Development of mirror coatings for gravitational-wave detectors

Gravitational waves are detected by measuring length changes between mirrors in the arms of kilometrelong Michelson interferometers. Brownian thermal noise arising from thermal vibrations of the mirrors can limit the sensitivity to distance changes between the mirrors, and, therefore, the ability to measure gravitational-wave signals. Thermal noise arising from the highly reflective mirror coatings will limit the sensitivity both of current detectors (when they reach design performance) and of planned future detectors. Therefore, the development of coatings with low thermal noise, which at the same time meet strict optical requirements, is of great importance. This article gives an overview of the current status of coatings and of the different approaches for coating improvement. This article is part of a discussion meeting issue ‘The promises of gravitational-wave astronomy’

Optical Absorption Measurements on Crystalline Silicon at 1550nm

Crystalline silicon is currently being discussed as test-mass material for future generations of gravitational wave detectors that will operate at cryogenic temperatures. We present optical absorption measurements on a large-dimension sample of crystalline silicon at a wavelength of 1550nm at room temperature. The absorption was measured in a monolithic cavity setup using the photo-thermal self-phase modulation technique. The result for the absorption coefficient of this float-zone sample with a specific resistivity of 11kOhm cm was measured to be \alpha_A=(264 +/- 39)ppm/cm.Comment: 11 pages, 6 figures, 1 tabl

High index top layer for multimaterial coatings

For application in future cryogenically cooled gravitational wave detectors, the thermal noise of low absorbing mirror coatings has to be reduced. The development of low mechanical and optical loss materials is challenging, but thermal noise reduction can be significantly supported by using a multimaterial coating design. We analyze the possible improvement of the total (optical and mechanical) loss of a three-material based coating obtained by optimizing the properties of the top layer of the coating stack. A top-layer material with sufficiently high refractive index could have a significantly higher optical and mechanical loss than currently used tantala, while still enabling reduction of the total coating loss. Restrictions on possible top-layer material properties are made, and the option of a crystalline top layer is discussed

Reduction of Classical Measurement Noise via Quantum-Dense Metrology

Quantum-dense metrology (QDM) constitutes a special case of quantum metrology in which two orthogonal phase space projections of a signal are simultaneously sensed beyond the shot noise limit. Previously it was shown that the additional sensing channel that is provided by QDM contains information that can be used to identify and to discard corrupted segments from the measurement data. Here, we demonstrate a proof-of-principle experiment in which this information is used for improving the sensitivity without discarding any measurement segments. Our measurement reached sub-shot-noise performance although initially strong classical noise polluted the data

Preconditioned low-rank Riemannian optimization for linear systems with tensor product structure

The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially with the number of dimensions, making the use of classic iterative solvers infeasible. During the last few years, low-rank tensor approaches have been developed that allow to mitigate this curse of dimensionality by exploiting the underlying structure of the linear operator. In this work, we focus on tensors represented in the Tucker and tensor train formats. We propose two preconditioned gradient methods on the corresponding low-rank tensor manifolds: A Riemannian version of the preconditioned Richardson method as well as an approximate Newton scheme based on the Riemannian Hessian. For the latter, considerable attention is given to the efficient solution of the resulting Newton equation. In numerical experiments, we compare the efficiency of our Riemannian algorithms with other established tensor-based approaches such as a truncated preconditioned Richardson method and the alternating linear scheme. The results show that our approximate Riemannian Newton scheme is significantly faster in cases when the application of the linear operator is expensive.Comment: 24 pages, 8 figure

Optical Absorption Measurement at 1550 nm on a Highly-Reflective Si/SiO2_2 Coating Stack

