Dynamics of the laser-cooling of a trapped ion

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

Ananyo Maitra, Dietrich G. Leibfried, Denis Ullmo +1 more

We study the stochastic dynamics of a particle in a periodically driven potential. For atomic ions trapped in radio-frequency Paul traps, noise heating and laser cooling typically act slowly in comparison with the unperturbed motion. These stochastic processes can be accounted for in terms of a probability distribution defined over the action variables, which would otherwise be conserved within the regular regions of the Hamiltonian phase space. We present a semiclassical theory of low-saturation laser cooling applicable from the limit of low-amplitude motion to large-amplitude motion, accounting fully for the time-dependent and anharmonic trap. We employ our approach to a detailed study of the stochastic dynamics of a single ion, drawing general conclusions regarding the nonequilibrium dynamics of laser-cooled trapped ions. We predict a regime of anharmonic motion in which laser cooling becomes diffusive (i.e., it is equally likely to cool the ion as it is to heat it), and can also turn into effective heating. This implies that a high-energy ion could be easily lost from the trap despite being laser cooled; however, we find that this loss can be counteracted using a laser detuning much larger than Doppler detuning.

Yoshiharu Maeno Yoshiharu Maeno, Maki Tachikawa, Yoshiki Moriwaki +1 more

We establish a theoretical model which quantitatively describes the dynamics of laser cooled ions confined in a radio-frequency (rf) trap. In our model the laser cooling efficiency and the rate of collisional radio-frequency (rf) heating are explicitly formulated. Considering the balance between these two effects, the ion temperature is determined at each trap parameter. This model precisely reproduces the laser-induced-fluorescence (LIF) line profile observed for 24 Mg+ ions.

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

Chang-Da-Ren Fang, Yao Huang, Hua Guan +2 more

We investigate the process of pulsed laser cooling using a self-constructed molecular dynamics simulation (MD-Simulation) program. We simulate the Doppler cooling process and pulsed laser Doppler cooling process of a single 40Ca+ ion, and the comparison with the experimental results shows that this self-constructed MD-Simulation program works well in the weak laser intensity situation. Furthermore, we analyze the pulsed laser Doppler cooling process of a single 27Al+ ion. This program can be used to analyze the molecular dynamic process of various situations of Doppler cooling in an ion trap, which could give predictions and experimental guidance.

D. Kielpinski, Blaise Gassend, Franz X. Kärtner