Arm Cavities Research Articles

Ultralight vector dark matter search with auxiliary length channels of gravitational wave detectors

Recently, a considerable amount of attention has been given to the search for ultralight dark matter by measuring the oscillating length changes in the arm cavities of gravitational wave detectors. Although gravitational wave detectors are extremely sensitive for measuring the differential arm length changes, the sensitivity to dark matter is largely attenuated, as the effect of dark matter is mostly common to arm cavity test masses. Here, we propose to use auxiliary length channels, which measure the changes in the power and signal recycling cavity lengths and the differential Michelson interferometer length. The sensitivity to dark matter can be enhanced by exploiting the fact that auxiliary interferometers are more asymmetric than two arm cavities. We show that the sensitivity to $U(1)_{B-L}$ gauge boson dark matter with masses below $7\times 10^{-14}$ eV can be greatly enhanced when our method is applied to a cryogenic gravitational wave detector KAGRA, which employs sapphire test masses and fused silica auxiliary mirrors. We show that KAGRA can probe more than an order of magnitude of unexplored parameter space at masses around $1.5 \times 10^{-14}$ eV, without any modifications to the existing interferometer.

Low phase noise squeezed vacuum for future generation gravitational wave detectors

Squeezed light has become a standard technique to enhance the sensitivity of gravitational wave detectors. Both optical losses and phase noise in the squeezed path can degrade the achievable improvements. Phase noise can be mitigated by having a high bandwidth servo to stabilize the squeezer phase to the light from the interferometer. In advanced LIGO, this control loop bandwidth is limited by the 4 km arm cavity free spectral range to about ∼15 kHz. Future generation gravitational-wave detectors are designed to employ much longer arm cavities. For cosmic explorer [], a 40 km arm length will limit the bandwidth to ∼1.5 kHz. We propose an alternative controls scheme that will increase the overall phase noise suppression by using the in-vacuum filter cavity as a reference for stabilizing the laser frequency of the squeezed light source. This will allow for rms phase noise of less than a milliradian—a negligible level for all future generations of gravitational-wave detectors [].

Auxiliary lasers for Advanced Virgo Gravitational Wave detector using single pass Second Harmonic Generation in Periodically Poled Lithium Niobate crystal

The Advanced Virgo (AdV) detector is composed of different degrees of freedom (DOFs) i.e. Michelson interferometer, two Fabry-Perot arm cavities, signal recycling cavity, and power recycling cavity. These DOFs need to be locked to precise accuracy with robust, fast and reliable control systems. The control signals used to lock all the DOFs are mildly decoupled in frequency and the optical response of the DOFs are nonlinear, where the linear range of operation is just some percentage of the fringe for each DOF, thus posing difficulty in resonance lock at input laser wavelength for all the cavities. In particular, the control status of the arm cavities can alter the state of the detector’s operational configuration. Using Auxiliary Lasers to lock the arm cavities at different wavelength offers flexible and robust lock of the detector and more spatial margin on the control signals. Second harmonic generation offers the most direct way to have laser beam with different wavelength and phase locked to the AdV input laser beam. We generated upto 97 mW of SH beam in single configuration at 532 nm using fibered amplified laser source at 1064 nm in a 10 mm long Poled Lithium Niobate crystal.

Newtonian-noise reassessment for the Virgo gravitational-wave observatory including local recess structures

The LIGO and Virgo Scientific Collaborations have cataloged ten confident detections from binary black holes and one from binary neutron stars in their first two observing runs, which has already brought up an immense desire among the scientists to study the Universe and to extend the knowledge of astrophysics from these compact objects. One of the fundamental noise sources limiting the achievable detector bandwidth is given by Newtonian noise arising from terrestrial gravity fluctuations. It is important to model Newtonian noise spectra very accurately as it cannot be monitored directly using current technology. In this article, we show the reduction in the Newtonian noise curve obtained by more accurately modelling the current configuration of the Virgo observatory. In Virgo, there are clean rooms or recess like structures underneath each test mirror forming the main two Fabry–Perot arm cavities of the detector. We compute the displacements originating from an isotropic Rayleigh field including the recess structure. We find an overall strain noise reduction factor of 2 in the frequency band from 12 to about 15 Hz relative to previous models. The reduction factor depends on frequency and also varies between individual test masses.

