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New Journal of Physics

Monitoring a single ion's motion by second-order photon correlations

D. Rotter, Manas Mukherjee, François Dubin, R. Blatt

Published Apr 10, 2008• 19 citations
Publisher

Abstract

For a single trapped ion, second-order time correlations of fluorescence photons are measured in a self-homodyne configuration by beating the fluorescence with itself. At the nanosecond timescale, the correlations are governed by electronic excitation and decay of the ion and anti-bunching in the resonance fluorescence is observed and quantitatively reproduced. On the other hand, at the microsecond timescale the motion of the ion determines the correlations: secular motional modes, their amplitude and relative coherence are measured. Besides precisely monitoring the trap frequencies, our observations also quantify the temporal stability of the trapping potential.

DOI
10.1088/1367-2630/10/4/043011

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For a single trapped ion, second-order time correlations of fluorescence photons are measured in a self-homodyne configuration by beating the fluorescence with itself. At the nanosecond timescale, the correlations are governed by electronic excitation and decay of the ion and anti-bunching in the resonance fluorescence is observed and quantitatively reproduced. On the other hand, at the microsecond timescale the motion of the ion determines the correlations: secular motional modes, their amplitude and relative coherence are measured. Besides precisely monitoring the trap frequencies, our observations also quantify the temporal stability of the trapping potential.
The three-dimensional localization of a single ion to the Lamb–Dicke limit in a radio-frequency trap has been combined with the technique of heterodyne detection to provide high-resolution spectroscopy of the fluorescent light of the ion. A coherent component with a linewidth of 0·7 Hz, corresponding to elastic scattering of the incident laser light, was observed in the heterodyne signal. The method may be extended to observe the narrow sidebands related to the secular motion in the trap, yielding information on the dynamics of the ion. Quantum properties of the fluorescent radiation can be detected by probing higher order field correlations. As an example we investigated the phenomenon of antibunching which appears as intensity anticorrelations of the emitted radiation. A measurement of intensity cross-correlations of the fluorescent light superimposed with a weak local oscillator is expected to permit the observation of squeezing in the resonance fluorescence of a single ion.
In this paper, we propose and demonstrate a new method for measuring the trap frequency from the fluorescence dynamics of an ion, initiated using fast trap-center displacement. Here, we observe the coherently excited motion of an ion in a harmonic trap using time-resolved fluorescence detection. Furthermore, Fourier analysis of the ion fluorescence signal was used to determine the trap frequency of an ion with high precision and reproducibility. The results show that our proposed method can be an alternative way to determine trap frequencies in an ion trap experiment.
We have developed a novel scheme to measure the secular motion of trapped ions. Employing pulsed excitation and analysis of the fluorescence of laser-cooled ions, we have measured the centre-of-mass mode frequency of single as well as entire ion crystals with a frequency precision better than 5 × 10 −4 within an interrogation time on the order of seconds, limited only by the fluorescence collection efficiency and the background noise. We have used this method to measure the mass of ions and observed charge exchange collisions between trapped calcium isotopes.