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arXiv:quant-ph/0003009 · Physical Review Letters

Motional Sidebands and Direct Measurement of the Cooling Rate in the Resonance Fluorescence of a Single Trapped Ion

Ch. Raab, Jürgen Eschner, J. Bolle, H. Oberst, Ferdinand Schmidt‐Kaler, R. Blatt

Published Jul 17, 2000• 55 citations
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Abstract

Resonance fluorescence of a single trapped ion is spectrally analyzed using a heterodyne technique. Motional sidebands due to the oscillation of the ion in the harmonic trap potential are observed in the fluorescence spectrum. From the width of the sidebands the cooling rate is obtained and found to be in agreement with the theoretical prediction.

DOI
10.1103/physrevlett.85.538

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Resonance fluorescence of a single trapped ion is spectrally analyzed using a heterodyne technique. Motional sidebands due to the oscillation of the ion in the harmonic trap potential are observed in the fluorescence spectrum. From the width of the sidebands the cooling rate is obtained and found to be in agreement with the theoretical prediction.
The resonance fluorescence spectrum of a laser-cooled trapped ion is theoretically studied in the Lamb-Dicke limit. Angular averaged spectrum around the elastic peak and the motional sidebands is calculated. The widths of the sidebands are shown to be given by the cooling rate of the ion in the trap. In the limit when the trapping force is strong a possibility of dispersive line shapes is predicted. The spectrum derived is also shown to reproduce in the low-intensity limit the earlier perturbative results.
The spectrum of resonance fluorescence of a single trapped and laser-cooled ion is studied theoretically. The quantum motion of the trapped particle manifests itself in the form of narrow motional sidebands in the fluorescence spectrum. For our calculations it is assumed that the ion is confined to dimensions much smaller than the optical wavelength (Lamb-Dicke limit) and the approach is valid for multilevel systems, general trapping potentials, and for both traveling-wave and standing-wave configurations. The motional sidebands in the spectrum have asymmetric amplitudes and this asymmetry is shown to depend on the ion energy, the detector position, and the choice of standing- or traveling-wave laser excitation.
The spectrum of resonance fluorescence of a single trapped and laser-cooled ion is studied theoretically. The quantum motion of the trapped particle manifests itself in the form of narrow motional sidebands in the fluorescence spectrum. For our calculations it is assumed that the ion is confined to dimensions much smaller than the optical wavelength (Lamb-Dicke limit) and the approach is valid for multilevel systems, general trapping potentials, and for both traveling-wave and standing-wave configurations. The motional sidebands in the spectrum have asymmetric amplitudes and this asymmetry is shown to depend on the ion energy, the detector position, and the choice of standing- or traveling-wave laser excitation.
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.
We investigate the temporal dynamics of Doppler cooling of an initially hot single trapped atom in the weak-binding regime using a semiclassical approach. We develop an analytical model for the simplest case of a single vibrational mode for a harmonic trap, and show how this model allows us to estimate the initial energy of the trapped particle by observing the time-dependent fluorescence during the cooling process. The experimental implementation of this temperature measurement provides a way to measure atom heating rates by observing the temperature rise in the absence of cooling. This method is technically relatively simple compared to conventional sideband detection methods, and the two methods are in reasonable agreement. We also discuss the effects of rf micromotion, relevant for a trapped atomic ion, and the effect of coupling between the vibrational modes on the cooling dynamics.
We report a demonstration and quantitative characterization of one-dimensional cavity cooling of a single trapped (88)Sr(+) ion in the resolved-sideband regime. We measure the spectrum of cavity transitions, the rates of cavity heating and cooling, and the steady-state cooling limit. The cavity cooling dynamics and cooling limit of 22.5(3) motional quanta, limited by the moderate coupling between the ion and the cavity, are consistent with a simple model [Phys. Rev. A 64, 033405 (2001)] without any free parameters, validating the rate equation model for cavity cooling.