Designing arm cavities free of parametric instability for gravitational wave detectors

Parametric instability is an intrinsic problem in high power laser interferometer gravitational wave detectors. Optical cavity modes interact with acoustic modes of the test masses, leading to laser power dependent exponential growth of acoustic vibration of the test masses. Future detectors are being planned with designed optical power as high as 5 MW. This increases the requirements for suppressing of parametric instability through various currently available methods. Parametric instabilities could also be alleviated through careful design of the acoustic mode structure and optical mode spacing. Here we study parametric instabilities in future gravitational wave detectors with arm lengths between 6 and 10 km. We show that by careful choice of test mass radii of curvature, dimensions and arm lengths it is possible to design detectors that are free of parametric instability up to 3 MW of intra-cavity power with large enough tolerance on mirror radii of curvature change. We present several case studies and give an example of a design with 6335 m arm cavities and test mass diameter of 52 cm that is parametric instability free. This design is relatively tolerant, staying free of instabilities for a 45 m change in test mass radius of curvature. Maintaining this radius of curvature could easily be done with good design and thermal compensation.

An arm length stabilization system for KAGRA and future gravitational-wave detectors

Modern ground-based gravitational wave (GW) detectors require a complex interferometer configuration with multiple coupled optical cavities. Since achieving the resonances of the arm cavities is the most challenging among the lock acquisition processes, the scheme called arm length stabilization (ALS) had been employed for lock acquisition of the arm cavities. We designed a new type of the ALS, which is compatible with the interferometers having long arms like the next generation GW detectors. The features of the new ALS are that the control configuration is simpler than those of previous ones and that it is not necessary to lay optical fibers for the ALS along the kilometer-long arms of the detector. Along with simulations of its noise performance, an experimental test of the new ALS was performed utilizing a single arm cavity of KAGRA. This paper presents the first results of the test where we demonstrated that lock acquisition of the arm cavity was achieved using the new ALS. We also demonstrated that the root mean square of residual noise was measured to be 8.2 Hz in units of frequency, which is smaller than the linewidth of the arm cavity and thus low enough to lock the full interferometer of KAGRA in a repeatable and reliable manner.

New algorithm for the Guided Lock technique for a high-Finesse optical cavity

A known criticality of optical cavities such as Fabry–Pérot resonant cavities is the presence of non-linear effects in the build-up of the laser fields inside the cavity itself, which can spoil the characteristics of the error signal used to control the cavity length, usually obtained with the Pound–Drever–Hall phase modulation–demodulation technique. The non-linear effects are primarily caused by high cavity speeds prior to acquiring longitudinal control of the cavity (or “lock”), and they are due to the frequency fluctuations of the laser and to the residual seismic motion affecting the system; such effects are amplified with the increasing of the Finesse of the cavity. In order to overcome this limitation, the cavity speed is effectively slowed down before engaging the lock using a non-linear technique, known as “Guided Lock”; here an optimized version of the algorithm will be presented, which relies on a better estimation of the cavity speed based only on optical signals. The application of this technique to the high-Finesse Fabry–Pérot arm cavities of the Advanced Virgo gravitational wave detector will be described. The novel algorithm was applied for the lock acquisition of the Advanced Virgo detector during the O2 Observing Run, in August 2017; the improved algorithm, by dynamically measuring the cavity speed, allowed to implement a predictive capability in slowing down the mirrors, thus improving the efficiency of the lock acquisition procedure for the arm cavities.

Numerical Investigation of Façade and Floor Glazing Systems

The use of point-supported systems in glass façades and floors has become widespread due to their excellent structural properties. The combination of glass and metal, frequently found in modern architectural norms and expressions, has highlighted the role of such systems and the need for constant optimization of their design. This research paper aims to examine the influence of modifying several geometrical parameters such as the thickness and the weight of the structural spider connectors, the arm-core ratio of the spider, the thickness of the glass panel and the spider arm cavities on the structural performance of a spider connector produced by one of the market-leading manufacturers. Therefore, a parametric finite element analysis is performed, where four alternative versions of the spider are constructed, in addition to the reference version, using ANSYS software program. The numerical model of the reference spider is verified against experimental data from the manufacturer of the structural spider connector. A total number of twelve case studies that consist of different combinations of spiders and glass’ thickness are examined, five for the façade and seven for the floor glazing system. The focus of the numerical investigation is placed on the spider itself and the results of the parametric finite element analysis are presented and discussed. The effectiveness of having core cavities and hollowed-out arms in spiders is proven. The use of stronger but heavier spiders is an acceptable alternative if they are connected to larger glass panels that results in reducing the number of spiders without increasing significantly the total weight of the glazing system.

