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Journal of Modern Optics

Photon Correlation Measurement of Ion Oscillation Frequencies in a Combined Trap

Kishan Dholakia, G. Horváth, D. M. Segal, Richard Claude Thompson

Published Nov 1, 1992• 16 citations
Publisher

Abstract

We present experimental verification of the oscillation frequencies of magnesium ions in a combined trap for a wide range of a.c. voltages and magnetic fields. We employ a new technique to measure these trap resonances using the distribution of time intervals between consecutively detected fluorescence photons.
DOI
10.1080/09500349214552201

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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.
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.
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.
Abstract The spectrum of the fluorescent radiation of a single trapped 24 Mg + -ion at low excitation intensity was investigated. The measurement was performed by heterodyning the fluorescent radiation with a sideband of the single mode laser radiation used to excite the ion, resulting in a linewidth of 6 Hz. Under identical experimental conditions, the antibunching in the photon statistics of the fluorescent radiation was also investigated. Heterodyne detection and photon correlation measurement are complementary featuring either the wave or the particle nature of the radiation. The combination of both techniques will allow to measure squeezing in resonance fluorescence.