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Japanese Journal of Applied Physics

Dynamics of Trapped Ions in the Presence of Laser Cooling and Radio-Frequency Heating

Yoshiharu Maeno Yoshiharu Maeno, Maki Tachikawa, Yoshiki Moriwaki, Tadao Shimizu

Published Feb 1, 1995• 14 citations
Publisher

Abstract

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.

DOI
10.1143/jjap.34.l174

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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.
The nonlinear dynamics of large ion clouds ($N\ensuremath{\ge}256$ ions) trapped in radio-frequency (rf) traps and coupled to laser cooling give rise to a bistable behavior of the temperature. Numerical simulations of the free evolution of a large three-dimensional spherical cloud is used to characterize how the oscillating field amplitude and the ion number control the rf-heating rate and the switching between the two stable states. We show that the heating rate does not significantly depend on the ion number but strongly depends on the oscillating field. This exhibits the major role played by the density of the ensemble. The competition between the radio-frequency heating and the laser cooling is also discussed. They are used to design scenarios to take advantage of the threshold effect to detect and quantify perturbations by an intruder.
We investigate the energy dynamics of noncrystallized (melted) ions, confined in a Paul trap. The nonperiodic Coulomb interaction experienced by melted ions forms a medium for nonconservative energy transfer from the radio-frequency (rf) field to the ions, a process known as rf heating. We study rf heating by analyzing numerical simulations of noncrystallized ion motion in Paul trap potentials, in which the energy of the ions' secular motion changes at discrete intervals, corresponding to ion-ion collisions. The analysis of these collisions is used as a basis to derive a simplified model of rf heating energy dynamics, from which we conclude that the rf heating rate is predominantly dependent on the rf field strength. We confirm the predictability of the model experimentally: Two trapped 40Ca+^{40}\mathrm{Ca}^{+}40Ca+ ions are deterministically driven to melt, and their fluorescence rate is used to infer the ions' energy. Under these experimental conditions, we investigate which Doppler cooling parameters are required for efficient recrystallization, and compare our results to simulations.
Fluorescence line profiles and their implications on the cooling dynamics of the Mg+{\mathrm{Mg}}^{+}Mg+ ions stored in a linear rf trap are studied. The line profile is dictated by the temperature of the ion cloud at different laser detunings. The upper bound of the lowest temperature was estimated for different values of the rf trapping potential amplitude and the buffer gas pressure. A general trend of this ultimate temperature to increase with the rf trapping voltage and buffer gas pressure is expected, with an abrupt change at some critical value corresponding to the transition to and from a strongly correlated liquid or crystal state. While on the one hand this expectation was confirmed when the buffer gas pressure was varied; on the other hand the influence of the amplitude of the trapping voltage on the ultimate temperature shows an interesting new feature of first dipping down before the sharp increase occurs.
We analyze the possibility of cooling ions with a single laser beam, due to the coupling between the three components of their motion induced by the Coulomb interaction. For this purpose, we numerically study the dynamics of ion clouds of up to 140 particles, trapped in a linear quadrupole potential and cooled with a laser beam propagating in the radial plane. We use molecular dynamics simulations and model the laser cooling by a stochastic process. For each component of the motion, we systematically study the dependence of the temperature on the anisotropy of the trapping potential. Results obtained using the full radio-frequency (rf) potential are compared to those of the corresponding pseudopotential. In the rf case, the rotation symmetry of the potential has to be broken to keep ions inside the trap. Then, as for the pseudopotential case, we show that the efficiency of the Coulomb coupling to thermalize the components of motion depends on the geometrical configuration of the cloud. Coulomb coupling appears to be not efficient when the ions organize as a line or a pancake and the three components of motion reach the same temperature only if the cloud extends in three dimensions.