Laser cooling of trapped particles III: The Lamb-Dicke limit

Giovanna Morigi, Jürgen Eschner, J. I. Cirac +1 more

We study laser cooling of two ions that are trapped in a harmonic potential and interact by Coulomb repulsion. Sideband cooling in the Lamb-Dicke regime is shown to work analogously to sideband cooling of a single ion. Outside the Lamb-Dicke regime, the incommensurable frequencies of the two vibrational modes result in a quasicontinuous energy spectrum that significantly alters the cooling dynamics. The cooling time decreases nonlinearly with the linewidth of the cooling transition, and the effect of dark states which may slow down the cooling is considerably reduced. We show that cooling to the ground state is also possible outside the Lamb-Dicke regime. We develop the model and use quantum Monte Carlo calculations for specific examples. We show that a rate equation treatment is a good approximation in all cases.

Juha Javanainen, Stig Stenholm

Juha Javanainen, Stig Stenholm

Giovanna Morigi, J. I. Cirac, Maciej Lewenstein +1 more

We propose a laser cooling scheme that allows to cool a single atom confined in a harmonic potential to the trap ground state $|0>$. The scheme assumes strong confinement, where the oscillation frequency in the trap is larger than the effective spontaneous decay width, but is not restricted to the Lamb-Dicke limit, i.e. the size of the trap ground state can be larger than the optical wavelength. This cooling scheme may be useful in the context of quantum computations with ions and Bose-Einstein condensation.

Juha Javanainen, Stig Stenholm

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.