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Physical Review A

Line shape of three-level ions in Paul traps

Michael Schubert, Ingo Siemers, R. Blatt

Published May 1, 1989• 24 citations
Publisher

Abstract

A cloud of three-level ions (${\mathrm{Ba}}^{+}$) confined in a Paul trap was illuminated with two lasers and the resulting fluorescence was observed as a function of the laser detunings from the ionic resonance. The observed spectra show features due to the oscillatory motion of the trapped ions. In order to describe the observed line shapes, calculations are presented in which the ion ensemble is separated in classes of velocity amplitudes of the oscillatory motion rather than velocity classes.

DOI
10.1103/physreva.39.5098

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Single, rf-trapped ions find various applications ranging from metrology to quantum computation. High-resolution interrogation of an extremely weak transition under best observation conditions requires an ion almost at rest. To avoid line-broadening effects such as the second order Doppler effect or rf heating in the absence of laser cooling, excess micromotion has to be eliminated as far as possible. We have tested a novel method to probe the motional state of a confined three-level ion. Actually, dark resonances observed with two counterpropagating laser beams are very sensitive to the trapped ion's velocity. Their contrast increases with reduced micromotion and allows in this way to control the oscillation amplitude of the stored ion. The influence of different parameters such as laser linewidth and power has been investigated experimentally and numerically.
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.