1,408 research outputs found
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 -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 ps. The same structure contains
QDs doped with single Mn ions, as detected in photoluminescence spectra.
Our work therefore paves the way toward investigating and controlling an
exciton coherence coupled, via ,- 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
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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
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