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arXiv:quant-ph/0003013 · Physical Review A

Resonance fluorescence spectrum of a trapped ion undergoing quantum jumps

V. Bühner, Chr. Tamm

Published May 3, 2000• 19 citations
arXivHTMLPDF

Abstract

We experimentally investigate the resonance fluorescence spectrum of single ${}^{171}\mathrm{Yb}$ and ${}^{172}\mathrm{Yb}$ ions that are laser cooled to the Lamb-Dicke regime in a radiofrequency trap. While the fluorescence scattering of ${}^{172}\mathrm{Yb}$ is continuous, the ${}^{171}\mathrm{Yb}$ fluorescence is interrupted by quantum jumps because a nonvanishing rate of spontaneous transitions leads to electron shelving in the metastable hyperfine sublevel ${}^{2}{D}_{3/2}(F=2).$ 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.

DOI
10.1103/physreva.61.061801

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Quantum Jumps in a Single Ion

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We briefly discuss the preparation of a single cold ion in an rf trap, and the concept of "quantum jumps" which requires a single atomic particle for verification. Recent corresponding experiments have demonstrated interruptions of the laser-excited resonance fluorescence, which are the signature of the particles performing quantum jumps to and from a metastable level, under weak excitation of the corresponding transition. The time density of the jumps obeys a Poissonian distribution in agreement with theoretical models. With three trapped ions, the high rate of multiple jumps suggests the presence of collective interaction.

Physica Scripta•Jan 1, 1988•25 citations
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.
The paper reports experimental investigations on 171 Yb ions confined in a radiofrequency Paul trap. Single ions are cooled and optically detected by laser excitation of the cycling F = 1 – F = 0 hyperfine component of the 2 S 1/2 – 2 P 1/2 resonance transition. The metastable 2 D 3/2 ( F = 1) level which is rapidly populated by decay from the 2 P 1/2 level is depleted by a second laser source. The resonance fluorescence signal exhibits dark periods due to a small rate of spontaneous transitions to the 2 D 3/2 ( F = 2) level which is coupled only weakly to the laser-cooling excitation cycle. Prospects for an optical frequency standard based on excitation of the narrow 2 S 1/2 ( F = 0) – 2 D 3/2 ( F = 2) transition of 171 Yb + at a wavelength of 435 nm are discussed.
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 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 performed laser spectroscopy of In+{\mathrm{In}}^{+}In+ ions stored in a radio-frequency trap. The 5s2{\mathit{s}}^{2}s2 1^{1}1S0{\mathit{S}}_{0}S0​\ensuremath{\rightarrow}5s5p 3^{3}3P1{\mathit{P}}_{1}P1​ transition at 230.6 nm was excited and its hyperfine splitting and isotope shift have been measured. The lifetime of the 3^{3}3P1{\mathit{P}}_{1}P1​ state was measured using intensity modulated laser excitation: \ensuremath{\tau}(3{(}^{3}(3P1{\mathit{P}}_{1}P1​)=0.44(4) \ensuremath{\mu}s. A single indium ion was laser cooled using this intercombination line and dark periods in the fluorescence were observed when the metastable 3^{3}3P0{\mathit{P}}_{0}P0​ state was populated by a magnetic dipole decay from 3^{3}3P1{\mathit{P}}_{1}P1​. The radiative lifetime of the forbidden transition 3^{3}3P0{\mathit{P}}_{0}P0​${\ensuremath{\rightarrow}}^{1}$S0{\mathit{S}}_{0}S0​ was determined from the duration of the dark periods: \ensuremath{\tau}(3{(}^{3}(3P0{\mathit{P}}_{0}P0​)=0.14(2) s. This value is compared to calculations based on perturbation theory. Prospects for an optical frequency standard using the narrow 5s2{\mathit{s}}^{2}s2 1^{1}1S0{\mathit{S}}_{0}S0​\ensuremath{\rightarrow}5s5p 3^{3}3P0{\mathit{P}}_{0}P0​ resonance at 236.5 nm of a single laser-cooled indium ion are discussed.
We performed laser spectroscopy of In+{\mathrm{In}}^{+}In+ ions stored in a radio-frequency trap. The 5s2{\mathit{s}}^{2}s2 1^{1}1S0{\mathit{S}}_{0}S0​\ensuremath{\rightarrow}5s5p 3^{3}3P1{\mathit{P}}_{1}P1​ transition at 230.6 nm was excited and its hyperfine splitting and isotope shift have been measured. The lifetime of the 3^{3}3P1{\mathit{P}}_{1}P1​ state was measured using intensity modulated laser excitation: \ensuremath{\tau}(3{(}^{3}(3P1{\mathit{P}}_{1}P1​)=0.44(4) \ensuremath{\mu}s. A single indium ion was laser cooled using this intercombination line and dark periods in the fluorescence were observed when the metastable 3^{3}3P0{\mathit{P}}_{0}P0​ state was populated by a magnetic dipole decay from 3^{3}3P1{\mathit{P}}_{1}P1​. The radiative lifetime of the forbidden transition 3^{3}3P0{\mathit{P}}_{0}P0​${\ensuremath{\rightarrow}}^{1}$S0{\mathit{S}}_{0}S0​ was determined from the duration of the dark periods: \ensuremath{\tau}(3{(}^{3}(3P0{\mathit{P}}_{0}P0​)=0.14(2) s. This value is compared to calculations based on perturbation theory. Prospects for an optical frequency standard using the narrow 5s2{\mathit{s}}^{2}s2 1^{1}1S0{\mathit{S}}_{0}S0​\ensuremath{\rightarrow}5s5p 3^{3}3P0{\mathit{P}}_{0}P0​ resonance at 236.5 nm of a single laser-cooled indium ion are discussed.
We briefly discuss the preparation of a single cold ion in an rf trap, and the concept of "quantum jumps" which requires a single atomic particle for verification. Recent corresponding experiments have demonstrated interruptions of the laser-excited resonance fluorescence, which are the signature of the particles performing quantum jumps to and from a metastable level, under weak excitation of the corresponding transition. The time density of the jumps obeys a Poissonian distribution in agreement with theoretical models. With three trapped ions, the high rate of multiple jumps suggests the presence of collective interaction.