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arXiv:1310.6294 · Physical Review A

Cotrapping different species in ion traps using multiple radio frequencies

Dimitrios Trypogeorgos, Christopher J. Foot

Published Aug 9, 2016• 32 citations
arXivHTMLPDF

Abstract

We consider the stability of systems subjected to periodic parametric driving in the context of ions confined by oscillating electric fields. The behavior of these systems can be understood in terms of a pseudopotential approximation and resonances arising from parametric excitation. We investigate the key properties of a way of operating a linear Paul trap with two radio frequencies that simultaneously confines two species with extremely different charge-to-mass ratios. The theoretical calculations have been verified by molecular dynamics simulations and normal modes analysis.

DOI
10.1103/physreva.94.023609

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We have developed an efficient computational scheme for integration of the classical Hamilton equations describing the ion dynamics confined in the radio-frequency field of the Paul trap. It has permitted a quantitative treatment of cold atom-ion resonant collisions in hybrid atom-ion traps with taking into account unremovable ion micromotion caused by the radio-frequency fields (V.S. Melezhik et. al., Phys. Rev. A100, 063406 (2019)). The important element of the hybrid atom-ion systems is the electromagnetic Paul trap confining the charged ion. The oscillating motion of the confined ion is defined by two frequencies of the Paul trap. It is the frequency of the order of 100 kHz due to the constant electric field and the radio-frequency of about 1-2 MHz defined by the alternating electromagnetic field of the ion trap. The necessity to accurately treat the ion motion in the combined field with two time scales defined by these two very different frequencies has demanded to develop the stable computational scheme for integration of the classical Hamilton equations for the ion motion. Moreover, the scheme must be stable on rather long time-interval of the ion collision with the cold atom ∼ 10 × 2/ defined by the atomic trap frequency ∼ 10 kHz and in the moment of the atom-ion collision when the Hamilton equations are strongly coupled. The developed numerical method takes into account all these features of the problem and makes it possible to integrate the system of coupled quantum-semiclassical equations with the necessary accuracy and quantitatively describes the processes of atomic-ion collisions in hybrid traps, including resonance effects.

