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Physical Review A

Precise test of quantum jump theory

Randall G. Hulet, David J. Wineland, Jonas Bergquist, Wayne M. Itano

Published Jun 1, 1988• 26 citations
Publisher

Abstract

Quantum jumps due solely to spontaneous Raman scattering between the Zeeman sublevels of a single $^{24}\mathrm{Mg}^{+}$ ion have been observed in the fluorescence emitted by the ion. A theory of quantum jumps for this system predicts that coherences between excited levels cause the ratio of the mean duration of the "fluorescence-on periods" to the mean duration of the "fluorescence-off periods" to be independent of laser intensity. The measured value agrees with the predicted one to within the measurement precision of 2%. The distribution of the durations of the off periods also agrees with theory.

DOI
10.1103/physreva.37.4544

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Quantum jumps due solely to spontaneous Raman scattering between the Zeeman sublevels of a single 24Mg+^{24}\mathrm{Mg}^{+}24Mg+ ion have been observed in the fluorescence emitted by the ion. A theory of quantum jumps for this system predicts that coherences between excited levels cause the ratio of the mean duration of the "fluorescence-on periods" to the mean duration of the "fluorescence-off periods" to be independent of laser intensity. The measured value agrees with the predicted one to within the measurement precision of 2%. The distribution of the durations of the off periods also agrees with theory.
A single laser, which is used to induce and detect spontaneous Raman transitions, can be used to observe quantum jumps in a single atom. The population dynamics of a particular system, consisting of two 2S1/2^{2}\mathrm{S}_{1/2}2S1/2​ ground-state levels and four 2P3/2^{2}\mathrm{P}_{3/2}2P3/2​ excited-state levels split by a magnetic field, is analyzed for a laser tuned near a particular transition. We find that the statistics of the fluorescence emitted by this system are described by the same formalism developed for the three-level V configuration irradiated by two light sources. Over a wide range of observation times, the fluorescence intensity will be two valued, either off or on, as has been verified for the V configuration. Some surprising and elegant features of this new system are described.
Several experiments performed at NBS using a single (or few) trapped atomic ions are described. We recently observed the ‘‘quantum jumps’’ in the fluorescence from a single ion of Mg+ due to spontaneous Raman transitions between the energy levels of the ion. In this system, a single laser is used to induce transitions between Zeeman sub‐levels of the ion. As with other realizations of quantum jumps, the dynamics of the population evolution is governed by an effective two‐level rate equation. A novel coherence phenomenon between excited state sub‐levels makes this system ideally suited for quantitatively testing the quantum jump theory. Our data are consistent with theory to within the measurement precision of 2%. Images of two to four ions which have been laser‐cooled until they ‘‘crystallize’’ are displayed and several other recent single ion experiments are mentioned.
We have recorded the laser-excited resonance fluorescence of one to three Ba+{\mathrm{Ba}}^{+}Ba+ ions and observed Bohr's "quantum jumps" when an ion decayed to the metastable 2D52^{2}D_{\frac{5}{2}}2D25​​ state, suddenly quenching its fluorescence. Most of the jumps mark Raman-Stokes scattering from the 2S12^{2}S_{\frac{1}{2}}2S21​​ and 2D32^{2}D_{\frac{3}{2}}2D23​​ levels.
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.
Recent experiments have found abrupt changes in the intensity of laser light scattered off single ions and atoms. These abrupt changes have been interpreted as resulting from Bohr's ``quantum jumps'' of the ion or atom from one state to another. In Bohr's description, such quantum jumps are not predicted by the Schr\"odinger equation and are introduced by additional postulates into quantum theory. We consider here an alternative explanation of these experiments using only properties of solutions of the Schr\"odinger equation and avoiding Bohr's added postulate.