Functional approximations with Stein's method of exchangeable pairs

We combine the method of exchangeable pairs with Stein's method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply this approach to estimate the distance of a sum of random variables, chosen from an array according to a random permutation, from a Gaussian mixture process. This result lets us prove a functional combinatorial central limit theorem. We also consider a graph-valued process and bound the speed of convergence of the distribution of its rescaled edge counts to a continuous Gaussian process.Comment: will appear in Annales de l'Institut Henri Poincar\'e, Probabilit\'es et Statistique

Stein's method of exchangeable pairs in multivariate functional approximations

In this paper we develop a framework for multivariate functional approximation by a suitable Gaussian process via an exchangeable pairs coupling that satisfies a suitable approximate linear regression property, thereby building on work by Barbour (1990) and Kasprzak (2020). We demonstrate the applicability of our results by applying it to joint subgraph counts in an Erd\H{o}s-Renyi random graph model on the one hand and to vectors of weighted, degenerate $U$-processes on the other hand. As a concrete instance of the latter class of examples, we provide a bound for the functional approximation of a vector of success runs of different lengths by a suitable Gaussian process which, even in the situation of just a single run, would be outside the scope of the existing theory

Harvesting, coupling and control of single exciton coherences in photonic waveguide antennas

We perform coherent non-linear spectroscopy of individual excitons strongly confined in single InAs quantum dots (QDs). The retrieval of their intrinsically weak four-wave mixing (FWM) response is enabled by a one-dimensional dielectric waveguide antenna. Compared to a similar QD embedded in bulk media, the FWM detection sensitivity is enhanced by up to four orders of magnitude, over a broad operation bandwidth. Three-beam FWM is employed to investigate coherence and population dynamics within individual QD transitions. We retrieve their homogenous dephasing in a presence of spectral wandering. Two-dimensional FWM reveals off-resonant F\"orster coupling between a pair of distinct QDs embedded in the antenna. We also detect a higher order QD non-linearity (six-wave mixing) and use it to coherently control the FWM transient. Waveguide antennas enable to conceive multi-color coherent manipulation schemes of individual emitters.Comment: 7 pages, 8 Figure

Vortices in exciton-polariton condensates with polarization splitting

The presence of polarization splitting of exciton-polariton branches in planar semiconductor microcavities has a pronounced effect on vortices in polariton condensates. We show that the TE-TM splitting leads to the coupling between the left and right half-vortices (vortices in the right and left circular components of the condensate), that otherwise do not interact. We analyze also the effect of linear polarization pinning resulted from a fixed splitting between two perpendicular linear polarizations. In this case, half-vortices acquire strings (solitons) attached to them. The half-vortices with strings can be detected by observing the interference fringes of light emitted from the cavity in two circular polarizations. The string affects the fringes in both polarizations. Namely, the half-vortex is characterized by an asymmetric fork-like dislocation in one circular polarization; the fringes in the other circular polarization are continuous, but they are shifted by crossing the string.Comment: 4 pages, 2 figs, Optics of Excitons in Confined Systems 11 (Madrid, 7-11 september 2009

Antireflective photonic structure for coherent nonlinear spectroscopy of single magnetic quantum dots

This work presents epitaxial growth and optical spectroscopy of CdTe quantum dots (QDs) in (Cd,Zn,Mg)Te barriers placed on the top of (Cd,Zn,Mg)Te distributed Bragg reflector. The formed photonic mode in our half-cavity structure permits to enhance the local excitation intensity and extraction efficiency of the QD photoluminescence, while suppressing the reflectance within the spectral range covering the QD transitions. This allows to perform coherent, nonlinear, resonant spectroscopy of individual QDs. The coherence dynamics of a charged exciton is measured via four-wave mixing, with the estimated dephasing time $T_2=(210\,\pm\,40)$ ps. The same structure contains QDs doped with single Mn$^{2+}$ ions, as detected in photoluminescence spectra. Our work therefore paves the way toward investigating and controlling an exciton coherence coupled, via $s$,$p$-$d$ exchange interaction, with an individual spin of a magnetic dopant.Comment: 6 pages, 5 figure

