Anti-reflection coated vacuum window for the Primordial Inflation Polarization ExploreR (PIPER) balloon-borne instrument.

Measuring the faint polarization signal of the cosmic microwave background (CMB) not only requires high optical throughput and instrument sensitivity but also control over systematic effects. Polarimetric cameras or receivers used in this setting often employ dielectric vacuum windows, filters, or lenses to appropriately prepare light for detection by cooled sensor arrays. These elements in the optical chain are typically designed to minimize reflective losses and hence improve sensitivity while minimizing potential imaging artifacts such as glint and ghosting. The Primordial Inflation Polarization ExploreR (PIPER) is a balloon-borne instrument designed to measure the polarization of the CMB radiation at the largest angular scales and characterize astrophysical dust foregrounds. PIPER's twin telescopes and detector systems are submerged in an open-aperture liquid helium bucket dewar. A fused-silica window anti-reflection (AR) coated with polytetrafluoroethylene is installed on the vacuum cryostat that houses the cryogenic detector arrays. Light passes from the skyward portions of the telescope to the detector arrays through this window, which utilizes an indium seal to prevent superfluid helium leaks into the vacuum cryostat volume. The AR coating implemented reduces reflections from each interface to <1% compared to ∼10% from an uncoated window surface. The AR coating procedure and room temperature optical measurements of the window are presented. The indium vacuum sealing process is also described in detail, and test results characterizing its integrity to superfluid helium leaks are provided.

The stability of fixed points for a Kuramoto model with Hebbian interactions.

We consider a variation of the Kuramoto model with dynamic coupling, where the coupling strengths are allowed to evolve in response to the phase difference between the oscillators, a model first considered by Ha, Noh, and Park. We demonstrate that the fixed points of this model, as well as their stability, can be completely expressed in terms of the fixed points and stability of the analogous classical Kuramoto problem where the coupling strengths are fixed to a constant (the same for all edges). In particular, for the "all-to-all" network, where the underlying graph is the complete graph, the problem reduces to the problem of understanding the fixed points and stability of the all-to-all Kuramoto model with equal edge weights, a problem that is well understood.