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Interest of a multipole trap to improve the frequency stability in microwave clocks based on confined ions

Marylise Marchenay

Published Dec 18, 2020• 0 citations
OpenAlex

Abstract

The stability properties of radio-frequency traps make them a technology of choice for the design of embedded microwave ion clocks for deep space navigation applications. The main effect limiting the frequency stability of such clocks is the frequency shift induced by the second order Doppler effect which fluctuates with the number of trapped ions. The use of radio-frequency multipole traps in the design of microwave clocks is motivated by a built-in reduction of the radio-frequency driven motion of the ions with the increase of the order of the multipole field. Experimental realizations by NASA-JPL of ion clocks involving higher order multipole traps have demonstrated a stability gain, but no direct measurement has yet been undertaken to clarify wherever this gain is a direct consequence of the number of electrodes in the trap or from a global optimization of the whole setup. One of the objectives of the TADOTI experiment is to conduct a comparative measurement of the velocity distribution over a laser cooled Ca+ ion cloud trapped in a quadrupole and an octupole trap. Observations of cold samples have shown an inhomogeneous spatial distribution of the trapped particles with clustering of the ions in local potential wells. Simulations attribute this organization to a symmetry breaking in the trap, induced by realistic mis-positioning of the electrodes. A prerequisite for the velocity distribution characterization is to restore to symmetry of the potential of the octupole trap by tuning the RF voltage applied to each electrode. This thesis focuses on the analytical description of the potential perturbations induced by the structural deformation of the trap, and proposes a characterization and compensation protocol of the perturbations, based on the localization of the laser-cooled ion in the trap. These tools can be used to create any configuration of three parallel ion clouds in the octupole trap.

Related papers

Interest of a multipole trap to improve the frequency stability in microwave clocks based on confined ions

Marylise Marchenay

Intérêt d'un piège multipolaire pour améliorer la stabilité en fréquence d'une horloge micro-ondes à ions confinés Les propriétés de stabilité des pièges radiofréquence sont d’intérêt pour la conception d'horloges micro-ondes à ions confinés embarquées pour la navigation en espace lointain. Le principal effet limitant la stabilité en fréquence de ces horloges est le décalage en fréquence induit par l'effet Doppler du second ordre qui fluctue avec le nombre d'ions. Les pièges RF multipolaires bénéficient d’une réduction structurelle de la composante du mouvement des ions due au champ RF avec l'augmentation de l'ordre du champ. Les réalisations expérimentales (NASA-JPL) impliquant des multipôles ont démontré un gain en stabilité, mais aucune mesure directe n'a encore été entreprise pour clarifier si ce gain est due au nombre d'électrodes RF ou à une optimisation globale du system. Notre objectif est de réaliser une mesure comparative de la distribution de vitesse d’un nuage d'ion Ca+ refroidi par laser et piégé dans un quadripôle et dans un octupole. Des observations de nuages froids ont montré que les ions s’accumulent dans des puits de potentiel locaux. Les simulations attribuent cette organisation à une rupture de symétrie dans le piège, induite par une erreur du positionnement des électrodes. Pour réaliser la mesure il est nécessaire de rétablir la symétrie du potentiel en ajustant la tension RF appliquée à chaque électrode. Cette thèse se concentre sur la description analytique des perturbations du potentiel induites par la déformation structurelle du piège, et propose un protocole de caractérisation et de compensation des perturbations, basé sur la position des ions froids dans le piège. Ces outils peuvent être utilisés pour contrôler la position radiale des ions dans l’octupole

•Dec 18, 2020•0 citations

Ion storage, cooling and applications in quantum frequency standards

Zheng Wang

This paper reviews the basic principles of ion storage and cooling in the first place, and presents simulation result using a molecular dynamics method on ion distribution and RF heating rate. Based on this result, we evaluate the influence of RF heating effect and micromotions of the ions on frequency standards. Compared to conventional quadrupole trap, a 12-pole trap is able to reduce the RF heating rate of the ion cloud and to enable narrowing the linewidth with the Ramsey method. Moreover, the effective potential in the 12-pole trap has a flat bottom and a steep wall, which is capable of reducing the second order Doppler effect caused by the micromotions and thus helpful to enhance the accuracy and stability of the clock. At last, we review previous work of JPL on high performance, 199Hg+ ion clocks and our present work of laser-cooled, 113Cd+ ion clock based on the multipole trap.