Converting the signal-recycling cavity into an unstable optomechanical filter to enhance the detection bandwidth of gravitational-wave detectors

Current and future interferometeric gravitational-wave detectors are limited predominantly by shot noise at high frequencies. Shot noise is reduced by introducing arm cavities and signal recycling, however, there exists a tradeoff between the peak sensitivity and bandwidth. This comes from the accumulated phase of signal sidebands when propagating inside the arm cavities. One idea is to cancel such a phase by introducing an unstable optomechanical filter. The original design proposed in [Phys.~Rev.~Lett.~{\bf 115},~211104 (2015)] requires an additional optomechanical filter coupled externally to the main interferometer. Here we consider a simplified design that converts the signal-recycling cavity itself into the unstable filter by using one mirror as a high-frequency mechanical oscillator and introducing an additional pump laser. However, the enhancement in bandwidth of this new design is less than the original design given the same set of optical parameters. The peak sensitivity improvement factor depends on the arm length, the signal-recycling cavity length, and the final detector bandwidth. For a 4~km interferometer, if the final detector bandwidth is around 2~kHz, with a 20~m signal-recycling cavity, the shot noise can be reduced by 10 decibels, in addition to the improvement introduced by squeezed light injection. We also find that the thermal noise of the mechanical oscillator is enhanced at low frequencies relative to the vacuum noise, while having a flat spectrum at high frequencies.

Numerical Investigation of Façade and Floor Glazing Systems

The use of point-supported systems in glass façades and floors has become widespread due to their excellent structural properties. The combination of glass and metal, frequently found in modern architectural norms and expressions, has highlighted the role of such systems and the need for constant optimization of their design. This research paper aims to examine the influence of modifying several geometrical parameters such as the thickness and the weight of the structural spider connectors, the arm-core ratio of the spider, the thickness of the glass panel and the spider arm cavities on the structural performance of a spider connector produced by one of the market-leading manufacturers. Therefore, a parametric finite element analysis is performed, where four alternative versions of the spider are constructed, in addition to the reference version, using ANSYS software program. The numerical model of the reference spider is verified against experimental data from the manufacturer of the structural spider connector. A total number of twelve case studies that consist of different combinations of spiders and glass’ thickness are examined, five for the façade and seven for the floor glazing system. The focus of the numerical investigation is placed on the spider itself and the results of the parametric finite element analysis are presented and discussed. The effectiveness of having core cavities and hollowed-out arms in spiders is proven. The use of stronger but heavier spiders is an acceptable alternative if they are connected to larger glass panels that results in reducing the number of spiders without increasing significantly the total weight of the glazing system.

Suppression of thermal transients in advanced LIGO interferometers using CO2 laser preheating

In high optical power interferometric gravitational wave detectors, such as Advanced LIGO, the thermal effects due to optical absorption in the mirror coatings and the slow thermal response of fused silica substrate cause time dependent changes in the mirror profile. After locking, high optical power builds up in the arm cavities. Absorption induced heating causes optical cavity transverse mode frequencies to drift over a period of hours, relative to the fundamental mode. At high optical power this can cause time dependent transient parametric instability, which can lead to interferometer disfunction. In this paper, we model the use of CO2 laser heating designed to enable the interferometer to be maintained in a thermal condition such that transient changes in the mirrors are greatly reduced. This can minimize transient parametric instability and compensate dark port power fluctuations. Modeling results are presented for both single compensation where a CO2 laser acting on one test mass per cavity, and double compensation using one CO2 laser for each test mass. Using parameters of the LIGO Hanford Observatory X-arm as an example, single compensation allows the maximum mode frequency shift to be limited to 6% of its uncompensated value. However, single compensation causes transient degradation of the contrast defect. Double compensation minimise contrast defect degradation and reduces transients to less than 1% if the CO2 laser spot is positioned within 2 mm of the cavity beam position.

Application of the guided lock technique to Advanced Virgo’s high-finesse cavities using reduced actuation

The recent upgrades of the Advanced Virgo experiment required an update of the locking strategy for the long, high-finesse arm cavities of the detector. In this work we will present a full description of the requirements and the constraints of such system in relation to the lock acquisition of the cavities; the focus of this work is the strategy used to accomplish this goal, which is the adaptation and use of the guided lock technique, which dynamically slows down a suspended optical cavity in order to make the lock possible. This work describes the first application of such locking technique to 3km long optical cavities, which are affected by stringent constraints as the low force available on the actuators, the high finesse and the maximum sustainable speed of the cavities, which is quite low due to a number of technical reasons that will be explained. A full set of optical time domain simulations has been developed in order to study the feasibility and the performance of this algorithm and will be throughout discussed, while finally the application on the real Advanced Virgo’s arm cavities will be reported.

