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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Nonlinear couplings and cooling dynamics in a large Paul trap designed for quantum information

Romain Dubessy, S. Removille, B. Dubost, S. Guibal, T. Coudreau, Luca Guidoni

Published Jun 1, 2007• 1 citation
Publisher

Abstract

Nonlinear coupling between the radial and axial motion of a hot ion cloud appear in a loss spectrum obtained by measuring the fraction of ions still trapped after a phase of excitation ("tickle") applied to a couple of electrodes, this technique allows us to identify the frequencies associated to the radial and axial motion of the ions. It was observed that interactions between ions induce coupling effects in large hot ions clouds trapped in a linear Paul trap. The features of such a coupling are captured by n-body numerical simulations.

DOI
10.1109/cleoe-iqec.2007.4386778

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Nonlinear coupling between the radial and axial motion of a hot ion cloud appear in a loss spectrum obtained by measuring the fraction of ions still trapped after a phase of excitation ("tickle") applied to a couple of electrodes, this technique allows us to identify the frequencies associated to the radial and axial motion of the ions. It was observed that interactions between ions induce coupling effects in large hot ions clouds trapped in a linear Paul trap. The features of such a coupling are captured by n-body numerical simulations.
Ion traps have been pivotal in opening new frontiers for the precision spectroscopy of stable ions. We report on the demonstration of an additional ion trap: the linear combined trap. This device is particularly well suited for trapping ions with unstable nuclei, due to its large range of stability parameters that facilitates external injection online to an accelerator. The motion of an ion in such a linear combined trap is investigated theoretically and experimentally. In the trap ions oscillate harmonically in the radial direction and move nearly harmonically between fixed boundaries along the longitudinal axis. The presence of a homogeneous magnetic field and the applied dc and rf electric fields, lead to a set of coupled Mathieu equations. Their approximate solutions exhibit motional frequencies, which are combinations of shifted macromotion frequencies and the cyclotron frequency. The dependence of these motional frequencies on the applied trapping fields was studied in detail. For the measurements we used small clouds of laser cooled B9e+ ions and crystallized B9e+ ions. The observed oscillation frequencies are compared to both the results of zeroth order analytical solutions and to numerical simulations in which the frequency spectrum was obtained from the ion orbits by using the fast fourier transform formalism. The various motional resonances were experimentally recorded by applying a weak dipole excitation field to one of the trap electrodes, and by simultaneously observing at resonance the changes in the fluorescence intensity. Depending on the detuning of the cooling laser the ions gain energy during the motional excitation process in such a way that they are shifted further in or out of optical resonance by the Doppler effect. This leads to either positive or negative ion motion signals at the various ion oscillation frequencies.
We describe the characteristics of a linear Paul trap. This setup is designed in order to trap a large number (∼ ⁣ ⁣100.000\sim\!\! 100.000∼100.000) of laser-cooled Sr+^{+}+ and Ba+^{+}+ ions used for quantum information processing. We present a study of the dynamics of an Ar+ ions cloud by detection of the trap losses induced by resonant excitation of the ions motion.
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.
We experimentally study two-dimensional (2D) Coulomb crystals in the "radial-2D" phase of a linear Paul trap. This phase is identified by a 2D ion lattice aligned entirely with the radial plane and is created by imposing a large ratio of axial to radial trapping potentials. Using arrays of up to 19 ^{171}Yb^{+} ions, we demonstrate that the structural phase boundaries of such crystals are well described by the pseudopotential approximation, despite the time-dependent ion positions driven by intrinsic micromotion. We further observe that micromotion-induced heating of the radial-2D crystal is confined to the radial plane. Finally, we verify that the transverse motional modes, which are used in most ion-trap quantum simulation schemes, are well-predictable numerically and remain decoupled and cold in this geometry. Our results establish radial-2D ion crystals as a robust experimental platform for realizing a variety of theoretical proposals in quantum simulation and computation.
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 qz{\mathit{q}}_{\mathit{z}}qz​\ensuremath{\lesssim}0.6, whereas rapid heating is seen for qz{\mathit{q}}_{\mathit{z}}qz​=0.8.