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Physical Review A

Instabilities of molecule motion in a linear ac trap

Peter Lützow, Melanie Schnell, Gerard Meijer

Published Jun 3, 2008• 8 citations
Publisher

Abstract

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 $\frac{1}{4}$ of the forcing frequency.

DOI
10.1103/physreva.77.063402

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arXiv:1109.2160•Journal of Applied Physics•Oct 1, 2012•20 citations
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.
A linear AC trap for polar molecules in high-field seeking states has been devised and implemented, and its characteristics have been investigated both experimentally and theoretically. The trap is loaded with slow 15ND3 molecules in their ground state (para-ammonia) from a Stark decelerator. The trap's geometry offers optimal access as well as improved loading. We present measurements of the dependence of the trap's performance on the switching frequency, which exhibit a characteristic structure due to nonlinear resonance effects. The molecules are found to oscillate in the trap under the influence of the trapping forces, which were analyzed using 3D numerical simulations. On the basis of expansion measurements, molecules with a velocity and a position spread of 2.1 m/s and 0.4 mm, respectively, are still accepted by the trap. This corresponds to a temperature of 2.0 mK. From numerical simulations, we find the phase-space volume that can be confined by the trap (the acceptance) to be 50 mm3 (m/s)3.
The parametric resonant behavior of ions inside a linear rf ion trap is studied both theoretically and experimentally. Theoretically, the resonant motion of ions inside an ideal ion trap is described by approximating the trapping rf field as a harmonic pseudopotential with the ions being excited by an additional quadrupolar ac voltage. The resulting damped Mathieu equation is studied and the regions of resonant instability are predicted by investigating the solutions. Experimentally, the parametric excitation of Mg+{\mathrm{Mg}}^{+}Mg+ ions is observed by subjecting the cloud of trapped ions to an additional quadrupolar ac field. The various ion motion resonances are detected through the disappearance of the laser-induced fluorescence signal. Weak damping is introduced by the presence of a low-pressure buffer gas. The experimental results are compared with the theoretical predictions.
A new ac/dc monopole trap for neutral polar particles, introduced and explored by Blumel (2011 Phys. Rev. A 83 045402 and 2011 Eur. Phys. J. D 64 85–101), is significantly advanced in several directions. (1) Previously shown to work only for polar classical particles and polar macro-molecules, the trap is shown to work for polar diatomic molecules. (2) A homogeneous electric field, optionally switched on for improved stability in the angular direction, leads to stable trapping in higher order stability regions of the Mathieu equation. (3) Based on the Floquet formalism, analytical and numerical calculations are presented that show that the trap is quantum mechanically stable. (4) Definition and derivation of a quantum pseudo-potential allow a qualitative understanding of the quantum trapping mechanism. (5) It is shown that the proposed ac/dc trap may be realized experimentally using currently available scanning tunnelling microscopy technology.
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.
Motivated by recent developments in ion trap design and fabrication, we investigate the stability of the motion of an ion in asymmetrical, planar versions of the linear Paul trap. The equations of motion of an ion in such a trap are generally coupled due to a nonzero relative angle θ between the principal axes of RF and DC fields, invalidating the assumptions behind the standard stability analysis for symmetric Paul traps. Using numerical methods, we obtain stability diagrams for the coupled system for various values of θ, generalizing the standard q-a stability diagrams. We then use multi-scale perturbation theory to obtain approximate formulas for the boundaries of the primary stability region and check our formulas against results from numerical analysis. Our results show that while the primary stability region is quite robust to changes in θ, a secondary stability region is highly variable, joining the primary stability region at the special case of θ=45°, which results in a significantly enlarged stability region for this particular angle. We conclude that while the standard stability diagrams for classical, symmetric Paul traps are not entirely accurate for asymmetric surface traps (or for other types of traps with a relative angle between the RF and DC axes), they are “safe” in the sense that operating conditions deemed stable according to standard stability plots are in fact stable for asymmetric traps, as well. By ignoring the coupling in the equations, one only underestimates the size of the primary stability region.