Laser sideband cooling with positive detuning

An experimental and theoretical study of laser sideband cooling of a trapped ion in a radiofrequency trap is presented. The influence of the micromotion in the time-dependent potential of a Paul trap can lead to a counterintuitive situation, where sideband cooling is possible for positive values of the laser detuning, i.e., for a laser frequency that is higher than the resonance frequency of the ion at rest. The cooling rate and the capture range are calculated in a semiclassical model. Experimental results of laser sideband cooling at positive detuning are demonstrated with a single trapped ${\mathrm{In}}^{+}$ ion stored in a miniature Paul trap.

Figure 1

Cooling rate as a function of the mean vibrational quantum number $⟨n⟩$ for $\delta ∕2\pi =+7\mathrm{MHz}$ (with $\omega ∕2\pi =1\mathrm{MHz}$, $\Omega ∕2\pi =10\mathrm{MHz}$) according to the semiclassical model. Cooling toward the vibrational ground state of the trap occurs as long as $⟨n⟩<500$.

Figure 2

Excitation spectra of a single trapped ${\mathrm{In}}^{+}$ ion as a function of laser detuning. (a) The ion is localized in the center of the trap; no additional micromotion sidebands are visible. (b) Due to electric dc fields the ion is shifted off the center of the trap leading to sidebands of the additional micromotion at $\delta =l\Omega$, with $l=-1,-2,-3$ $(\Omega ∕2\pi =10.03\mathrm{MHz})$. (c) After jumping with the laser detuning from $\delta ∕2\pi =-3\text{MHz to}+7\mathrm{MHz}$, a similar line profile at $+10\mathrm{MHz}$ as in (a) at zero detuning is obtained. The observation of this narrow resonance is the experimental proof for cooling at positive detuning (note the shift of the frequency scale).

Figure 3

Numerical calculation of (a) fluorescence and (b) mean kinetic energy as a function of laser detuning according to the semiclassical model of sideband cooling in a Paul trap. The fluorescence intensity is normalized to the emission of the ion at resonance; parameters correspond to those of Figs. 2b and 2c.