Theory of Photon Blockade by an Optical Cavity with One Trapped Atom

In our recent paper [1], we reported observations of photon blockade by one atom strongly coupled to an optical cavity. In support of these measurements, here we provide an expanded discussion of the general phenomenology of photon blockade as well as of the theoretical model and results that were presented in Ref. [1]. We describe the general condition for photon blockade in terms of the transmission coefficients for photon number states. For the atom-cavity system of Ref. [1], we present the model Hamiltonian and examine the relationship of the eigenvalues to the predicted intensity correlation function. We explore the effect of different driving mechanisms on the photon statistics. We also present additional corrections to the model to describe cavity birefringence and ac-Stark shifts. [1] K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, Nature 436, 87 (2005).Comment: 10 pages, 6 figure

Design, analysis, and presentation of crossover trials

OBJECTIVE: Although crossover trials enjoy wide use, standards for analysis and reporting have not been established. We reviewed methodological aspects and quality of reporting in a representative sample of published crossover trials. METHODS: We searched MEDLINE for December 2000 and identified all randomized crossover trials. We abstracted data independently, in duplicate, on 14 design criteria, 13 analysis criteria, and 14 criteria assessing the data presentation. RESULTS: We identified 526 randomized controlled trials, of which 116 were crossover trials. Trials were drug efficacy (48%), pharmacokinetic (28%), and nonpharmacologic (30%). The median sample size was 15 (interquartile range 8-38). Most (72%) trials used 2 treatments and had 2 periods (64%). Few trials reported allocation concealment (17%) or sequence generation (7%). Only 20% of trials reported a sample size calculation and only 31% of these considered pairing of data in the calculation. Carry-over issues were addressed in 29% of trial's methods. Most trials reported and defended a washout period (70%). Almost all trials (93%) tested for treatment effects using paired data and also presented details on by-group results (95%). Only 29% presented CIs or SE so that data could be entered into a meta-analysis. CONCLUSION: Reports of crossover trials frequently omit important methodological issues in design, analysis, and presentation. Guidelines for the conduct and reporting of crossover trials might improve the conduct and reporting of studies using this important trial design

Significance testing as perverse probabilistic reasoning

Truth claims in the medical literature rely heavily on statistical significance testing. Unfortunately, most physicians misunderstand the underlying probabilistic logic of significance tests and consequently often misinterpret their results. This near-universal misunderstanding is highlighted by means of a simple quiz which we administered to 246 physicians at two major academic hospitals, on which the proportion of incorrect responses exceeded 90%. A solid understanding of the fundamental concepts of probability theory is becoming essential to the rational interpretation of medical information. This essay provides a technically sound review of these concepts that is accessible to a medical audience. We also briefly review the debate in the cognitive sciences regarding physicians' aptitude for probabilistic inference