Trade-off between quantum and thermal fluctuations in mirror coatings yields improved sensitivity of gravitational-wave interferometers

We propose a simple way to improve the laser gravitational-wave detectors sensitivity by means of reduction of the number of reflective coating layers of the core optics mirrors. This effects in the proportional decrease of the coating thermal noise, the most notorious among the interferometers technical noise sources. The price for this is the increased quantum noise, as well as high requirements for the pump laser power and power at the beamsplitter. However, as far as these processes depend differently on the coating thickness, we demonstrate that a certain trade-off is possible, yielding a 20-30% gain (for diverse gravitational wave signal types and interferometer configurations), providing that feasible values of laser power and power on the beamsplitter are assumed.Comment: 11 pages, 4 figures, 4 table

Quantum noise of non-ideal Sagnac speed meter interferometer with asymmetries

The speed meter concept has been identified as a technique that can potentially provide laser-interferometric measurements at a sensitivity level which surpasses the Standard Quantum Limit (SQL) over a broad frequency range. As with other sub-SQL measurement techniques, losses play a central role in speed meter interferometers and they ultimately determine the quantum noise limited sensitivity that can be achieved. So far in the literature, the quantum noise limited sensitivity has only been derived for lossless or lossy cases using certain approximations (for instance that the arm cavity round trip loss is small compared to the arm cavity mirror transmission). In this article we present a generalised, analytical treatment of losses in speed meters that allows accurate calculation of the quantum noise limited sensitivity of Sagnac speed meters with arm cavities. In addition, our analysis allows us to take into account potential imperfections in the interferometer such as an asymmetric beam splitter or differences of the reflectivities of the two arm cavity input mirrors. Finally,we use the examples of the proof-of-concept Sagnac speed meter currently under construction in Glasgow and a potential implementation of a Sagnac speed meter in the Einstein Telescope (ET) to illustrate how our findings affect Sagnac speed meters with meter- and kilometre-long baselines.Comment: 22 pages, 8 figures, 1 table, (minor corrections and changes made to text and figures in version 2

To the practical design of the optical lever intracavity topology of gravitational-wave detectors

The QND intracavity topologies of gravitational-wave detectors proposed several years ago allow, in principle, to obtain sensitivity significantly better than the Standard Quantum Limit using relatively small anount of optical pumping power. In this article we consider an improved more ``practical'' version of the optical lever intracavity scheme. It differs from the original version by the symmetry which allows to suppress influence of the input light amplitude fluctuation. In addition, it provides the means to inject optical pumping inside the scheme without increase of optical losses. We consider also sensitivity limitations imposed by the local meter which is the key element of the intracavity topologies. Two variants of the local meter are analyzed, which are based on the spectral variation measurement and on the Discrete Sampling Variation Measurement, correspondingly. The former one, while can not be considered as a candidate for a practical implementation, allows, in principle, to obtain the best sensitivity and thus can be considered as an ideal ``asymptotic case'' for all other schemes. The DSVM-based local meter can be considered as a realistic scheme but its sensitivity, unfortunately, is by far not so good just due to a couple of peculiar numeric factors specific for this scheme. From our point of view search of new methods of mechanical QND measurements probably based on improved DSVM scheme or which combine the local meter with the pondermotive squeezing technique, is necessary.Comment: 27 pages, 6 figure

Design of a speed meter interferometer proof-of-principle experiment

The second generation of large scale interferometric gravitational wave detectors will be limited by quantum noise over a wide frequency range in their detection band. Further sensitivity improvements for future upgrades or new detectors beyond the second generation motivate the development of measurement schemes to mitigate the impact of quantum noise in these instruments. Two strands of development are being pursued to reach this goal, focusing both on modifications of the well-established Michelson detector configuration and development of different detector topologies. In this paper, we present the design of the world's first Sagnac speed meter interferometer which is currently being constructed at the University of Glasgow. With this proof-of-principle experiment we aim to demonstrate the theoretically predicted lower quantum noise in a Sagnac interferometer compared to an equivalent Michelson interferometer, to qualify Sagnac speed meters for further research towards an implementation in a future generation large scale gravitational wave detector, such as the planned Einstein Telescope observatory.Comment: Revised version: 16 pages, 6 figure

Optimizing the regimes of Advanced LIGO gravitational wave detector for multiple source types

We develop here algorithms which allow to find regimes of signal-recycled Fabry-Perot--Michelson interferometer (for example, Advanced LIGO), optimized concurrently for two (binary inspirals + bursts) and three (binary inspirals + bursts + millisecond pulsars) types of gravitational waves sources. We show that there exists a relatevely large area in the interferometer parameters space where the detector sensitivity to the first two kinds of sources differs only by a few percent from the maximal ones for each kind of source. In particular, there exists a specific regime where this difference is ~0.5 for both of them. Furthermore we show that even more multipurpose regimes are also possible, that provide significant sensitivity gain for millisecond pulsars with only minor sensitivity degradation for binary inspirals and bursts.Comment: 10 pages, 14 figures, 3 tables. Minor corrections in main text are done in version 2 and two plots and one table are added for the sake of clarity of the obtained result