How good is your Laplace approximation of the Bayesian posterior? Finite-sample computable error bounds for a variety of useful divergences

The Laplace approximation is a popular method for providing posterior mean and variance estimates. But can we trust these estimates for practical use? One might consider using rate-of-convergence bounds for the Bayesian Central Limit Theorem (BCLT) to provide quality guarantees for the Laplace approximation. But the bounds in existing versions of the BCLT either: require knowing the true data-generating parameter, are asymptotic in the number of samples, do not control the Bayesian posterior mean, or apply only to narrow classes of models. Our work provides the first closed-form, finite-sample quality bounds for the Laplace approximation that simultaneously (1) do not require knowing the true parameter, (2) control posterior means and variances, and (3) apply generally to models that satisfy the conditions of the asymptotic BCLT. In fact, our bounds work even in the presence of misspecification. We compute exact constants in our bounds for a variety of standard models, including logistic regression, and numerically demonstrate their utility. We provide a framework for analysis of more complex models.Comment: Major update to the structure of the paper and discussion of the main result

Measurements of natural radioactivity in historical glasses

Natural radioactive components of historical glasses and two methods of the respective measurement of the radioactivity are discussed. The evaluation of radioactivity of glass objects using a Geiger-Müller counter and high-resolution gamma ray spectrometry is presented. Α survey of the Warsaw National Museum glass collection with a Geiger-Müller counter allowed distinguishing the vessels made of potassium and sodium glass by their level of natural radioactivity. Gamma spectrometry, on the other hand, enables estimating a specific radionuclide content. Special attention is given to uranium glasses. One 19th Century Bohemian vessel, coloured with a uranium compound, was carefully examined using gamma spectrometry. K2O and U content were estimated to be 16.2 and 0.33 %, respectively

A room temperature 19-channel magnetic field mapping device for cardiac signals

We present a multichannel cardiac magnetic field imaging system built in Fribourg from optical double-resonance Cs vapor magnetometers. It consists of 25 individual sensors designed to record magnetic field maps of the beating human heart by simultaneous measurements on a grid of 19 points over the chest. The system is operated as an array of second order gradiometers using sophisticated digitally controlled feedback loops.Comment: 3 pages, 3 figures, submitted to Applied Physics Letter

Coherence dynamics and quantum-to-classical crossover in an exciton-cavity system in the quantum strong coupling regime

Interaction between light and matter generates optical nonlinearities, which are particularly pronounced in the quantum strong coupling regime. When a single bosonic mode couples to a single fermionic mode, a Jaynes-Cummings (JC) ladder is formed, which we realize here using cavity photons and quantum dot excitons. We measure and model the coherent anharmonic response of this strongly coupled exciton-cavity system at resonance. Injecting two photons into the cavity, we demonstrate a root 2 larger polariton splitting with respect to the vacuum Rabi splitting. This is achieved using coherent nonlinear spectroscopy, specifically four-wave mixing, where the coherence between the ground state and the first (second) rung of the JC ladder can be interrogated for positive (negative) delays. With increasing excitation intensity and thus rising average number of injected photons, we observe spectral signatures of the quantum-to-classical crossover of the strong coupling regime.Peer reviewe

Microcavity controlled coupling of excitonic qubits

Controlled non-local energy and coherence transfer enables light harvesting in photosynthesis and non-local logical operations in quantum computing. The most relevant mechanism of coherent coupling of distant qubits is coupling via the electromagnetic field. Here, we demonstrate the controlled coherent coupling of spatially separated excitonic qubits via the photon mode of a solid state microresonator. This is revealed by two-dimensional spectroscopy of the sample's coherent response, a sensitive and selective probe of the coherent coupling. The experimental results are quantitatively described by a rigorous theory of the cavity mediated coupling within a cluster of quantum dots excitons. Having demonstrated this mechanism, it can be used in extended coupling channels - sculptured, for instance, in photonic crystal cavities - to enable a long-range, non-local wiring up of individual emitters in solids