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Physical Review A

Resonant excitation of trapped molecules in a molecular synchrotron

Peter C. Zieger, Chris J. Eyles, Gerard Meijer, Hendrick L. Bethlem

Published Apr 26, 2013• 2 citations
Publisher

Abstract

We characterize a synchrotron for polar molecules that consists of forty straight hexapoles arranged in a circle. By modulating either the voltages or the duration of the high-voltage pulses that are applied to the hexapoles, we shake the transverse and longitudinal well. If the frequency of the modulation matches a characteristic frequency of a stored molecule, the amplitude of the motion is resonantly excited, leading to a decrease in the number of molecules that are stored. From this, we determine the longitudinal, vertical, and radial frequencies that characterize the motion of the molecules inside the synchrotron and obtain knowledge about the couplings between the longitidinal and transverse motion. The measured frequencies are in good agreement with those obtained from three-dimensional trajectory calculations.

DOI
10.1103/physreva.87.043425

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We characterize a synchrotron for polar molecules that consists of forty straight hexapoles arranged in a circle. By modulating either the voltages or the duration of the high-voltage pulses that are applied to the hexapoles, we shake the transverse and longitudinal well. If the frequency of the modulation matches a characteristic frequency of a stored molecule, the amplitude of the motion is resonantly excited, leading to a decrease in the number of molecules that are stored. From this, we determine the longitudinal, vertical, and radial frequencies that characterize the motion of the molecules inside the synchrotron and obtain knowledge about the couplings between the longitidinal and transverse motion. The measured frequencies are in good agreement with those obtained from three-dimensional trajectory calculations.
We present a synchrotron for polar molecules consisting of 40 straight hexapoles arranged in a circle with a 50 cm diameter. The mechanical design and alignment procedure as well as the trigger scheme used to switch the voltages applied to the hexapoles are described in detail. The stability of the synchrotron is demonstrated by measurements in which multiple packets are stored for over 13 s, during which they have completed over 1000 round trips and traveled a distance of over one mile. Furthermore, we demonstrate the simultaneous trapping of 26 packets; 13 revolving clock-wise and 13 counter clock-wise, that are injected into the synchrotron by two Stark decelerator beamlines. We discuss the opportunities for using the synchrotron as a low-energy collider.
A molecular synchrotron offers unique possibilities to study molecular collisions at low energies. For such a study, it is imperative that the velocity of the stored molecules can be tuned over a wide range. Bunching elements, used to provide the necessary longitudinal focusing forces in a synchrotron, introduce instabilities for certain velocities of the stored molecules. Here we present an experimental study of these motional resonances and show how they can be avoided. A packet of ND3\mathrm{N}{\mathrm{D}}_{3}ND3​ molecules is stably confined in the synchrotron as its injection velocity is continuously scanned from 60m∕s60\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s}60m∕s $({E}_{\mathrm{kin}}=3.0\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1})\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}87.5\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s}$ $({E}_{\mathrm{kin}}=6.4\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1})$.
Limited by the construction demands, the state-of-the-art molecular synchrotrons consist of only 40 segments that hardly make a good circle. Imperfections in the circular structure will lead to the appearance of unstable velocity regions (i.e. stopbands), where molecules of certain forward velocity will be lost from the structure. In this paper, we propose a stopband-free molecular synchrotron. It contains 1570 ring electrodes, which nearly make a perfect circle, capable of confining both light and heavy polar molecules in the low-field-seeking states. Molecular packets can be conveniently manipulated with this synchrotron by various means, like acceleration, deceleration or even trapping. Trajectory calculations are carried out using a pulsed (88)SrF molecular beam with a forward velocity of 50 m/s. The results show that the molecular beam can make more than 500 round trips inside the synchrotron with a 1/e lifetime of 6.2 s. The synchrotron can find potential applications in low-energy collision and reaction experiments or in the field of precision measurements, such as the searches for electric dipole moment of elementary particles.
The stability of a linear ac trap for neutral polar molecules is investigated both theoretically and experimentally. While the overall stability is found to be well described by the linearized equations of motion within the usual framework of stability diagrams, instabilities similar to those observed in anharmonic radio-frequency ion traps occur inside the nominal stable regions. These motional resonances are caused by strong anharmonic contributions to the trapping fields, that inevitably appear in ac traps for polar molecules. Nonlinear resonant energy transfer from the high-frequency source to molecules inside the trap is observed for the particles' fundamental frequency of transverse oscillation being 14\frac{1}{4}41​ of the forcing frequency.
We explore the quantum dynamics of heteronuclear atomic collisions in waveguides and demonstrate the existence of a novel mechanism for the resonant formation of polar molecules. The molecular formation probabilities can be tuned by changing the trap frequencies that characterize the transverse modes of the atomic species. The origin of this effect is the confinement-induced mixing of the relative and center of mass motions in the atomic collision process leading to a coupling of the diatomic continuum to the center of mass excited molecular states in closed transverse channels.
Using calculations and mathematical modeling, we demonstrate the feasibility of constructing a synchrotron storage ring for neutral polar molecules. The lattice is a racetrack type 3.6 m in circumference consisting of two 180° arcs, six bunchers, and two long straight sections. Each straight section contains two triplet focusing lenses and space for beam injection and experiments. The design also includes a matched injector and a linear decelerator. Up to 60 bunches can be loaded and simultaneously stored in the ring. The molecules are injected at 90 m/s but the velocity of the circulating beam can be decelerated to 60 m/s after injection. The modeling uses deuterated ammonia (14N2H3) molecules in a weak-field seeking state. A beam that survives 400 turns (15 s), has horizontal and vertical acceptances of 35 and 70 mm mrad, respectively, and an energy acceptance of ±2%.