This paper reproves a general form of the Green-Lazarsfeld 'generic vanishing' theorem and more recent strengthenings, as well as giving some new applications.

Herbert Clemens Christopher Hacon

Let $X$ be a normal complex space such that the tangent sheaf $T_X$ is locally free and locally admits a basis consisting of pairwise commuting vector fields. Then $X$ is smooth.

Clemens Jörder

We obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

Jakub Konieczny Mariusz Lemańczyk Clemens Müllner

We show that a set of non-negative reals is the distance set of a separable complete metric space if and only if it is either countable or is an analytic set which has 0 as a limit point. We also consider spaces with simpler distance sets.

John D. Clemens

M\"ossbauer nuclei feature exceptionally narrow resonances at hard x-ray energies, which render them ideal probes for structure and dynamics in condensed-matter systems, and a promising platform for x-ray quantum optics and fundamental tests. However, a direct spectroscopy at modern x-ray sources such as synchrotrons or x-ray free electron lasers is challenging, because of the broad spectral bandwidth of the delivered x-ray pulses, and because of a limited spectral resolution offered by x-ray optics and detectors. To overcome these challenges, here, we propose a spectroscopy technique based on a spectrally narrow reference absorber that is rapidly oscillating along the propagation direction of the x-ray light. The motion induces sidebands to the response of the absorber, which we scan across the spectrum of the unknown target to gain spectral information. The oscillation further introduces a dependence of the detected light on the motional phase at the time of x-ray excitation as an additional controllable degree of freedom. We show how a Fourier analysis with respect to this phase enables one to selectively extract parts of the recorded intensity after the actual experiment, throughout the data analysis. This allows one to improve the spectral recovery by removing unwanted signal contributions. Our method is capable of gaining spectral information from the entire measured intensity, and not only from the intensity at late times after the excitation, such that a significantly higher part of the signal photons can be used. Furthermore, it not only enables one to measure the amplitude of the spectral response, but also its phase.

Benedikt Herkommer Jörg Evers

Future quantum technology relies crucially on building quantum networks with high fidelity. To achieve this challenging goal, it is of utmost importance to connect single quantum systems in a way such that their emitted single-photons overlap with the highest possible degree of coherence. This requires perfect mode overlap of the emitted light of different emitters, which necessitates the use of single mode fibers. Here we present an advanced manufacturing approach to accomplish this task: we combine 3D printed complex micro-optics such as hemispherical and Weierstrass solid immersion lenses as well as total internal reflection solid immersion lenses on top of single InAs quantum dots with 3D printed optics on single mode fibers and compare their key features. Interestingly, the use of hemispherical solid immersion lenses further increases the localization accuracy of the emitters to below 1 nm when acquiring micro-photoluminescence maps. The system can be joined together and permanently fixed. This integrated system can be cooled by dipping into liquid helium, by a Stirling cryocooler or by a closed-cycle helium cryostat without the necessity for optical windows, as all access is through the integrated single mode fiber. We identify the ideal optical designs and present experiments that prove excellent high-rate single-photon emission by high-contrast Hanbury Brown and Twiss experiments.

Marc Sartison Ksenia Weber Simon Thiele Lucas Bremer Sarah Fischbach Thomas Herzog Sascha Kolatschek Stephan Reitzenstein Alois Herkommer Peter Michler Simone Luca Portalupi Harald Giessen

Deterministic sources of quantum light are becoming increasingly relevant in the development of quantum communication, particularly in deployed fiber networks. Therefore, efficient fiber-coupled sources at telecom wavelength are highly sought after. With this goal in mind, we systematically investigate the fiber coupling performance of quantum dots in optical resonators under three experimental configurations. We quantify coupling efficiency and sensitivity to spatial displacement for single-mode fibers with 3D printed optics on their tip, and benchmark their behavior over a commercial cleaved-cut fiber and a standard optical setup. The reduction of the required optical elements when operating with a lensed or a bare fiber allows for an increased end-to-end efficiency by a factor of up to 3.0 +/- 0.2 over a standard setup. For the perspective of realizing a mechanically stable fiber-coupled source, we precisely quantify the spatial tolerance to fiber-cavity misalignment, observing less than 50 % count rate drop for several micrometers displacement. These results will play a key role in the future development of fiber-coupled sources of quantum light.

Nam Tran Pavel Ruchka Sara Jakovljevic Benjamin Breiholz Peter Gierß Ponraj Vijayan Carlos Eduardo Jimenez Alois Herkommer Michael Jetter Simone Luca Portalupi Harald Giessen Peter Michler

This is the part II of our series of two papers, "Clemens' conjecture: part I", "Clemens' conjecture: part II". Continuing from part I, in this paper we turn our attention to general quintic threefolds. In a universal quintic threefold X, we construct a family of quasi-regular deformation B_b such that the generic member in this family is non-deviated, but some special member is deviated. By the result from part I, this is impossible unless there is no one parameter family of smooth rational curves in a generic quintic threefold.

Bin Wang

Proving statements about linear operators expressed in terms of identities often leads to finding elements of certain form in noncommutative polynomial ideals. We illustrate this by examples coming from actual operator statements and discuss relevant algorithmic methods for finding such polynomials based on noncommutative Gr\"obner bases. In particular, we present algorithms for computing the intersection of a two-sided ideal with a one-sided ideal as well as for computing homogeneous polynomials in two-sided ideals and monomials in one-sided ideals. All methods presented in this work are implemented in the Mathematica package OperatorGB.

Clemens Hofstadler Clemens G. Raab Georg Regensburger

We report on pair interaction measurements in charged colloidal systems in confined and unconfined geometries by means of optical microscopy. At very small particle distances we observe minute distortions in the optical images which can lead to artifacts in the pair potentials as derived by digital video microscopy. In particular, these distortions can pretend long-range attractions observed in charged colloidal suspensions.

Joerg Baumgartl Jose Luis Arauz-Lara Clemens Bechinger