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arXiv:1004.5202 · Physical Review A

Ion dynamics in a linear radio-frequency trap with a single cooling laser

Mathieu Marciante, C. Champenois, A. Calisti, J. Pedregosa-Gutierrez, Martina Knoop

Published Sep 9, 2010• 23 citations

Abstract

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.

DOI: 10.1103/physreva.82.033406

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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.

A simple method of cooling the transverse motion of an ion cloud in a linear Paul trap with a single axial laser is proposed. Transverse thermal oscillations of ions are indirectly damped by the longitudinal laser friction via an additional radio-frequency potential that resonantly couples two degrees of freedom. The fundamental mechanism of the present cooling scheme is theoretically described with the help of a harmonic oscillator model. It is shown that the indirect cooling rate can be considerably enhanced when the frequencies of the transverse and longitudinal ion oscillations satisfy a certain relation. The validity of theoretical predictions is confirmed through molecular dynamics simulations in which the detailed three-dimensional configuration of a typical Paul trap is incorporated.

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 have carried out a molecular-dynamics simulation of hundreds of ions confined in a Paul trap. The simulation includes the trapped particles' micromotion and interparticle Coulomb interactions. We have implemented a random walk in velocity to bring the secular motion to a given temperature which we have numerically measured. When the coupling \ensuremath{\Gamma} is large the ions form concentric shells which undergo a quadrupole oscillation at the rf frequency, while the ions within a shell form a 2D hexagonal lattice. Ion clouds at 5 mK show no rf heating for

{\mathit{q}}_{\mathit{z}}

\ensuremath{\lesssim}0.6, whereas rapid heating is seen for

{\mathit{q}}_{\mathit{z}}

=0.8.

An investigation of the sympathetic cooling \nmethod for the studies of large ultra-cold molecular ions in a quadrupole ion trap has been conducted.Molecular dynamics simulations are performed to study the rf heating mechanisms in the ion trap. The dependence of \nrf heating rates on the ion temperature, trapping parameters, \nand the number of ions is obtained. New rf heating mechanism \naffecting ultra-cold ion clouds exposed to laser radiation is described.The saturation spectroscopy setup of the hyperfine spectra \nof the molecular iodine has been built to provide an accurate frequency reference for the laser wavelength. This reference is used to obtain the fluorescence lineshapes of \nthe laser cooled Mg

^+

ions under different trapping conditions.The ion temperatures are deduced from the measurements, and \nthe influence of the rf heating rates on the fluorescence lineshapes \nis also discussed. Cooling of the heavy (

m=720

a.u.) fullerene ions to under 10K by the means of the sympathetic cooling by the Mg

^+

ions(

m=24

a.u.) is demonstrated. The single-photon imaging system has been developed and used to obtain the images of the Mg

^+

ion crystal structures at mK temperatures.

Additional radio-frequency (rf) potentials applied to linear multipole traps create extra field nodes in the radial plane which allow one to confine single ions, or strings of ions, in totally rf field-free regions. The number of nodes depends on the order of the applied multipole potentials and their relative distance can be easily tuned by the amplitude variation of the applied voltages. Simulations using molecular dynamics show that strings of ions can be laser cooled down to the Doppler limit in all directions of space. Once cooled, organized systems can be moved with very limited heating, even if the cooling process is turned off.