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arXiv:physics/0304013 · Physical Review A

Tests for nonrandomness in quantum jumps

Dana J. Berkeland, Daisy A. Raymondson, V. M. Tassin

Published May 7, 2004• 23 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.69.052103

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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×\else\texttimes\fi10\ensuremath−4<6.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}<6.5\ifmmode×\else\texttimes\fi10\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.
Quantum mechanical effects which are manifested in measurements on trapped atomic ions are reviewed. Observation of these effects is facilitated by the long storage times of a fixed number of laser-cooled ions and by high detection sensitivities, primarily through the observation of scattered laser light. We discuss the observation of quantum jumps and the application of quantum jumps to measurement of atomic ion lifetimes and spectra, detection of antibunching of light, the quantum Zeno effect and quantum projection noise. Experiments which detect nonclassical features of fluorescent light from single or a few trapped ions are briefly reviewed. Finally, we discuss experiments which reveal quantum effects in the motion of trapped ions. We briefly describe possible future extensions for each of these topics.
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A theory of quantum jumps in a system of few trapped ions is formulated. The V configuration of the energy levels and incoherent pumping are assumed. The master equation is derived in terms of the SU(3) collective operators for the V system. Numerical results for the intensity-intensity correlations for up to five ions are presented. Analytical results for a system of two ions are derived separating out dynamics at two difference time scales and by eliminating adiabatically the fast variables. From the analytical results, the underlying three-state Markov process that can be used to characterize the quantum jumps in the two-ion system is identified. Probability distributions for various off-on time intervals are presented.>
Introduction The quantum theory of atoms and molecules had its origin in the famous 1913 paper of Bohr [186] in which he suggested that the interaction of radiation and atoms occurred with the transition of an atom from one stationary internal state to another, accompanied by the emission or absorption of radiation of a frequency determined by the energy difference between these states. These transitions came to be known as ‘quantum jumps’. Since all experiments until the late 1970s used to be carried out with large ensembles of atoms and molecules, these jumps were masked and could not be directly observed; they were only inferred from spectroscopic data. In fact, with the advent of quantum mechanics they eventually came to be regarded as artefacts of Bohr's simple-minded semi-classical model. But with the availability of coherent light sources and single ions prepared in ion traps [187], [188], and optically cooled [189], [190], the issue has been reopened with the experimental demonstration of quantum jumps in single ions [191], [192], [193]. These experiments have also opened up the contentious issue of wave function collapse or reduction on measurement, as they can be regarded as making collapse visible on the oscilloscope screen [191]. Evidence of the discrete nature of quantum transitions in a single quantum system had been accumulating from the observation of photon anti-bunching in single-atom resonance fluorescence [194], the tunneling of single electrons in metal–oxide-–semiconductor junctions [195] and spin-flips of individual electrons in a Penning trap [196].
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.
We use a recent stochastical diffusion model of quantum evolution to represent the evolution of a three-level quantum system undergoing quantum jumps. This is possible because the continuous change in the quantum state in this diffusion model is so rapid that it appears to be instantaneous in comparison with the time between transitions. Experimental data from a study of the intermittent fluorescence of a single trapped 24Mg+ ion and equivalent theoretical data are shown to be strikingly similar. Statistical comparisons of the data are also made.