Future laser-interferometric gravitational wave detectors (GWDs) will potentially employ test mass mirrors from crystalline silicon and a laser wavelength of $1550\,\rm{nm}$, which corresponds to a photon energy below the silicon bandgap. Silicon might also be an attractive high-refractive index material for the dielectric mirror coatings. Films of amorphous silicon (a-Si), however, have been found to be significantly more absorptive at $1550\,\rm{nm}$ than crystalline silicon (c-Si). Here, we investigate the optical absorption of a Si/SiO$_2$ dielectric coating produced with the ion plating technique. The ion plating technique is distinct from the standard state-of-the-art ion beam sputtering technique since it uses a higher processing temperature of about 250$^\circ$C, higher particle energies, and generally results in higher refractive indices of the deposited films. Our coating stack was fabricated for a reflectivity of $R=99.95\,\%$ for s-polarized light at $1550\,\rm{nm}$ and for an angle of incidence of 44$^\circ$. We used the photothermal self-phase modulation technique to measure the coating absorption in s-polarization and p-polarization. We obtained $\alpha^{\rm coat}_{s}=(1035 \pm 42)\,\rm{ppm}$ and $\alpha^{\rm coat}_{p}=(1428 \pm 97)\,\rm{ppm}$. These results correspond to an absorption coefficient which is lower than literature values for a-Si which vary from $100\,\rm{/cm}$ up to $2000\,\rm{/cm}$. It is, however, still orders of magnitude higher than expected for c-Si and thus still too high for GWD applications

Mapping the optical absorption of a substrate-transferred crystalline AlGaAs coating at 1.5 µm

The sensitivity of 2nd and 3rd generations of interferometric gravitational wave detectors will be limited by thermal noise of the test-mass mirrors and highly reflective coatings. Recently developed crystalline coatings show a promising thermal noise reduction compared to presently used amorphous coatings. However, stringent requirements apply to the optical properties of the coatings as well. We have mapped the optical absorption of a crystalline AlGaAs coating which is optimized for high reflectivity for a wavelength of 1064nm. The absorption was measured at 1550nm where the coating stack transmits approximately 70% of the laser light. The measured absorption was lower than (30.2 +/- 11.1)ppm which is equivalent to (3.6 +/- 1.3)ppm for a coating stack that is highly reflective at 1530nm. While this is a very promising low absorption result for alternative low--loss coating materials, further work will be necessary to reach the requirements of <1ppm for future gravitational wave detectors. Jessica Steinlechner, Iain W Martin, Angus Bell, Garrett Cole, Jim Hough, Steven Penn, Sheila Rowan, Sebastian Steinlechne

Strong Einstein-Podolsky-Rosen steering with unconditional entangled states

In 1935 Schr\"odinger introduced the terms entanglement and steering in the context of the famous gedanken experiment discussed by Einstein, Podolsky, and Rosen (EPR). Here, we report on a sixfold increase of the observed EPR-steering effect as quantified by the Reid-criterion. We achieved an unprecedented low conditional variance product of about 0.04 < 1, where 1 is the upper bound below which steering is present. The steering effect was observed on an unconditional two-mode-squeezed entangled state that contained a total vacuum state contribution of less than 8%, including detection imperfections. Together with the achieved high interference contrast between the entangled state and a bright coherent laser field, our state is compatible with efficient applications in high-power laser interferometers and fiber-based networks for entanglement distribution.Comment: 5 pages, 3 figure

Effect of stress and temperature on the optical properties of silicon nitride membranes at 1550 nm

Future gravitational-wave detectors operated at cryogenic temperatures are expected to be limited by thermal noise of the highly reflective mirror coatings. Silicon nitride is an interesting material for such coatings as it shows very low mechanical loss, a property related to low thermal noise, which is known to further decrease under stress. Low optical absorption is also required to maintain the low mirror temperature. Here, we investigate the effect of stress on the optical properties at 1,550 nm of silicon nitride membranes attached to a silicon frame. Our approach includes the measurement of the thermal expansion coefficient and the thermal conductivity of the membranes. The membrane and frame temperatures are varied, and translated into a change in stress using finite element modeling. The resulting product of the optical absorption and thermo-optic coefficient (dn/dT) is measured using photothermal common-path interferometry