QND measurements for future gravitational-wave detectors

Second-generation interferometric gravitational-wave detectors will be operating at the Standard Quantum Limit, a sensitivity limitation set by the trade off between measurement accuracy and quantum back action, which is governed by the Heisenberg Uncertainty Principle. We review several schemes that allows the quantum noise of interferometers to surpass the Standard Quantum Limit significantly over a broad frequency band. Such schemes may be an important component of the design of third-generation detectors.Comment: 22 pages, 6 figures, 1 table; In version 2, more tutorial information on quantum noise in GW interferometer and several new items into Reference list were adde

Laser interferometry with translucent and absorbing mechanical oscillators

The sensitivity of laser interferometers can be pushed into regimes that enable the direct observation of quantum behaviour of mechanical oscillators. In the past, membranes with subwavelength thickness (thin films) have been proposed as high-mechanical-quality, low-thermal-noise oscillators. Thin films from a homogenous material, however, generally show considerable light transmission accompanied by heating due to light absorption, which typically reduces the mechanical quality and limits quantum opto-mechanical experiments in particular at low temperatures. In this work, we experimentally analyze a Michelson-Sagnac interferometer including a translucent silicon nitride (SiN) membrane with subwavelength thickness. We find that such an interferometer provides an operational point being optimally suited for quantum opto-mechanical experiments with translucent oscillators. In case of a balanced beam splitter of the interferometer, the membrane can be placed at a node of the electro-magnetic field, which simultaneously provides lowest absorption and optimum laser noise rejection at the signal port. We compare the optical and mechanical model of our interferometer with experimental data and confirm that the SiN membrane can be coupled to a laser power of the order of one Watt at 1064 nm without significantly degrading the membrane's quality factor of the order 10^6, at room temperature

Local-Oscillator Noise Coupling in Balanced Homodyne Readout for Advanced Gravitational Wave Detectors

The second generation of interferometric gravitational wave detectors are quickly approaching their design sensitivity. For the first time these detectors will become limited by quantum back-action noise. Several back-action evasion techniques have been proposed to further increase the detector sensitivity. Since most proposals rely on a flexible readout of the full amplitude- and phase-quadrature space of the output light field, balanced homodyne detection is generally expected to replace the currently used DC readout. Up to now, little investigation has been undertaken into how balanced homodyne detection can be successfully transferred from its ubiquitous application in table-top quantum optics experiments to large-scale interferometers with suspended optics. Here we derive implementation requirements with respect to local oscillator noise couplings and highlight potential issues with the example of the Glasgow Sagnac Speed Meter experiment, as well as for a future upgrade to the Advanced LIGO detectors.Comment: 7 pages, 5 figure

Effects of static and dynamic higher-order optical modes in balanced homodyne readout for future gravitational waves detectors

With the recent detection of Gravitational waves (GW), marking the start of the new field of GW astronomy, the push for building more sensitive laser-interferometric gravitational wave detectors (GWD) has never been stronger. Balanced homodyne detection (BHD) allows for a quantum noise (QN) limited readout of arbitrary light field quadratures, and has therefore been suggested as a vital building block for upgrades to Advanced LIGO and third generation observatories. In terms of the practical implementation of BHD, we develop a full framework for analyzing the static optical high order modes (HOMs) occurring in the BHD paths related to the misalignment or mode matching at the input and output ports of the laser interferometer. We find the effects of HOMs on the quantum noise limited sensitivity is independent of the actual interferometer configuration, e.g. Michelson and Sagnac interferometers are effected in the same way. We show that misalignment of the output ports of the interferometer (output misalignment) only effects the high frequency part of the quantum noise limited sensitivity (detection noise). However, at low frequencies, HOMs reduce the interferometer response and the radiation pressure noise (back action noise) by the same amount and hence the quantum noise limited sensitivity is not negatively effected in that frequency range. We show that the misalignment of laser into the interferometer (input misalignment) produces the same effect as output misalignment and additionally decreases the power inside the interferometer. We also analyze dynamic HOM effects, such as beam jitter created by the suspended mirrors of the BHD. Our analyses can be directly applied to any BHD implementation in a future GWD. Moreover, we apply our analytical techniques to the example of the speed meter proof of concept experiment under construction in Glasgow. We find that for our experimental parameters, the performance of our seismic isolation system in the BHD paths is compatible with the design sensitivity of the experiment

Demonstration of a switchable damping system to allow low-noise operation of high-Q low-mass suspension systems

Low mass suspension systems with high-Q pendulum stages are used to enable quantum radiation pressure noise limited experiments. Utilising multiple pendulum stages with vertical blade springs and materials with high quality factors provides attenuation of seismic and thermal noise, however damping of these high-Q pendulum systems in multiple degrees of freedom is essential for practical implementation. Viscous damping such as eddy-current damping can be employed but introduces displacement noise from force noise due to thermal fluctuations in the damping system. In this paper we demonstrate a passive damping system with adjustable damping strength as a solution for this problem that can be used for low mass suspension systems without adding additional displacement noise in science mode. We show a reduction of the damping factor by a factor of 8 on a test suspension and provide a general optimisation for this system.Comment: 5 pages, 5 figure