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AIP conference proceedings

A study of trapped ion dynamics by photon-correlation and pulse-probe techniques

J. Rink, Kishan Dholakia, G. Horváth, K. Horvath, José Luis Hernández‐Pozos, W. Power, D. M. Segal, Richard Claude Thompson, Thomas Walker

Published Jan 1, 1995• 0 citations
Publisher

Abstract

We demonstrate non‐evasive methods for observing ion and ion cloud oscillation frequencies in a quadrupole ion trap. These trap resonances are measured for small clouds using a photon correlation technique. For large clouds the rotation frequency can be detected with the help of an additional pulsed probe laser. We show applications of the photon correlation method such as estimating the dynamic properties of a combined trap and detecting ion crystals.

DOI
10.1063/1.47889

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We demonstrate non‐evasive methods for observing ion and ion cloud oscillation frequencies in a quadrupole ion trap. These trap resonances are measured for small clouds using a photon correlation technique. For large clouds the rotation frequency can be detected with the help of an additional pulsed probe laser. We show applications of the photon correlation method such as estimating the dynamic properties of a combined trap and detecting ion crystals.
This thesis describes experimental work performed on laser cooled magnesium ions, confined in a quadrupole ion trap operating in the Penning or the combined mode. Information is gained about the dynamical motion of the ions. This is done by analyzing the time delays between scattered fluorescence photons in the case of small ion clouds (generally less than ten ions). For larger clouds (upwards of 100 ions), a fraction of the ions is "tagged" and a subsequent study made of the time evolution of the fluorescence. We have developed an innovative, non-invasive method for measuring ion oscillation frequencies which is based on analyzing photon-photon correlations present in the emitted ion fluorescence. This technique has been used to measure all three Penning trap frequencies for a wide range of dc voltage. The data have been fitted to theory and we have obtained a global fit of these data to one set of trap parameters. We also demonstrate that our technique enables us to measure space-charge shifted values of the trap resonances. This method has also been applied to the combined trap and we report experimental verification of the predicted trap resonances for a wide range of trapping parameters. These data fit well to theory. This is for all three oscillation frequencies for one set of trap parameters consistent with the data for the Penning trap. \nFurther experiments are reported concerned with the dynamics of larger ion clouds in a Penning trap. A pulsed laser is used to "tag" a small number of the ions in large ion clouds. This removes those ions from the cooling cycle by placing them in a metastable state. Subsequently, we have monitored the time evolution of the fluorescence. By analyzing these data we have been able to determine cloud rotation frequencies for large ensembles of ions.
We present a method for measuring ion-oscillation frequencies in quadrupole traps (Paul, Penning, and combined traps). The method depends on a statistical analysis of the delays between detected fluorescence photons. We have used the method to verify the oscillation frequencies for magnesium ions in a Penning trap as a function of the dc voltage applied to the trap electrodes. We demonstrate that, as expected, the method measures the space-charge shifted (individual-ion) oscillation frequency and not the frequency at which the ion cloud as a whole moves. However, our data suggest that for most of our operating conditions, the space-charge shift is negligible. We also discuss the effect of the contact potential arising from areas of the trap electrodes that are coated by excess Mg from the atomic beam used. We show that this extra potential shifts the center of the Penning trap and makes it unstable for low values of the applied voltage.
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.
In this paper, direct observation of micromotion for multiple ions in a laser-cooled trapped ion crystal is discussed along with a measurement technique for micromotion amplitude. Micromotion is directly observed using a time-resolving, single-photon-sensitive camera that provides both fluorescence and position data for each ion on the nanosecond time scale. Micromotion amplitude and phase for each ion in the crystal are measured, allowing this method to be sensitive to tilts and shifts of the ion chain from the null of the radio-frequency quadrupole potential in the linear trap. Spatial resolution makes this micromotion detection technique suitable for complex ion configurations, including two-dimensional geometries. It does not require any additional equipment or laser beams, and the modulation of the cooling lasers or trap voltages is not necessary for detection as it is in other methods.
This paper introduces the dynamics of charged particles in a radiofrequency trap in a very general manner to point out the differences between the dynamics in a quadrupole and in a multipole trap. When dense samples are trapped, the dynamics is modified by the Coulomb repulsion between ions. To take into account this repulsion, we propose to use a method, originally developed for particles in a Penning trap, that models the ion cloud as a cold fluid. This method can not reproduce the organization of cold clouds as crystals but it allows one to scale the size of large samples with the trapping parameters and the number of trapped ions, for different linear geometries of trap.