Entanglement generated by dissipation and steady state entanglement of two macroscopic objects

Entanglement is a striking feature of quantum mechanics and an essential ingredient in most applications in quantum information. Typically, coupling of a system to an environment inhibits entanglement, particularly in macroscopic systems. Here we report on an experiment where dissipation continuously generates entanglement between two macroscopic objects. This is achieved by engineering the dissipation using laser and magnetic fields, and leads to robust event-ready entanglement maintained for 0.04 s at room temperature. Our system consists of two ensembles containing about 10(12) atoms and separated by 0.5 m coupled to the environment composed of the vacuum modes of the electromagnetic field. By combining the dissipative mechanism with a continuous measurement, steady state entanglement is continuously generated and observed for up to 1 h.     

220 μJ monolithic single-frequency Q-switched fiber laser at 2 μm by using highly Tm-doped germanate fibers

We report a unique all fiber-based single-frequency Q-switched laser in a monolithic master oscillator power amplifier configuration at ~1920 nm by using highly Tm-doped germanate fibers for the first time. The actively Q-switched fiber laser seed was achieved by using a piezo to press the fiber in the fiber Bragg grating cavity and modulate the fiber birefringence, enabling Q-switching with pulse width and repetition rate tunability. A single-mode polarization maintaining large core 25 μm highly Tm-doped germanate fiber was used in the power amplifier stage. For 80 ns pulses with 20 kHz repetition rate, we achieved 220 μJ pulse energy, which corresponds to a peak power of 2.75 kW with transform-limited linewidth.     

Product approximations for a class of quantum anharmonic oscillators

In this article, we investigate analytically and numerically a class of non-autonomous Schrödinger equations in one space dimension describing the dynamics of quantum anharmonic oscillators driven by time-dependent quartic interactions. We do so within a suitably constructed Faedo–Galerkin scheme by analyzing several product approximations for their solutions, which involve various exponential operator splittings. Our main objective is to study the convergence rates and the accuracy of such approximations, among which there are extensions of the Trotter–Kato product formula and several other variants. Crucial to our analysis is the knowledge of the lowest energy level and of the corresponding eigensolution to the associated time-independent problem, which we also compute within the very same framework.     

The Gorenstein conjecture fails for the tautological ring of \mathcal{\overline{M}}_{2,n}

We prove that for N equal to at least one of the integers 8, 12, 16, 20 the tautological ring $R^{\bullet}(\overline {\mathcal {M}}_{2,N})$ is not Gorenstein. In fact, our N equals the smallest integer such that there is a non-tautological cohomology class of even degree on $\overline {\mathcal {M}}_{2,N}$ . By work of Graber and Pandharipande, such a class exists on $\overline {\mathcal {M}}_{2,20}$ , and we present some evidence indicating that N is in fact 20.     

Quantitative Bestimmung des Schwefels durch Wasserstoffsuperoxyd

Ohne Zusammenfassung     

Relative Volume Comparison with Integral Curvature Bounds

In this paper we shall generalize the Bishop-Gromov relative volume comparison estimate to a situation where one only has an integral bound for the part of the Ricci curvature which lies below a given number. This will yield several compactness and pinching theorems. Submitted: August 1996, revised: July 1997