Delayed-choice quantum eraser for the undergraduate laboratory

In a delayed-choice quantum eraser, interference fringes are obtained by erasing which-way information after the interfering particle has already been irreversibly detected. Following an introductory review of delayed-choice experiments and quantum erasure, we describe the experimental realization of an optical delayed-choice quantum eraser, suitable for advanced undergraduates, based on polarization-entangled pairs of single photons. In our experiment, the delay of the erasure is implemented using two different setups. The first setup employs an arrangement of mirrors to increase the optical path length of the photons carrying which-way information. In the second setup, we use fiber-optic cables to elongate the path of these photons after their passage through the polarization analyzer but prior to their arrival at the detector. We compare our results to data obtained in the absence of a delay and find excellent agreement. This shows that the timing of the erasure is irrelevant, as also predicted by quantum mechanics. The experiment can serve as a valuable pedagogical tool for conveying the fundamentals of quantum mechanics.Comment: 13 pages, 5 figures, identical to published versio

Observation of the quantum paradox of separation of a single photon from one of its properties

We report an experimental realization of the quantum paradox of the separation of a single photon from one of its properties (the so-called "quantum Cheshire cat"). We use a modified Sagnac interferometer with displaced paths to produce appropriately pre- and postselected states of heralded single photons. Weak measurements of photon presence and circular polarization are performed in each arm of the interferometer by introducing weak absorbers and small polarization rotations and analyzing changes in the postselected signal. The absorber is found to have an appreciable effect only in one arm of the interferometer, while the polarization rotation significantly affects the signal only when performed in the other arm. We carry out both sequential and simultaneous weak measurements and find good agreement between measured and predicted weak values. In the language of Aharonov et al. and in the sense of the ensemble averages described by weak values, the experiment establishes the separation of a particle from one its properties during the passage through the interferometer.Comment: 9 pages, 4 figures, identical to published versio

Measurement and Prediction of Oxygen Transfer in Activated Sludge based on Ex Situ Off-gas Monitoring

This dissertation examines oxygen transfer dynamics of activated sludge aeration systems in wastewater treatment plants (WWTP). The method of ex situ off-gas testing and its measurement uncertainty when determining the α-factor were studied. The variation of the α-factor was measured in conventional activated sludge (CAS) and two-stage systems with pilot-scale long-term ex situ off-gas testing. A data-driven approach to predict oxygen transfer based on supervised machine learning is presented. The key results of this cumulative dissertation and its three papers (P1-P3) are as follows: - ASCE 18-18 describes the ex situ off-gas method as an alternative to in situ off-gas testing with off-gas hoods on the activated sludge surface. P1 showed that results from ex situ and in situ tests cannot be compared because sludge inflow into an ex situ bubble column systematically increased the α-factor. Still, ex situ off-gas testing offers unique advantages for piloting and research of oxygen transfer because operation of an external bubble column is more flexible than in situ off-gas testing. - By comparing ex situ off-gas measurements under the same conditions, P1 demonstrated that α-factors can be quantified at a relative standard deviation of about ± 2.8 %. This is significantly more accurate than previously reported uncertainties between ± 5 to 15 %. A sensitivity analysis in P1 revealed that recording the oxygen concentration in the off-gas was the most important parameter to conduct reliable oxygen transfer tests, exceeding the relevance of dissolved oxygen (DO) and airflow rate measurement by far. - α-factors are generally higher in the second stage of a two-stage WWTP because oxygen transfer inhibiting substances, e.g., surfactants and TOC, are partially removed in the first stage. In P2, α-factors for design load cases were determined as 0.45 for αmean and 0.33/0.54 for αmin/αmax in the first stage (HRAS), and as 0.80 for αmean and 0.69/0.91 for αmin/αmax in the second stage. α-factors in situ would be lower because these values were recorded with ex situ off-gas tests. - The α0-factor was introduced in P3 to compare oxygen transfer in activated sludge from aerated and non-aerated zones. It considers differences of in situ and ex situ DO under non-steady state DO conditions. An increase of the α0-factor along an upstream anoxic tank of a CAS process was observed, thus suggesting biosorption and/or biodegradation of oxygen transfer inhibiting substances. - The α0-factor was predicted by Random Forest models for different activated sludge stages within an RMSE (root-mean-square error) of 0.024 and 0.033 (R2 between 0.84 and 0.92). Models were trained with 17 predictor variables based on WWTP operating data. The data-driven approach can consider potential interactions of influences on oxygen transfer, but the final models are typically unable to generalize for conditions not included in training data

Ergebnisse der Albanien-Expedition 1961 des Deutschen Entomologischen Institutes. 68. Beitrag. Hymenoptera: Apidae III (Genus Nomada Scopoli).

