Jofre Pedregosa-Gutierrez

In radio-frequency trap, the temperature of ion ensembles converges towards a hot equilibrium due to radio-frequency heating. This effect is detrimental to the stability of trapped ensembles and is the justification of cooling. The intensity of this radio-frequency heating increases with the amplitude of the radio-frequency field $q_x$. Using an analytical empirical formula, we show that the lifetime of the ion ensemble $t_0$ under cold condition increases with $q_x$ according to a power law $t_0\propto q_x^A$, and does not vary significantly for the several ion quantities $N$ tested. The temperature of the explosive onset $B$ decreases linearly with $q_x$. We also show that non-linear instabilities due to trapping parameters decreases $t_0$ and $B$, and produce a local increase of heating rate for certain temperature ranges.

The non-linear dynamics of large ion clouds ($N \geq 256 $ ions) trapped in radio-frequency traps and coupled to laser-cooling give rise to a bistable behaviour of the temperature. Numerical simulations of the free evolution of a large three-dimensional spherical cloud is used to characterise 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 depends 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 scenarii to take advantage of the threshold effect to detect and quantify perturbations by an intruder.

The problem for molecular identification knows many solutions which include mass spectrometers whose mass sensitivity depends on the performance of the detector involved. The purpose of this article is to show by means of molecular dynamics simulations, how a laser-cooled ion cloud, confined in a linear radio-frequency trap, can reach the ultimate sensitivity providing the detection of individual charged heavy molecular ions. In our simulations, we model the laser-cooled Ca + ions as two-level atoms, confined thanks to a set of constant and time oscillating electrical fields. A singly-charged molecular ion with a mass of 10 6 amu is propelled through the ion cloud. The induced change in the fluorescence rate of the lather is used as the detection signal. We show that this signal is due to a significant temperature variation triggered by the Coulombian repulsion and amplified by the radio-frequency heating induced by the trap itself. We identify the optimum initial energy for the molecular ion to be detected and furthermore, we characterize the performance of the detector for a large range of confinement voltages.

Radio-frequency linear multipole traps have been shown to be very sensitive to mis-positioning of their electrodes, which results in a symmetry breaking and leads to extra local minima in the trapping potential \cite{pedregosa17} disturbing the operation of the trap. In this work, we analytically describe the RF-potential of a realistic octupole trap by including lower order terms to the well-established equation for a perfectly symmetric octupole trap. We describe the geometry by a combination of identified defects, characterised by simple analytical expressions. A complete equation is proposed for a trap with any electrode deviation relying on a combination of the simple cases where the defects are taken individually. Our approach is validated by comparison between analytical and numerical results for defect sizes up to 4\% of the trap radius. As described in \cite{pedregosa18}, an independent fine-tuning of the amplitude of the RF voltage applied on each electrode can be used to mitigate the geometrical defects of a realistic trap. In a different way than in \cite{pedregosa18}, the knowledge of an analytical equation for the potential allows to design the set of RF-voltages required for this compensation, based on the experimental measurement of the ion position in the trap, without information concerning the exact position of each electrode, and with a small number of iterations. The requirements, performances and limitations of this protocol are discussed via comparison of numerical simulations and analytical results.

A novel protocol of interrogation based on coherent population trapping in an N-level scheme atomic system leads to dark resonances involving three different photons. An ensemble of several hundreds of radiofrequency-trapped ions is probed by three lasers simultaneously locked onto the same optical frequency comb, resulting in high-contrast spectral lines referenced to an atomic transition in the THz domain. We discuss the cause of uncertainties and limitations for this method and show that reaching a sub-kHz resolution is experimentally accessible via this interrogation protocole.

Radiofrequency multipole traps have been used for some decades in cold collision experiments, and are gaining interest for precision spectroscopy due to their low mi-cromotion contribution, and the predicted unusual cold-ion structures. However, the experimental realisation is not yet fully controlled, and open questions in the operation of these devices remain. We present experimental observations of symmetry breaking of the trapping potential in a macroscopic octupole trap with laser-cooled ions. Numerical simulations have been performed in order to explain the appearance of additional local potential minima, and be able to control them in a next step. We characterize these additional potential minima, in particular with respect to their position, their potential depth and their probability of population as a function of the radial and angular displacement of the trapping rods.

The manipulation of trapped charged particles by electric fields is an accurate, robust and reliable technique for many applications or experiments in high-precision spectroscopy. The transfer of the ion sample between multiple traps allows the use of a tailored environment in quantum information, cold chemistry, or frequency metrology experiments. In this article, we experimentally study the transport of ion clouds of up to 50 000 ions. The design of the trap makes ions very sensitive to any mismatch between the assumed electric potential and the actual local one. Nevertheless, we show that being fast (100 $μ$s to transfer over more than 20 mm) increases the transport efficiency to values higher than 90 %, even with a large number of ions. For clouds of less than 2000 ions, a 100 % transfer efficiency is observed.

Efficient transport of cold atoms or ions is a subject of increasing concern in many experimental applications reaching from quantum information processing to frequency metrology. For the scalable quantum computer architectures based on the shuttling of individual ions, different transport schemes have been developed, which allow to move single atoms minimizing their energy gain. In this article we discuss the experimental implementation of the transport of a three-dimensional ion cloud in a macroscopic linear radiofrequency (RF) trap. The present work is based on numerical simulations done by molecular dynamics taking into account a realistic experimental environment. The deformation of the trapping potential and the spatial extension of the cloud during transport appears to be the major source of the ion energy gain. The efficiency of transport in terms of transfer probability and ion number is also discussed.

While the linear radiofrequency trap finds various applications in high-precision spectroscopy and quantum information, its higher-order cousin, the linear multipole trap, is almost exclusively employed in physical chemistry. Recently, first experiments have shown interesting features by laser-cooling multipole-trapped ion clouds. Multipole traps show a flatter potential in their centre and therefore a modified density distribution compared to quadrupole traps. Micromotion is an important issue and will certainly influence the dynamics of crystallized ion structures. Our experiment tends to investigate possible crystallization processes in the multipole. In a more general way, we are interested in the study of the dynamics and thermodynamics of large ion clouds in traps of different geometry.

We analyse 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 with the anisotropy of the trapping potential. Results obtained using the full radio-frequency (rf) potential are compared to those of the corresponding pseudo-potential. In the rf case, the rotation symmetry of the potential has to be broken to keep ions inside the trap. Then, as for the pseudo-potential 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 organise as a line or a pancake and the three components of motion reach the same temperature only if the cloud extends in three dimensions.