined in an electrodynamic trap and irradiated by laser light close to the resonances ${S}_{1/2}\ensuremath{-}{P}_{1/2}$ (493 nm) and ${P}_{1/2}\ensuremath{-}{D}_{3/2}$ (650 nm). The motional state of the ions is monitored by a spatially resolving photomultiplier. Depending on detuning and intensity of the cooling lasers, macroscopically different motional states corresponding to different ion temperatures are observed. We also derive the ions' temperature from detailed analytical calculations of laser cooling taking into account the Zeeman structure of the energy levels involved. The observed motional states perfectly match the calculated temperatures. Significant heating is observed in the vicinity of the dark resonances of the Zeeman-split ${S}_{1/2}\ensuremath{-}{D}_{3/2}$ Raman transitions. Here two-photon processes dominate the interaction between lasers and ions. Parameter regimes of laser light are identified that imply most efficient laser cooling.
Laser cooling of trapped ions in a standing- and running-wave configuration is discussed theoretically. The ions are assumed to be spatially localized on the scale provided by the wavelength of the laser (Lamb-Dicke limit). A master equation for the center-of-mass distribution of the ion is derived for a multilevel system, and explicit results are presented for two- and three-level systems and harmonic trapping potentials. For the two-level system located at the node of the standing wave, we find final temperatures that are a factor of 2 lower than the limit for a running wave and cooling rates that do not saturate with the laser intensity. At the point of maximum gradient of the standing wave, blue detuned cooling is found that is analogous to the Sisyphus cooling of free atoms. For a three-level system we compare our results with those of Wineland, Dalibard, and Cohen-Tannoudji [J. Opt. Soc. Am. B 9, 32 (1992)].
A technique for cooling atoms in two dimensions to temperatures below the single photon recoil limit k{sub B}T{sub rec} = (hk){sup 2}/2M is demonstrated. This technique combines velocity selection using stimulated Raman transitions and dissipation by spontaneous emission. It is an extension of the one dimensional cooling technique that was demonstrated recently. Experimental results for sodium atoms are presented, and the limits on the minimal cooling temperatures are analyzed. Finally, the possibility of applying the Raman cooling technique to atoms in a dipole trap is discussed.
Optical dipole traps can provide strong, state-independent confinement of atoms. Unfortunately, the spatially dependent light shifts of optical transitions in dipole traps can interfere with conventional laser cooling techniques. These limitations may be overcome by cooling trapped atoms with stimulated Raman transitions. In particular, the lights shifts of ground state sublevels can be equal, so that the Raman cooling transition is unperturbed. Cooling in the sideband limit, to the quantum ground state of motion, should be possible. We have confined {sup 85}Rb atoms in a far-detuned optical dipole trap, and indirectly measured extremely low heating rates of the trapped atoms. We have also driven velocity-sensitive stimulated Raman transitions of the trapped atoms. The high resolution of these stimulated Raman resonances should allow us to resolve the motional sidebands and to directly cool the trapped atoms.