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Physical Review A

Photon antibunching and sub-Poissonian statistics from quantum jumps in one and two atoms

Wayne M. Itano, Jonas Bergquist, David J. Wineland

Published Jul 1, 1988• 53 citations
Publisher

Abstract

Antibunching and sub-Poissonian statistics of the 11-\ensuremath{\mu}m photon emission from the ${5d}^{10}{6p}^{2}{P}_{\frac{1}{2}}$ to ${5d}^{6}{6s}^{2}^{2}D_{\frac{3}{2}}$ transition in one and two trapped ${\mathrm{Hg}}^{+}$ ions have been inferred from the quantum jumps of the laser-induced fluorescence of the first resonance transition at 194 nm. Each downward step in fluorescence was assumed to mark the emission of an 11-\ensuremath{\mu}m photon. Signals from two ions were consistent with the assumption that quantum jumps in the two ions occurred independently. Mandel's $Q$ parameter was determined to be approximately -0.25 for one and two ions.

DOI
10.1103/physreva.38.559

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Antibunching and sub-Poissonian statistics of the 11-\ensuremath{\mu}m photon emission from the 5d106p2P12{5d}^{10}{6p}^{2}{P}_{\frac{1}{2}}5d106p2P21​​ to {5d}^{6}{6s}^{2}^{2}D_{\frac{3}{2}} transition in one and two trapped Hg+{\mathrm{Hg}}^{+}Hg+ ions have been inferred from the quantum jumps of the laser-induced fluorescence of the first resonance transition at 194 nm. Each downward step in fluorescence was assumed to mark the emission of an 11-\ensuremath{\mu}m photon. Signals from two ions were consistent with the assumption that quantum jumps in the two ions occurred independently. Mandel's QQQ parameter was determined to be approximately -0.25 for one and two ions.
We detect the radiatively driven electric quadrupole transition to the metastable 2D52^{2}D_{\frac{5}{2}}2D25​​ state in a single, laser-cooled Hg II ion by monitoring the abrupt cessation of the fluorescence signal from the laser-excited $^{2}S_{\frac{1}{2}}\ensuremath{\rightarrow}^{2}P_{\frac{1}{2}}$ first resonance line. When the ion "jumps" back from the metastable DDD state to the ground SSS state, the $S\ensuremath{\rightarrow}P$ resonance fluorescence signal immediately returns. The statistical properties of the quantum jumps are investigated; for example, photon antibunching in the emission from the DDD state is observed with 100% efficiency.
The photon pair correlation in the laser-excited fluorescence of a single trapped and cooled Ba+{\mathrm{Ba}}^{+}Ba+ ion shows antibunching and, in addition, novel nonclassical phenomena absent in the fluorescence of two-level atoms. They include excessive transient values of the correlation caused by optical pumping, and temporally extended sub-Poissonian photon emission probability which arises from the transient excitation of nonabsorbing Raman coherence. The fluorescence also displays sub-Poissonian photon statistics.
One of the experiments made possible by the trapping and cooling of a single atom is to observe the quantum jumps to a metastable state in the atom by monitoring the resonance fluorescence of a strong transition in which at least one of the states is coupled to the metastable state. When the atomic electron moves to the metastable state, the fluorescence from the strongly driven transition disappears. When the electron drops back into the strongly driven transition, the fluorescence abruptly returns. Statistical analysis of these random interruptions to the fluorescence signal implies photon antibunching in the emission of the weak photon.
Statistics of fluorescence photons emitted by a single two-level atom interacting with a continuous wave laser field are analyzed. The photon-counting distribution is calculated for the so-called intermediate fluorescence photons, i.e., those counted during the time interval between instants at which photons are emitted. The result is a sub-Poissonian (narrower than Poisson) distribution, which agrees with experimental observations. This intermediate-photon distribution is used to calculate the average number of fluorescence photons, the second factorial moment of the photon-counting distribution, and Mandel’s Q parameter commonly used to evaluate the deviation of photon statistics from the Poisson distribution. The theoretical expressions obtained for moments of the intermediate-photon distribution are different from well-known Mandel’s formulas.
Two manifestations of the quantum nature of coherent, resonant light scattering from atoms are photon antibunching and sub-Poissonian statistics. The existence of both effects has been demonstrated previously; in the present work, using individual barium atoms, measurements of the dependence of the latter effect on the frequency of the radiation field are presented. The distinction between the two phenomena is demonstrated by data that exhibit antibunching, yet have a photon counting distribution with variance equal to the Poisson value.