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Journal of Physics B Atomic Molecular and Optical Physics

Quantum jumps in singly ionized magnesium

Hebe Powell, Martijn A. van Eijkelenborg, William M. Irvine, D. M. Segal, Richard Claude Thompson

Published Jan 10, 2002• 13 citations
Publisher

Abstract

The quantum jump statistics for the three stable isotopes of Mg + have been studied experimentally. Single ions of magnesium were held and laser cooled in a Penning trap. Quantum jumps were observed by collecting the resonance fluorescence near 280 nm from the cooled ion. The jump rate was analysed to find ratios of the average time the ion spends fluorescing, `on' time, to the average time it spends in the dark state, `off' time: for both 24 Mg + and 26 Mg + this value was found to be 15.9±1.2, in agreement with a theoretical value of 16.0. The presence of hyperfine structure in 25 Mg + means that while the jump rate for 24 Mg + and 26 Mg + remains unaltered for both available cooling transitions, for the odd isotope the on to off ratio is predicted to be 11.8 and 22.8 for the lower and upper transitions respectively. Experimental values for these ratios were found to be 10.2 ± 0.7 and 22.0 ± 0.6. The occurrence of so-called nuclear jumps in 25 Mg + is investigated qualitatively. These rare jumps are produced as a result of the hyperfine splitting, which is only present in the odd isotope. Although the data indicate some evidence for this type of jump, it is not possible to draw any firm conclusions due to the small number of events observed.

DOI
10.1088/0953-4075/35/2/301

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Tests for nonrandomness in quantum jumps

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In a fundamental test of quantum mechanics, we have observed $228 000$ quantum jumps of a single trapped and laser cooled $^{88}\mathrm{Sr}^{+}$ ion. This represents a statistical increase of two orders of magnitude over previous similar analyses of quantum jumps. Compared to other searches for nonrandomness in quantum-mechanical processes, using quantum jumps simplifies the interpretation of data by eliminated multiparticle effects and providing near-unit detection efficiency of transitions. We measure the fractional reduction in the entropy of information to be $<6.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ when the value of any interval between quantum jumps is known. We also find that the number of runs of successively increasing or decreasing interval times agrees with the theoretically expected values. Furthermore, we analyze $238 000$ quantum jumps from two simultaneously confined ions and find that the number of apparently coincidental transitions is as expected. Finally, we observe 8400 spontaneous decays of two simultaneously trapped ions and find that the number of apparently coincidental decays from the metastable state agrees with the expected value. We find no evidence for short- or long-term correlations in the intervals of the quantum jumps or in the decay of the quantum states, in agreement with quantum theory.

arXiv:physics/0304013•Physical Review A•May 7, 2004•23 citations
The quantum jump statistics for the three stable isotopes of Mg + have been studied experimentally. Single ions of magnesium were held and laser cooled in a Penning trap. Quantum jumps were observed by collecting the resonance fluorescence near 280 nm from the cooled ion. The jump rate was analysed to find ratios of the average time the ion spends fluorescing, on' time, to the average time it spends in the dark state, off' time: for both 24 Mg + and 26 Mg + this value was found to be 15.9±1.2, in agreement with a theoretical value of 16.0. The presence of hyperfine structure in 25 Mg + means that while the jump rate for 24 Mg + and 26 Mg + remains unaltered for both available cooling transitions, for the odd isotope the on to off ratio is predicted to be 11.8 and 22.8 for the lower and upper transitions respectively. Experimental values for these ratios were found to be 10.2 ± 0.7 and 22.0 ± 0.6. The occurrence of so-called nuclear jumps in 25 Mg + is investigated qualitatively. These rare jumps are produced as a result of the hyperfine splitting, which is only present in the odd isotope. Although the data indicate some evidence for this type of jump, it is not possible to draw any firm conclusions due to the small number of events observed.
Summary form only given. We have performed a study of quantum jumps in single magnesium ions held in a Penning trap. This system is unusual in that quantum jumps may be observed using only a single laser frequency which serves to laser cool the ion (providing fluorescence for detection), shelve the ion in a metastable state (via an off-resonant Raman transition) and also to repump the ion from the metastable state back into the cooling cycle (again via a Raman transition). Single /sup 24/Mg/sup +/ ions have been studied in a Penning trap before but we have predicted and now observed a number of interesting effects that occur only in /sup 25/Mg/sup +/. We have also trapped single ions of /sup 26/Mg/sup +/ and confirmed that their quantum jump behaviour is similar to that of /sup 24/Mg/sup +/ as expected. The novel features in the behaviour of /sup 25/Mg/sup +/ are due to the presence of hyperfine structure in this 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.
This thesis describes experimental work performed on laser cooled magnesium ions, confined in a quadrupole ion trap operating in the Penning or the combined mode. Information is gained about the dynamical motion of the ions. This is done by analyzing the time delays between scattered fluorescence photons in the case of small ion clouds (generally less than ten ions). For larger clouds (upwards of 100 ions), a fraction of the ions is "tagged" and a subsequent study made of the time evolution of the fluorescence. We have developed an innovative, non-invasive method for measuring ion oscillation frequencies which is based on analyzing photon-photon correlations present in the emitted ion fluorescence. This technique has been used to measure all three Penning trap frequencies for a wide range of dc voltage. The data have been fitted to theory and we have obtained a global fit of these data to one set of trap parameters. We also demonstrate that our technique enables us to measure space-charge shifted values of the trap resonances. This method has also been applied to the combined trap and we report experimental verification of the predicted trap resonances for a wide range of trapping parameters. These data fit well to theory. This is for all three oscillation frequencies for one set of trap parameters consistent with the data for the Penning trap. \nFurther experiments are reported concerned with the dynamics of larger ion clouds in a Penning trap. A pulsed laser is used to "tag" a small number of the ions in large ion clouds. This removes those ions from the cooling cycle by placing them in a metastable state. Subsequently, we have monitored the time evolution of the fluorescence. By analyzing these data we have been able to determine cloud rotation frequencies for large ensembles of ions.
In a fundamental test of quantum mechanics, we have observed 228000228 000228000 quantum jumps of a single trapped and laser cooled 88Sr+^{88}\mathrm{Sr}^{+}88Sr+ ion. This represents a statistical increase of two orders of magnitude over previous similar analyses of quantum jumps. Compared to other searches for nonrandomness in quantum-mechanical processes, using quantum jumps simplifies the interpretation of data by eliminated multiparticle effects and providing near-unit detection efficiency of transitions. We measure the fractional reduction in the entropy of information to be $<6.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ when the value of any interval between quantum jumps is known. We also find that the number of runs of successively increasing or decreasing interval times agrees with the theoretically expected values. Furthermore, we analyze 238000238 000238000 quantum jumps from two simultaneously confined ions and find that the number of apparently coincidental transitions is as expected. Finally, we observe 8400 spontaneous decays of two simultaneously trapped ions and find that the number of apparently coincidental decays from the metastable state agrees with the expected value. We find no evidence for short- or long-term correlations in the intervals of the quantum jumps or in the decay of the quantum states, in agreement with quantum theory.