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arXiv:1906.01007 · Journal of Statistical Mechanics Theory and Experiment

Quantum jump statistics with a shifted jump operator in a chiral waveguide

Dario Cilluffo, Salvatore Lorenzo, G. Massimo Palma, Francesco Ciccarello

Published Oct 1, 2019• 7 citations
arXivHTMLPDF

Abstract

Abstract Resonance fluorescence, consisting of light emission from an atom driven by a classical oscillating field, is well-known to yield a sub-Poissonian photon counting statistics. This occurs when only emitted light is detected, which corresponds to a master equation (ME) unraveling in terms of the canonical jump operator describing spontaneous decay. Formally, an alternative ME unraveling is possible in terms of a shifted jump operator. We show that this shift can result in sub-Poissonian, Poissonian or super-Poissonian quantum jump statistics. This is shown in terms of the Mandel Q parameter in the limit of long counting times, which is computed through large deviation theory. We present a waveguide-QED setup, comprising a chiral waveguide coupled to a driven atom, where photon counting is described by the considered class of shifted jump operators.

DOI
10.1088/1742-5468/ab371c

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Abstract Resonance fluorescence, consisting of light emission from an atom driven by a classical oscillating field, is well-known to yield a sub-Poissonian photon counting statistics. This occurs when only emitted light is detected, which corresponds to a master equation (ME) unraveling in terms of the canonical jump operator describing spontaneous decay. Formally, an alternative ME unraveling is possible in terms of a shifted jump operator. We show that this shift can result in sub-Poissonian, Poissonian or super-Poissonian quantum jump statistics. This is shown in terms of the Mandel Q parameter in the limit of long counting times, which is computed through large deviation theory. We present a waveguide-QED setup, comprising a chiral waveguide coupled to a driven atom, where photon counting is described by the considered class of shifted jump operators.
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 investigate the emission characteristics of a measurement-driven quantum emitter in a continuously monitored optical environment. The quantum emitter is stimulated by observing the Pauli spin along its transition dipole that maximally noncommutes with the Hamiltonian of the emitter. It also exchanges energy resonantly with the optical environment, observable as quantum jumps corresponding to the absorption or emission of a photon and the null events where the quantum emitter did not make a jump. We characterize the finite-time statistics of quantum jumps and estimate their covariance and precision using the large deviation principle. While the statistics of absorption and emission events are generically sub-Poissonian with an improved precision by at most a factor of two compared to Poissonian jumps, our analysis also reveals a spin-measurement-induced transition from super-Poissonian to sub-Poissonian in their sum. We conclude by describing generalized quantum measurement strategies using mode-entangled optical beams to access the predicted counting statistics in experiments, with implications extending to optimal quantum clocks.
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 have discussed the photon statistics of the spectral components of N-atom time-dependent resonance fluorescence. It is shown that in contrast to the stationary limit, sub-Poissonian photon statistics in the sidebands occur for any number N of atoms including the case N\ensuremath{\gg}1. Reduction in Mandel's parameters Q+1{\mathit{Q}}_{+1}Q+1​ is found with increasing numbers of atoms. The typical time for the presence of sub-Poissonian statistics is proportional to 1/N.
Photons spontaneously emitted from single atoms are necessarily antibunched in time. The statistics of the photon time record, however, can show sub-Poissonian or even super-Poissonian statistics and depend strongly on the time interval used for analysis. In this work we have analyzed photon arrival times from resonantly excited barium atoms in an atomic beam observed under single-atom conditions. The time-interval dependence of photon statistics is presented, showing the connection between antibunching and sub-Poissonian statistics (at times comparable to the spontaneous-decay lifetime of the atom) as well as the evolution of the statistics in the long-time limit.
In this paper we investigate theoretically the behaviour of a quantum optical oscillator, consisting of two-level atoms strongly coupled to a cavity mode, in the optical domain. In contrast with the usual laser theory, we include explicitly the effects of atomic spontaneous emission and of cavity decay in the interaction of the atoms with the cavity field, using a quantum mechanical master equation approach. It is shown that such an oscillator produces sub-Poissonian light with a large degree of noise reduction even for the case when the atom–field coupling constant is only marginally larger than the spontaneous decay rate.