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Physical Review A

Distortion of spectral line profiles of laser-cooled ions in a radio-frequency ion trap

Taro Hasegawa, Daisuke Tanooka, Tadao Shimizu

Published Sep 1, 1998• 6 citations
Publisher

Abstract

The laser-cooled ions in a radio-frequency ion show a variety of peculiar line profiles as functions of laser intensity and trap potential. All these line profiles are well reproduced by a calculation based on the present theoretical model, in which the ion motion in a trap in the presence of laser radiation pressure is analyzed. The results give information about collisions of ions, and are utilized for the accurate spectroscopic measurement of the ion responses.

DOI
10.1103/physreva.58.2327

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The laser-cooled ions in a radio-frequency ion show a variety of peculiar line profiles as functions of laser intensity and trap potential. All these line profiles are well reproduced by a calculation based on the present theoretical model, in which the ion motion in a trap in the presence of laser radiation pressure is analyzed. The results give information about collisions of ions, and are utilized for the accurate spectroscopic measurement of the ion responses.
We formulated a model to reproduce the spectral shape of in situ mass spectra of sympathetically cooled molecular ions trapped in a linear radio-frequency-quadrupole. The molecular ions are sympathetically cooled by laser cooled ions. The mass spectrum is obtained by observing fluorescence emitted from the laser-cooled ions as we excite the resonant motion of the sympathetically cooled molecular ions in the trap. The model, which uses a pseudopotential and space-charge approach, reproduces the mass spectra of molecules. The model suggests that the variation of the space-charge density of the laser-cooled ions can produce in-trap kinetic excitation without the loss of the excited ions from the trap.
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.
The resonance fluorescence spectrum of a laser-cooled trapped ion is theoretically studied in the Lamb-Dicke limit. Angular averaged spectrum around the elastic peak and the motional sidebands is calculated. The widths of the sidebands are shown to be given by the cooling rate of the ion in the trap. In the limit when the trapping force is strong a possibility of dispersive line shapes is predicted. The spectrum derived is also shown to reproduce in the low-intensity limit the earlier perturbative results.
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.
An experimental study of sideband laser cooling of trapped ions in miniature radio-frequency traps is presented. In+{\mathrm{In}}^{+}In+ ions are laser cooled by exciting the narrow intercombination line ${5s}^{2}{}^{1}{S}_{0}\ensuremath{\rightarrow}5s5p{}^{3}{P}_{1}$, which shows resolved sidebands due to the vibrational motion of the ions in the trap. The influence of the micromotion at the frequency of the oscillating trapping field is investigated. Heating processes through coupling with the trapping field occur for certain regions of negative laser detuning. A method of bichromatic sideband cooling is introduced that combines efficient cooling from high temperatures with the possibility of reaching low mean vibrational quantum numbers 〈n〉<1〈n〉<1〈n〉<1 by using narrow optical transitions. This technique allows recording of high-resolution excitation spectra of the cooling transition in the Lamb-Dicke regime and thus determination of 〈n〉〈n〉〈n〉. Single ions as well as two-ion Coulomb crystals have been cooled to temperatures below $100 \ensuremath{\mu}\mathrm{K}$, and population of the ground state of motion to more than 50% over long time scales is demonstrated. These values are close to the lower limit for the detection of vibrational excitation with the present method.