An experimental technique which permits the study of single three-level atoms prior to quantum jumps to a shelving state has been used to study the second-order photon statistics of laser-excited barium atoms. Measured values of Mandel's Q parameter agree with the theory derived for two-level atoms. This result illustrates the extent to which the presence of additional levels can be ignored in certain systems: Although the third level in this system is responsible for the quantum jumps, prior to each jump the system's behavior is within experimental errors, exactly like that of a two-level atom. The negative values of Q obtained for a range of laser intensities demonstrate the sub-Poisson character of the emission.
An experimental technique which permits the study of single three-level atoms prior to quantum jumps to a shelving state has been used to study the second-order photon statistics of laser-excited barium atoms. Measured values of Mandel's Q parameter agree with the theory derived for two-level atoms. This result illustrates the extent to which the presence of additional levels can be ignored in certain systems: Although the third level in this system is responsible for the quantum jumps, prior to each jump the system's behavior is within experimental errors, exactly like that of a two-level atom. The negative values of Q obtained for a range of laser intensities demonstrate the sub-Poisson character of the emission.
A single three-level atom with the ground state strongly coupled to an excited state and weakly coupled to a third intermediate state exhibits a telegraph signal of fluorescent emission when driven by laser light at the strong coupling frequency. The ``on'' periods correspond to normal resonance fluorescence, whereas the ``off'' periods correspond to the atom being ``shelved'' in the intermediate state. Such a system has interesting statistical properties. The photon statistics during the ``on'' periods correspond to two-level behavior and are close to Poisson in nature. However, the photon number distribution of a succession of ``on'' periods exhibits Bose-Einstein statistics. Thus the three-level system can exhibit both ``quiet'' and ``noisy'' behavior. The mathematical connection between the two cases is established, and an atomic beam experiment is described which records a mixture of the two statistical extremes. The composition of the mixture is varied, and the data are shown to be well represented by an analysis based upon the model developed.
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.
We calculate from the quantum regression theorem the entire photon-counting statistics for the fluorescence from a laser-driven two-level system weakly coupled to a metastable third level, and compare the result with the statistics of a dichotomic Markov process. The comparison shows, that at least in the limit of an infinite intensity of the laser in a single experiment the sequence of photon counts should display randomly alternating periods with no counts and a nonzero counting rate as if the atom executed ``quantum jumps'' to and from the metastable state.
Antibunching and sub-Poissonian statistics of the 11-\ensuremath{\mu}m photon emission from the 5d106p2P21 to ${5d}^{6}{6s}^{2}^{2}D_{\frac{3}{2}}$ transition in one and two trapped 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.
A single-atom optical clock proposed over ten years ago utilizes an amplification scheme which only recently was recognized as a novel problem in quantum statistics. The atom, a three-state system, has two coupled transitions that are driven continuously by two external fields, one being an allowed transition (1\ensuremath{\leftrightarrows}3) and the other a forbidden transition (2\ensuremath{\leftrightarrows}3) where \ensuremath{\Vert}3〉 is the lowest state. It has been argued that the weak transition, which is difficult to detect, could be monitored by the presence or absence of spontaneous emission of the strong transition. Thus, when the atom is shelved in the metastable state \ensuremath{\Vert}2〉, the strong transition is extinguished, but when the atom executes a single quantum jump (2\ensuremath{\rightarrow}3), it triggers a succession of perhaps a million quantum jumps (macroscopic quantum jumps) in the strong transition, an amplification that can be detected easily. This intuitive argument for alternating bright and dark intervals assumes, however, that the atom is always in an eigenstate. Should the atom be in a superposition state, because of coherent excitation, one could imagine that the weak transition would merely reduce the intensity of the strong transition slightly. This issue is resolved, in favor of the first intuitive argument, by calculating the photon-counting statistics, the probability W(n,T) of observing precisely n photon-counting events in a collection T in a quantum-mechanically consistent way. The results cannot be described by classical statistics. A compact analytic form is obtained for W(n,T) by considering the entire hierarchy of correlation functions where the emission interval peaks sharply about a particular n with a Poisson distribution and can be comparable in length to the darkness interval (n=0) while the other values of n display vanishingly small probabilities.
Four-level atom dynamics is studied in a ladder system in the nine parameter space consisting of driving field strengths, detunings and decay constants, ${{\ensuremath{\Omega}}_{1},{\ensuremath{\Omega}}_{2},{\ensuremath{\Omega}}_{3},{\ensuremath{\Delta}}_{1},{\ensuremath{\Delta}}_{2},{\ensuremath{\Delta}}_{3},{\ensuremath{\Gamma}}_{2},{\ensuremath{\Gamma}}_{3},{\ensuremath{\Gamma}}_{4}}$. One can selectively excite or induce two-level behavior between particular levels of ones choice by appropriately tuning the driving field strengths at three-photon resonance. The dynamics may be classified into two main regions of interest (i) small ${\ensuremath{\Omega}}_{2}$ coupling the \ensuremath{\mid}2⟩-\ensuremath{\mid}3⟩ transition and (ii) large ${\ensuremath{\Omega}}_{2}$. In case (i) one sees two-level behavior consisting of adjacent levels and in a particular region in the parameter space, there is an intermittent shelving of the electrons in one of the two subsystems. In case (ii) the levels consist of the ground state and the upper most level. Emission statistics is studied using the delay function approach in both the cases. In case (i), the behavior of the second order correlation function g2(t), is similar to that of two-level emission for low ${\ensuremath{\Omega}}_{1}$ coupling the \ensuremath{\mid}1⟩-\ensuremath{\mid}2⟩ transition, and the correlation increases with ${\ensuremath{\Omega}}_{1}$ for smaller time delays. While, in case (ii) when, in addition, ${\ensuremath{\Omega}}_{3}$ coupling the \ensuremath{\mid}3⟩-\ensuremath{\mid}4⟩ transitionis kept low, g2(t) shows superpoissonian distribution, which may be attributed to three-photon processes.