Der vorliegende Beitrag behandelt die Nomada-Ausbeute (Apoidea) der Albanien-Expedition des Deutschen Entomologischen Instituts. Es lagen 29 Exemplare in 12 Arten vor, von denen eine Art für die Wissenschaft neu ist: Nomada lucidula spec. nov., zugleich auch aus Griechenland, der Türkei und Israel bekannt geworden. Von Nomada pastoralis Eversmann wird das noch unbekannte Männchen beschrieben. Die spärlichen Literaturangaben über die Nomada-Fauna Albaniens wurden nicht berücksichtigt, da diese nur nach überprüfung der Belegexemplare verwertbar wären; deshalb sind praktisch alle 12 festgestellten Arten als erste sichere Nachweise für die Fauna Albaniens anzusehen.Nomenklatorische Handlungenlucidula Schwarz, 1967 (Nomada), spec. n.The present paper is concerned with the Nomada (Apoidea) collected by the expedition to Albania by Deutsches Entomologisches Institut. It covers 29 specimens of 12 species, one species being new: Nomada lucidula spec. nov., which is also known from Greece, Turkey and Israel. The hitherto unknown male of Nomada pastoralis Eversmann is described. The infrequent references to the Nomada of Albania made in previous publications were ignored, as those data might be evaluated only if the respective specimens were examined. Nomenclatural Actslucidula Schwarz, 1967 (Nomada), spec. n

Delayed-choice quantum eraser for the undergraduate laboratory

In a delayed-choice quantum eraser, interference fringes are obtained by erasing which-way information after the interfering particle has already been irreversibly detected. Following an introductory review of delayed-choice experiments and quantum erasure, we describe the experimental realization of an optical delayed-choice quantum eraser, suitable for advanced undergraduates, based on polarization-entangled pairs of single photons. In our experiment, the delay of the erasure is implemented using two different setups. The first setup employs an arrangement of mirrors to increase the optical path length of the photons carrying which-way information. In the second setup, we use fiber-optic cables to elongate the path of these photons after their passage through the polarization analyzer but prior to their arrival at the detector. We compare our results to data obtained in the absence of a delay and find excellent agreement. This shows that the timing of the erasure is irrelevant, as also predicted by quantum mechanics. The experiment can serve as a valuable pedagogical tool for conveying the fundamentals of quantum mechanics

Observation of the quantum paradox of separation of a single photon from one of its properties

We report an experimental realization of the quantum paradox of the separation of a single photon from one of its properties (the so-called quantum Cheshire cat ). We use a modified Sagnac interferometer with displaced paths to produce appropriately pre- and postselected states of heralded single photons. Weak measurements of photon presence and circular polarization are performed in each arm of the interferometer by introducing weak absorbers and small polarization rotations and analyzing changes in the postselected signal. The absorber is found to have an appreciable effect only in one arm of the interferometer, while the polarization rotation significantly affects the signal only when performed in the other arm. We carry out both sequential and simultaneous weak measurements and find good agreement between measured and predicted weak values. In the language of Aharonov et al. and in the sense of the ensemble averages described by weak values, the experiment establishes the separation of a particle from one its properties during the passage through the interferometer

Indirekte modellprädiktive Regelung von Windenergieanlagen sowie deren energie-optimale und deren schädigungsarme Konfiguration

Die vorliegende Arbeit beschäftigt sich mit der Anwendung der indirekten Methoden zur automatisierten Lösung von einer bestimmten Klasse von Optimalen Steuerungsproblemen im Rahmen einer modellprädiktiven Regelung für Windenergieanlagen. In einem zweiten Teil wird der Einfluss dieser Regelungsmethode auf die Festigkeit des Triebstranges untersucht. Diese führt zu einer überproportionalen Beanspruchung und damit zu einer Reduktion der Betriebsfestigkeit. Es gilt entsprechende Randbedingungen für die der Regelung zugrunde liegenden Optimalen Steuerungsprobleme zu finden, so dass weiterhin die Energieausbeute maximiert werden kann, gleichzeitig jedoch die Beanspruchung durch die Regelung begrenzt wird