An implementation of Deflate in Coq

The widely-used compression format "Deflate" is defined in RFC 1951 and is based on prefix-free codings and backreferences. There are unclear points about the way these codings are specified, and several sources for confusion in the standard. We tried to fix this problem by giving a rigorous mathematical specification, which we formalized in Coq. We produced a verified implementation in Coq which achieves competitive performance on inputs of several megabytes. In this paper we present the several parts of our implementation: a fully verified implementation of canonical prefix-free codings, which can be used in other compression formats as well, and an elegant formalism for specifying sophisticated formats, which we used to implement both a compression and decompression algorithm in Coq which we formally prove inverse to each other -- the first time this has been achieved to our knowledge. The compatibility to other Deflate implementations can be shown empirically. We furthermore discuss some of the difficulties, specifically regarding memory and runtime requirements, and our approaches to overcome them

Phase Control of Squeezed Vacuum States of Light in Gravitational Wave Detectors

Quantum noise will be the dominant noise source for the advanced laser interferometric gravitational wave detectors currently under construction. Squeezing-enhanced laser interferometers have been recently demonstrated as a viable technique to reduce quantum noise. We propose two new methods of generating an error signal for matching the longitudinal phase of squeezed vacuum states of light to the phase of the laser interferometer output field. Both provide a superior signal to the one used in previous demonstrations of squeezing applied to a gravitational-wave detector. We demonstrate that the new signals are less sensitive to misalignments and higher order modes, and result in an improved stability of the squeezing level. The new signals also offer the potential of reducing the overall rms phase noise and optical losses, each of which would contribute to achieving a higher level of squeezing. The new error signals are a pivotal development towards realizing the goal of 6 dB and more of squeezing in advanced detectors and beyond

High power and ultra-low-noise photodetector for squeezed-light enhanced gravitational wave detectors

Current laser-interferometric gravitational wave detectors employ a self-homodyne readout scheme where a comparatively large light power (5–50 mW) is detected per photosensitive element. For best sensitivity to gravitational waves, signal levels as low as the quantum shot noise have to be measured as accurately as possible. The electronic noise of the detection circuit can produce a relevant limit to this accuracy, in particular when squeezed states of light are used to reduce the quantum noise. We present a new electronic circuit design reducing the electronic noise of the photodetection circuit in the audio band. In the application of this circuit at the gravitational-wave detector GEO 600 the shot-noise to electronic noise ratio was permanently improved by a factor of more than 4 above 1 kHz, while the dynamic range was improved by a factor of 7. The noise equivalent photocurrent of the implemented photodetector and circuit is about 5 µA/ √\ud Hz above 1 kHz with a maximum detectable photocurrent of 20 mA. With the new circuit, the observed squeezing level in GEO 600 increased by 0.2 dB. The new circuit also creates headroom for higher laser power and more squeezing to be observed in the future in GEO 600 and is applicable to other optics experiments

Influence of Optically Quenched Superconductivity on Quasiparticle Relaxation Rates in Bi2Sr2CaCu2O8+delta

We use time- and angle-resolved photoemission to measure quasiparticle relaxation dynamics across a laser-induced superconducting phase transition in Bi2Sr2CaCu2O8+delta. Whereas low-fluence measurements reveal picosecond dynamics, sharp femtosecond dynamics emerge at higher fluence. Analyses of data as a function of energy, momentum, and doping indicate that the closure of the near-nodal gap and disruption of macroscopic coherence are primary mechanisms driving this onset. The results demonstrate the important influence of transient electronic structure on relaxation dynamics, which is relevant for developing an understanding of nonequilibrium phase transitions.Comment: 6 pages, 4 figure

First demonstration of 6 dB quantum noise reduction in a kilometer scale gravitational wave observatory

Photon shot noise, arising from the quantum-mechanical nature of the light, currently limits the sensitivity of all the gravitational wave observatories at frequencies above one kilohertz. We report a successful application of squeezed vacuum states of light at the GEO\,600 observatory and demonstrate for the first time a reduction of quantum noise up to $6.03 \pm 0.02$ dB in a kilometer-scale interferometer. This is equivalent at high frequencies to increasing the laser power circulating in the interferometer by a factor of four. Achieving this milestone, a key goal for the upgrades of the advanced detectors, required a better understanding of the noise sources and losses, and implementation of robust control schemes to mitigate their contributions. In particular, we address the optical losses from beam propagation, phase noise from the squeezing ellipse, and backscattered light from the squeezed light source. The expertise gained from this work carried out at GEO 600 provides insight towards the implementation of 10 dB of squeezing envisioned for third-generation gravitational wave detectors

Bilinear noise subtraction at the GEO 600 observatory

We develop a scheme to subtract off bilinear noise from the gravitational wave strain data and demonstrate it at the GEO 600 observatory. Modulations caused by test mass misalignments on longitudinal control signals are observed to have a broadband effect on the mid-frequency detector sensitivity ranging from 50 Hz to 500 Hz. We estimate this bilinear coupling by making use of narrow-band signal injections that are already in place for noise projection purposes. A coherent bilinear signal is constructed by a two-stage system identification process where the involved couplings are approximated in terms of stable rational functions. The time-domain filtering efficiency is observed to depend upon the system identification process especially when the involved transfer functions cover a large dynamic range and have multiple resonant features. We improve upon the existing filter design techniques by employing a Bayesian adaptive directed search strategy that optimizes across the several key parameters that affect the accuracy of the estimated model. The resulting post-offline subtraction leads to a suppression of modulation side-bands around the calibration lines along with a broadband reduction of the mid-frequency noise floor. The filter coefficients are updated periodically to account for any non-stationarities that can arise within the coupling. The observed increase in the astrophysical range and a reduction in the occurrence of non-astrophysical transients suggest that the above method is a viable data cleaning technique for current and future gravitational wave observatories