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Quantum-Atom Optics Downunder (QAO)

Quantum Stochastic Heating of a Trapped Ion through Resonance Fluorescence

Levente Horvath, Matthew J. Collett, H. J. Carmichael, Robert A. Fisher

Published Jan 1, 2007• 0 citations
Publisher

Abstract

The resonant heating of a harmonically trapped ion by a standing-wave light field is described as a quantum stochastic process combining a coherent Schrödinger evolution with Bohr-Einstein quantum jumps. The dependence of the center-of-mass motion on Lamb-Dicke parameter is studied. For Lamb-Dicke parameters greater than unity we demonstrate significant departures from the diffusion process that holds in the limit of small momentum “kicks”; a strong inhibition of the heating of the ion (fluorescence) occurs. Heating rates are calculated as a Monte-Carlo average from both the full quantum stochastic process and its semi-quantum approximation.

DOI
10.1364/qao.2007.qtuc1

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The resonant heating of a harmonically trapped ion by a standing-wave light field is described as a quantum stochastic process combining a coherent Schrödinger evolution with Bohr-Einstein quantum jumps. The dependence of the center-of-mass motion on Lamb-Dicke parameter is studied. For Lamb-Dicke parameters greater than unity we demonstrate significant departures from the diffusion process that holds in the limit of small momentum “kicks”; a strong inhibition of the heating of the ion (fluorescence) occurs. Heating rates are calculated as a Monte-Carlo average from both the full quantum stochastic process and its semi-quantum approximation.
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 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.
We experimentally investigate the resonance fluorescence spectrum of single 171Yb{}^{171}\mathrm{Yb}171Yb and 172Yb{}^{172}\mathrm{Yb}172Yb ions that are laser cooled to the Lamb-Dicke regime in a radiofrequency trap. While the fluorescence scattering of 172Yb{}^{172}\mathrm{Yb}172Yb is continuous, the 171Yb{}^{171}\mathrm{Yb}171Yb fluorescence is interrupted by quantum jumps because a nonvanishing rate of spontaneous transitions leads to electron shelving in the metastable hyperfine sublevel 2D3/2(F=2).{}^{2}{D}_{3/2}(F=2).2D3/2​(F=2). The average duration of the resulting dark periods can be varied by changing the intensity of a repumping laser field. Optical heterodyne detection is employed to analyze the fluorescence spectrum near the Rayleigh elastic scattering peak. It is found that the stochastic modulation of the fluorescence emission by quantum jumps gives rise to a Lorentzian component in the fluorescence spectrum, and that the linewidth of this component varies according to the average duration of the dark fluorescence periods. The experimental observations are in quantitative agreement with theoretical predictions.