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Physical Review A

Parametric excitations of trapped ions in a linear rf ion trap

Xujun Zhao, Vladimir L. Ryjkov, Hans A. Schuessler

Published Dec 26, 2002• 27 citations
Publisher

Abstract

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 ${\mathrm{Mg}}^{+}$ 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.

DOI
10.1103/physreva.66.063414

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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.
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.
Fluorescence line profiles and their implications on the cooling dynamics of the Mg+{\mathrm{Mg}}^{+}Mg+ ions stored in a linear rf trap are studied. The line profile is dictated by the temperature of the ion cloud at different laser detunings. The upper bound of the lowest temperature was estimated for different values of the rf trapping potential amplitude and the buffer gas pressure. A general trend of this ultimate temperature to increase with the rf trapping voltage and buffer gas pressure is expected, with an abrupt change at some critical value corresponding to the transition to and from a strongly correlated liquid or crystal state. While on the one hand this expectation was confirmed when the buffer gas pressure was varied; on the other hand the influence of the amplitude of the trapping voltage on the ultimate temperature shows an interesting new feature of first dipping down before the sharp increase occurs.
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.
Ba+ and Yb+ ions were trapped with buffer gas in a rf ion trap. The number and the storagetime of the trapped ions were determined by the rf resonance method. It was shown thatthe motion of the trapped ions was expressed by an external forced oscillation equation with anonlinear term in the case the fabricated trap was imperfect. Due to this nonlinear effect, thesubharmonic oscillation was induced, and thus the number and the storage time of the trappedions were decreased and shortened, respectively. The temperature and the spatial distributionof the trapped ions were determined by the fluorescence detection method.
Characteristics of the Yb+ ion cloud trapped in a rf trap in the presence of He buffer gas were determined by fluorescence detection as well as the rf resonance method. Combining the results obtained by the two methods, we determined the spatial ion density distribution and found that the trapped ions were thermalized by collisions with the He buffer gas. It was confirmed by both methods that the harmonic motion of the trapped ions was excited by the trapping field leaked to the rf resonance detection circuit (subharmonic oscillation), and moreover, by the fluorescence detection method, that the probing rf field used for the rf resonance method was indispensable as “the initial push” for exciting the amplitude.
Excitation of the motional frequencies of clouds of H2+ and N2+ ions, confined in a Paul trap, by an additionally applied radiofrequency quadrupole field leads to the observation of parametric resonances that are predicted to occur at frequencies 2ωz/n, n=1,2,3…, where ωz is the axial secular frequency. In the case of clouds of N2+ ions resonances up to n=10 are detected. They can be explained by parametric instabilities of the center-of-mass motion in the axial direction. The fractional resonances are observable only if the excitation field surpasses a critical strength. We find an odd-even staggering of the thresholds.