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Physical Review Letters

Photon antibunching and non-Poissonian fluorescence of a single three-level ion

Michael Schubert, Ingo Siemers, R. Blatt, Werner Neuhauser, P. E. Toschek

Published May 18, 1992• 74 citations
Publisher

Abstract

The photon pair correlation in the laser-excited fluorescence of a single trapped and cooled ${\mathrm{Ba}}^{+}$ 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.

DOI
10.1103/physrevlett.68.3016

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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.
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.
The statistical fluctuations of light can, under certain circumstances, exhibit a number of interesting nonclassical features. These include photon antibunching, sub-Poissonian statistics, and squeezing, all of which exist only in a quantum field. The three effects are distinct, and do not necessarily go together, although the first two are sometimes mistakenly treated as interchangeable. Both photon antibunching and sub-Poissonian statistics have been observed in experiments on resonance fluorescence from single atoms, which is described. Squeezing has not yet been seen experimentally, although many nonlinear processes are expected to give rise to it. The squeezed state can be recognized in heterodyne or homodyne experiments, where the squeezing becomes manifest as sub-Poissonian photon fluctuations.
We investigate the transient and the steady-state behaviour of the photon statistics of a single-atom laser, consisting of a three-level Λ system, driven by an incoherent external pump field and strongly coupled to a single mode of an optical cavity. For several limiting cases we are able to obtain analytical results. A comparison with standard multi-atom laser theory reveals a surprisingly good agreement down to very small intracavity photon numbers. Under appropriate operating conditions a calculation of the second-order intensity correlation function yields sub-Poissonian statistics as well as strong antibunching induced by the nonlinear dynamics of the atom.
The autocorrelation g(2){\mathit{g}}^{(2)}g(2)(\ensuremath{\tau}) of the photon-counting signal from laser-induced light scattering off a single trapped and laser-cooled Ba+{\mathrm{Ba}}^{+}Ba+ ion shows dramatic nonclassical effects: g(2){\mathit{g}}^{(2)}g(2)(\ensuremath{\tau}) increasing upon delay \ensuremath{\tau} close to zero (``antibunching'') is accompanied (i) by its extreme peak values, (ii) by long transients and long appearance of subunity values (``sub-Poissonian light''), both extending much beyond the lifetime of the ion's resonance level, and (iii) by modulation from magnetic precession, as is common with quantum beats. These phenomena highlight the internal multilevel structure of the ion, hint at optical pumping, and prove the coherent evolution of the ion's internal state. The preparation of the ion in a coherent superposition by spontaneous decay is demonstrated. The counting variance of the scattered light, measured in terms of Mandel's Q parameter, deviates from that of classical light by up to \ensuremath{\Delta}Q=-7\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$.
We consider a single two-level atom in an optical cavity, in which the system is driven by a coherent driving field. In the bad-cavity limit, when the cavity loss rate is taken to be large compared to the atomic decay rate and atom-field coupling, the cavity field can be adiabatically eliminated from the equations of motion for the atomic operators. The main effect of the cavity in this limit is the enhancement of spontaneous emission into the cavity mode. For this model, the second-order intensity correlation function g(2)() has been shown to exhibit photon antibunching, sub-Poissonian photon number distributions, and other nonclassical effects.1 In this paper, analytic results are presented for g(2)() for both the transmitted and fluorescent light fields when broadband squeezed light is injected into the cavity. Effects of the squeezing on nonclassical behavior is examined.