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Physical Review A•Oct 20, 2005•26 citations
We consider the stability of systems subjected to periodic parametric driving in the context of ions confined by oscillating electric fields. The behavior of these systems can be understood in terms of a pseudopotential approximation and resonances arising from parametric excitation. We investigate the key properties of a way of operating a linear Paul trap with two radio frequencies that simultaneously confines two species with extremely different charge-to-mass ratios. The theoretical calculations have been verified by molecular dynamics simulations and normal modes analysis.
We consider the stability of systems subjected to periodic parametric driving such that their equations of motion are ordinary differential equations with periodic coefficients and carry out a detailed analysis of important aspects of such systems in the context of the confinement of ions by oscillating electric fields. We show how they can be understood in terms of a pseudopotential approximation and resonances arising from the parametric excitation and investigate the properties of a novel linear Paul trap configuration operating with two radio-frequencies to simultaneously confine two species with extremely different charge-to-mass ratios. The theoretical calculations have been verified by molecular dynamics simulations and normal modes analysis.
We present a theoretical study of trapping an electron in a two-frequency Paul trap, motivated by future hybrid architecture consisting of a doubly charged calcium ion (Ca2+^{2+}2+) and an electron. By isolating the electron from ionic-electron interactions, we formulate the equations of motion for the electron in the time-dependent trap potentials and cast them in the Hill form. Stability and dynamics are then analysed in terms of the dimensionless q-parameters, which encode the applied voltages, drive frequencies, trap geometry, and the particle's charge-to-mass ratio. Under the combined action of the two radio-frequency fields, the trapped electron's classical motion is shown to be approximated well by a slow secular oscillation modulated by two distinct motion sidebands originating from the low- and high-frequency RF drives. The approximation method presented here enables a quick evaluation of the relation between the device-design q-parameters and the electron motion. It offers a crucial foundation for developing physical models of electron-ion interactions in electron-ion traps.
Radiofrequency (RF) traps enable highly controlled interactions between charged particles, including reactions between cold molecular ions, sympathetic cooling of one ion species with another, and quantum logic spectroscopy. However, the charge-to-mass (Q/m) selectivity of RF traps limits the range of objects that can be confined simultaneously in the same trap. Here, we confine two particles-a nanoparticle and an atomic ion-in the same radiofrequency trap although their charge-to-mass ratios differ by six orders of magnitude. The confinement is enabled by a dual-frequency voltage applied to the trap electrodes. We introduce a robust loading procedure under ultrahigh vacuum and characterize the stability of both particles. It is observed that slow-field micromotion, an effect specific to the dual-field setting, plays a crucial role for ion localization. Our results lay the groundwork for controlled interactions between diverse charged particles, regardless of the difference in their charge or mass, with applications from antimatter synthesis to the generation of macroscopic quantum states of motion.
We have developed an efficient computational scheme for integration of the classical Hamilton equations describing the ion dynamics confined in the radio-frequency field of the Paul trap. It has permitted a quantitative treatment of cold atom-ion resonant collisions in hybrid atom-ion traps with taking into account unremovable ion micromotion caused by the radio-frequency fields (V.S. Melezhik et. al., Phys. Rev. A100, 063406 (2019)). The important element of the hybrid atom-ion systems is the electromagnetic Paul trap confining the charged ion. The oscillating motion of the confined ion is defined by two frequencies of the Paul trap. It is the frequency of the order of 100 kHz due to the constant electric field and the radio-frequency of about 1-2 MHz defined by the alternating electromagnetic field of the ion trap. The necessity to accurately treat the ion motion in the combined field with two time scales defined by these two very different frequencies has demanded to develop the stable computational scheme for integration of the classical Hamilton equations for the ion motion. Moreover, the scheme must be stable on rather long time-interval of the ion collision with the cold atom ∼ 10 × 2/ defined by the atomic trap frequency ∼ 10 kHz and in the moment of the atom-ion collision when the Hamilton equations are strongly coupled. The developed numerical method takes into account all these features of the problem and makes it possible to integrate the system of coupled quantum-semiclassical equations with the necessary accuracy and quantitatively describes the processes of atomic-ion collisions in hybrid traps, including resonance effects.
Linear Paul traps use radio frequency fields to confine ions for long times in deep potentials. The simplicity and versatility of these devices has led to their use in a wide variety of fields, from mass spectroscopy to quantum information. Within the past fifteen years, beginning with pioneering work at UConn, Paul traps have been combined with atom traps to form hybrid atom-ion traps. Hybrid traps serve as platforms for measuring ion-atom interaction rates, sympathetically cooling atomic and molecular ions, and studying the behavior of trapped ions. This work discusses simulations, analytical theory, and experiments in a hybrid trap that show a previously unknown dynamical effect in a population of trapped ions. The steady state trapped ion number in a Paul trap is non-monotonic with the loading rate of the Paul trap. This effect is universal to both Linear and 3D Paul traps and is likely to be found in other types of ion traps as well because it is the result of the Coulomb interaction in the presence of a trap. This behavior also affects the decay of ions from the trap. Understanding the loading and decay behavior from a saturated Linear Paul trap is important for the study of ion-atom interactions in a hybrid trap when the ions lack optical transitions.
We discuss a radio-frequency (rf) ion trap, the rotating-radio-frequency (rotating-rf) trap, in which the motion of a charged particle is described by trigonometric functions rather than the usual Mathieu functions of a normal rf trap. In the rotating-rf trap, a rotating quadrupole electric field confines charged particles, whereas in a normal rf trap, an oscillating quadrupole electric field does. Ion motion in a rotating-rf trap is a superposition of two nondegenerate circular secular motions and two corresponding circular micromotions. The cases of applying a uniform dc magnetic field or a quadrupole dc electric field in addition to the rotating-rf field are also discussed. Confinement in a rotating-rf trap can be tighter than in a normal linear rf trap with the same experimental parameter values.