Semiclassical Laser Cooling of Trapped Ions in a One-Dimensional Standing Wave

Mang Feng, Wenhua Hai, Xiwen Zhu +3 more

Ferdinand Schmidt‐Kaler, Jürgen Eschner, R. Blatt +3 more

J. I. Cirac, R. Blatt, P. Zoller +1 more

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)].

Shuo Zhang, Chun-Wang Wu, Ping‐Xing Chen

We propose a dark-state cooling scheme of trapped ion systems using standing waves in the Lamb-Dicke limit. By exploiting the property of standing waves, the heating effects caused by the carrier and the blue sideband transitions vanish and lower final phonon number can be achieved. Different from other dark-state cooling schemes, our scheme is more robust under the fluctuations of laser intensities.

Wayne M. Itano, Jonas Bergquist, J. J. Bollinger +1 more

R. L. de Matos Filho, W. Vogel

Laser sideband cooling of trapped ions is studied in a standing wave for localization conditions far from the Lamb-Dicke limit. Cooling is shown to be possible even in the antinode of a standing wave, where in the Lamb-Dicke limit only heating appears. Tuning the laser to the second-sideband increases the cooling effect significantly. Moreover, second-sideband cooling is expected to yield a nonclassical, sub-Poissonian occupation statistics of the vibrational states of the ion.