Zhongguo kexue. Wulixue Lixue Tianwenxue•Jan 1, 2011•0 citations

Correcting symmetry imperfections in linear multipole traps

J. Pedregosa-Gutierrez, C. Champenois, M. Houssin +2 more

Multipole radio-frequency (RF) traps are central to collisional experiments in cryogenic environments. They also offer possibilities to generate new type of ion crystals topologies and in particular the potential to create infinite 1D/2D structures: ion rings and ion tubes. However, multipole traps have also been shown to be very sensitive to geometrical misalignment of the trap rods, leading to additional local trapping minima. The present work proposes a method to correct non-ideal potentials, by modifying the applied RF amplitudes for each trap rod. This approach is discussed for the octupole trap, leading to the restitution of the ideal Mexican-Hat-like pseudo-potential, expected in multipole traps. The goodness of the compensation method is quantified in terms of the choice of the diagnosis area, the residual trapping potential variations, the required adaptation of the applied RF voltage amplitudes, and the impact on the trapped ion structures. Experimental implementation for macroscopic multipole traps is also discussed, in order to propose a diagnostic method with respect to the resolution and stability of the trap drive. Using the proposed compensation technique, we discuss the feasibility of generating a homogeneous ion ring crystal, which is a measure of quality for the obtained potential well.

arXiv:1807.10500•Review of Scientific Instruments•Dec 1, 2018•7 citations

离子存储、冷却及在量子频标中的应用

Lijun Wang, ShiGuang WANG, Zhengbo Wang +1 more

This paper reviews the basic principles of ion storage and cooling in the first place, and presents simulation result using a molecular dynamics method on ion distribution and RF heating rate. Based on this result, we evaluate the influence of RF heating effect and micromotions of the ions on frequency standards. Compared to conventional quadrupole trap, a 12-pole trap is able to reduce the RF heating rate of the ion cloud and to enable narrowing the linewidth with the Ramsey method. Moreover, the effective potential in the 12-pole trap has a flat bottom and a steep wall, which is capable of reducing the second order Doppler effect caused by the micromotions and thus helpful to enhance the accuracy and stability of the clock. At last, we review previous work of JPL on high performance, 199Hg+ ion clocks and our present work of laser-cooled, 113Cd+ ion clock based on the multipole trap.

Zhongguo kexue. Wulixue Lixue Tianwenxue•Apr 1, 2011•2 citations

An analytical approach to symmetry breaking in multipole RF-traps

Marylise Marchenay, J. Pedregosa-Gutierrez, Martina Knoop +2 more

Abstract Radio-frequency (RF) 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 as shown in Pedregosa-Gutierrez et al (2018 J. Mod. Opt. 65 529) 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, characterized 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 Pedregosa-Gutierrez et al (2018 Rev. Sci. Instrum. 89 123101), 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 Pedregosa-Gutierrez et al (2018 Rev. Sci. Instrum. 89 123101), 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 positions 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.

arXiv:2012.08198•Quantum Science and Technology•Mar 1, 2021•4 citations

Motional Stability of a Nonlinear Parametric Oscillator: Ion Storage in the RF Octupole Trap

J. Walz, Ingo Siemers, Michael Schubert +2 more

We demonstrate confinement of ion clouds in a radio-frequency anharmonic electric potential and investigate the stability of this nonlinear parametric oscillator. Measurements of excitation spectra and the spatial distribution of trapped ion clouds are presented. Further applications of r.f. multipole traps to high-resolution spectroscopy are discussed.

