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Journal of the Physical Society of Japan

Collective Phenomena Induced by Ion Mixturesin a RF Ion Trap

Akihiro Kajita, Masahiro Kimura, Shunsuke Ohtani, Hiroyuki Tawara, Yahachi Saito

Published Sep 15, 1991• 5 citations
Publisher

Abstract

Collective motions and anharmonic oscillations induced by a mixture of two ion species with different masses in a rf ion trap are reported. The absorption spectra of the probing rf power by the resonant oscillations of ion clouds have been observed for several ion species with various mixing ratios. It is shown that significant nonlinear effects manifest themselves strongly when the mass difference is in a certain range. One of such nonlinear effects, the first observation of significant hysteresis in the absorption spectrum of the probing rf field, is understood to be due to the anharmonic force term of the third order induced by the interactions of two ion clouds. The term has been estimated by fitting the observed absorption profile to the approximate solution of Duffing's equation.

DOI
10.1143/jpsj.60.2996

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Collective motions and anharmonic oscillations induced by a mixture of two ion species with different masses in a rf ion trap are reported. The absorption spectra of the probing rf power by the resonant oscillations of ion clouds have been observed for several ion species with various mixing ratios. It is shown that significant nonlinear effects manifest themselves strongly when the mass difference is in a certain range. One of such nonlinear effects, the first observation of significant hysteresis in the absorption spectrum of the probing rf field, is understood to be due to the anharmonic force term of the third order induced by the interactions of two ion clouds. The term has been estimated by fitting the observed absorption profile to the approximate solution of Duffing's equation.
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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.
Sympathetic cooling of Ca+,{\mathrm{Ca}}^{+},Ca+, Zn+,{\mathrm{Zn}}^{+},Zn+, Sr+,{\mathrm{Sr}}^{+},Sr+, Ba+,{\mathrm{Ba}}^{+},Ba+, and Yb+{\mathrm{Yb}}^{+}Yb+ as guest ions with laser-cooled 24Mg+{}^{24}{\mathrm{Mg}}^{+}24Mg+ as host ions in a rf ion trap is carried out, and resonant frequencies of their motion in the trap potential are measured. Various oscillation modes of the sympathetically cooled ions are observed. The resonant frequency of the oscillation mode is different from the frequency of either the collective oscillation frequency of the trapped ions or the oscillation frequency of each ion without host ions. This difference is well explained by a theoretical model in which coupled equations of motion of the host ion cloud with a single guest ion are considered.
When ions of slightly different mass and the same charge are stored in a radio-frequency electric quadrupole trap, a collective oscillation is observed rather than the independent motions usually assumed. A high-temperature model of ion clouds, each characterized by ions of one mass, shows that the ions of each cloud move as a unit and exhibit a correlated motion with the other clouds when a strong coupling condition is satisfied. This phenomenon is expected to arise whenever more than one ion is trapped and might be observable in neutral atom traps as well.
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.
In an experiment using a Paul trap, we create a H2+{\mathrm{H}}_{2}^{+}H2+​ ion cloud by electron ionization of the background gas at ${10}^{\ensuremath{-}9}$-mbar residual pressure. Exciting the ions parametrically at twice the frequency of the secular motion of ions in the rrr or zzz direction, we observe a narrow resonance at some distance from the motional resonance center if the amplitude of the exciting field exceeds a threshold value. The threshold value decreases with increasing ion number. Since the narrow resonance does not shift with ion number, we interpret it as a collective resonance of the center of mass of the ion cloud. The resonance shape exhibits the typical form of a driven anharmonic oscillator. The conclusions drawn from the experiments are supported by detailed analytical and numerical computations.