Europhysics Letters (EPL)•Jan 10, 1993•10 citations
The stability properties of radio-frequency traps make them a technology of choice for the design of embedded microwave ion clocks for deep space navigation applications. The main effect limiting the frequency stability of such clocks is the frequency shift induced by the second order Doppler effect which fluctuates with the number of trapped ions. The use of radio-frequency multipole traps in the design of microwave clocks is motivated by a built-in reduction of the radio-frequency driven motion of the ions with the increase of the order of the multipole field. Experimental realizations by NASA-JPL of ion clocks involving higher order multipole traps have demonstrated a stability gain, but no direct measurement has yet been undertaken to clarify wherever this gain is a direct consequence of the number of electrodes in the trap or from a global optimization of the whole setup. One of the objectives of the TADOTI experiment is to conduct a comparative measurement of the velocity distribution over a laser cooled Ca+ ion cloud trapped in a quadrupole and an octupole trap. Observations of cold samples have shown an inhomogeneous spatial distribution of the trapped particles with clustering of the ions in local potential wells. Simulations attribute this organization to a symmetry breaking in the trap, induced by realistic mis-positioning of the electrodes. A prerequisite for the velocity distribution characterization is to restore to symmetry of the potential of the octupole trap by tuning the RF voltage applied to each electrode. This thesis focuses on the analytical description of the potential perturbations induced by the structural deformation of the trap, and proposes a characterization and compensation protocol of the perturbations, based on the localization of the laser-cooled ion in the trap. These tools can be used to create any configuration of three parallel ion clouds in the octupole trap.
Intérêt d'un piège multipolaire pour améliorer la stabilité en fréquence d'une horloge micro-ondes à ions confinés Les propriétés de stabilité des pièges radiofréquence sont d’intérêt pour la conception d'horloges micro-ondes à ions confinés embarquées pour la navigation en espace lointain. Le principal effet limitant la stabilité en fréquence de ces horloges est le décalage en fréquence induit par l'effet Doppler du second ordre qui fluctue avec le nombre d'ions. Les pièges RF multipolaires bénéficient d’une réduction structurelle de la composante du mouvement des ions due au champ RF avec l'augmentation de l'ordre du champ. Les réalisations expérimentales (NASA-JPL) impliquant des multipôles ont démontré un gain en stabilité, mais aucune mesure directe n'a encore été entreprise pour clarifier si ce gain est due au nombre d'électrodes RF ou à une optimisation globale du system. Notre objectif est de réaliser une mesure comparative de la distribution de vitesse d’un nuage d'ion Ca+ refroidi par laser et piégé dans un quadripôle et dans un octupole. Des observations de nuages froids ont montré que les ions s’accumulent dans des puits de potentiel locaux. Les simulations attribuent cette organisation à une rupture de symétrie dans le piège, induite par une erreur du positionnement des électrodes. Pour réaliser la mesure il est nécessaire de rétablir la symétrie du potentiel en ajustant la tension RF appliquée à chaque électrode. Cette thèse se concentre sur la description analytique des perturbations du potentiel induites par la déformation structurelle du piège, et propose un protocole de caractérisation et de compensation des perturbations, basé sur la position des ions froids dans le piège. Ces outils peuvent être utilisés pour contrôler la position radiale des ions dans l’octupole
This paper reviews the basic principles of ion storage and cooling in the first place, and presents simulation result using a molecular dynamics method on ion distribution and RF heating rate. Based on this result, we evaluate the influence of RF heating effect and micromotions of the ions on frequency standards. Compared to conventional quadrupole trap, a 12-pole trap is able to reduce the RF heating rate of the ion cloud and to enable narrowing the linewidth with the Ramsey method. Moreover, the effective potential in the 12-pole trap has a flat bottom and a steep wall, which is capable of reducing the second order Doppler effect caused by the micromotions and thus helpful to enhance the accuracy and stability of the clock. At last, we review previous work of JPL on high performance, 199Hg+ ion clocks and our present work of laser-cooled, 113Cd+ ion clock based on the multipole trap.
Multipole radio-frequency (RF) traps are central to collisional experiments in cryogenic environments. They also offer possibilities to generate new type of ion crystals topologies and in particular the potential to create infinite 1D/2D structures: ion rings and ion tubes. However, multipole traps have also been shown to be very sensitive to geometrical misalignment of the trap rods, leading to additional local trapping minima. The present work proposes a method to correct non-ideal potentials, by modifying the applied RF amplitudes for each trap rod. This approach is discussed for the octupole trap, leading to the restitution of the ideal Mexican-Hat-like pseudo-potential, expected in multipole traps. The goodness of the compensation method is quantified in terms of the choice of the diagnosis area, the residual trapping potential variations, the required adaptation of the applied RF voltage amplitudes, and the impact on the trapped ion structures. Experimental implementation for macroscopic multipole traps is also discussed, in order to propose a diagnostic method with respect to the resolution and stability of the trap drive. Using the proposed compensation technique, we discuss the feasibility of generating a homogeneous ion ring crystal, which is a measure of quality for the obtained potential well.
This paper reviews the basic principles of ion storage and cooling in the first place, and presents simulation result using a molecular dynamics method on ion distribution and RF heating rate. Based on this result, we evaluate the influence of RF heating effect and micromotions of the ions on frequency standards. Compared to conventional quadrupole trap, a 12-pole trap is able to reduce the RF heating rate of the ion cloud and to enable narrowing the linewidth with the Ramsey method. Moreover, the effective potential in the 12-pole trap has a flat bottom and a steep wall, which is capable of reducing the second order Doppler effect caused by the micromotions and thus helpful to enhance the accuracy and stability of the clock. At last, we review previous work of JPL on high performance, 199Hg+ ion clocks and our present work of laser-cooled, 113Cd+ ion clock based on the multipole trap.
Abstract Radio-frequency (RF) 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 as shown in Pedregosa-Gutierrez et al (2018 J. Mod. Opt. 65 529) 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, characterized 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 Pedregosa-Gutierrez et al (2018 Rev. Sci. Instrum. 89 123101), 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 Pedregosa-Gutierrez et al (2018 Rev. Sci. Instrum. 89 123101), 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 positions 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.