The influence of dual-recycling on parametric instabilities at Advanced LIGO

Laser interferometers with high circulating power and suspended optics, such as the LIGO gravitational wave detectors, experience an optomechanical coupling effect known as a parametric instability: the runaway excitation of a mechanical resonance in a mirror driven by the optical field. This can saturate the interferometer sensing and control systems and limit the observation time of the detector. Current mitigation techniques at the LIGO sites are successfully suppressing all observed parametric instabilities, and focus on the behaviour of the instabilities in the Fabry–Perot arm cavities of the interferometer, where the instabilities are first generated. In this paper we model the full dual-recycled Advanced LIGO design with inherent imperfections. We find that the addition of the power- and signal-recycling cavities shapes the interferometer response to mechanical modes, resulting in up to four times as many peaks. Changes to the accumulated phase or Gouy phase in the signal-recycling cavity have a significant impact on the parametric gain, and therefore which modes require suppression.

First Demonstration of Electrostatic Damping of Parametric Instability at Advanced LIGO.

Interferometric gravitational wave detectors operate with high optical power in their arms in order to achieve high shot-noise limited strain sensitivity. A significant limitation to increasing the optical power is the phenomenon of three-mode parametric instabilities, in which the laser field in the arm cavities is scattered into higher-order optical modes by acoustic modes of the cavity mirrors. The optical modes can further drive the acoustic modes via radiation pressure, potentially producing an exponential buildup. One proposed technique to stabilize parametric instability is active damping of acoustic modes. We report here the first demonstration of damping a parametrically unstable mode using active feedback forces on the cavity mirror. A 15 538Hz mode that grew exponentially with a time constant of 182sec was damped using electrostatic actuation, with a resulting decay time constant of 23sec. An average control force of 0.03nN was required to maintain the acoustic mode at its minimum amplitude.

Study of parametric instability in gravitational wave detectors with silicon test masses

Parametric instability is an intrinsic risk in high power laser interferometer gravitational wave detectors, in which the optical cavity modes interact with the acoustic modes of the mirrors, leading to exponential growth of the acoustic vibration. In this paper, we investigate the potential parametric instability for a proposed next generation gravitational wave detector, the LIGO Voyager blue design, with cooled silicon test masses of size 45 cm in diameter and 55 cm in thickness. It is shown that there would be about two unstable modes per test mass at an arm cavity power of 3 MW, with the highest parametric gain of ∼76. While this is less than the predicted number of unstable modes for Advanced LIGO (∼40 modes with max gain of ∼32 at the designed operating power of 830 kW), the importance of developing suitable instability suppression schemes is emphasized.

Folding gravitational-wave interferometers

The sensitivity of kilometer-scale terrestrial gravitational wave interferometers is limited by mirror coating thermal noise. Alternative interferometer topologies can mitigate the impact of thermal noise on interferometer noise curves. In this work, we explore the impact of introducing a single folding mirror into the arm cavities of dual-recycled Fabry–Perot interferometers. While simple folding alone does not reduce the mirror coating thermal noise, it makes the folding mirror the critical mirror, opening up a variety of design and upgrade options. Improvements to the folding mirror thermal noise through crystalline coatings or cryogenic cooling can increase interferometer range by as much as a factor of two over the Advanced LIGO reference design.

Resonant dampers for parametric instabilities in gravitational wave detectors

Advanced gravitational wave interferometric detectors will operate at their design sensitivity with nearly $\ensuremath{\sim}1\text{ }\text{ }\mathrm{MW}$ of laser power stored in the arm cavities. Such large power may lead to the uncontrolled growth of acoustic modes in the test masses due to the transfer of optical energy to the mechanical modes of the arm cavity mirrors. These parametric instabilities have the potential to significantly compromise the detector performance and control. Here we present the design of ``acoustic mode dampers'' that use the piezoelectric effect to reduce the coupling of optical to mechanical energy. Experimental measurements carried on an Advanced LIGO-like test mass have shown a tenfold reduction in the amplitude of several mechanical modes, thus suggesting that this technique can greatly mitigate the impact of parametric instabilities in advanced detectors.

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 generalized, 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 to illustrate how our findings affect Sagnac speed meters with metre- and kilometre-long baselines.

Achieving resonance in the Advanced LIGO gravitational-wave interferometer

Interferometric gravitational-wave detectors are complex instruments comprised of a Michelson interferometer enhanced by multiple coupled cavities. Active feedback control is required to operate these instruments and keep the cavities locked on resonance. The optical response is highly nonlinear until a good operating point is reached. The linear operating range is between and 1% of a fringe for each degree of freedom. The resonance lock has to be achieved in all five degrees of freedom simultaneously, making the acquisition difficult. Furthermore, the cavity linewidth seen by the laser is only Hz, which is four orders of magnitude smaller than the linewidth of the free running laser. The arm length stabilization system is a new technique used for arm cavity locking in Advanced LIGO. Together with a modulation technique utilizing third harmonics to lock the central Michelson interferometer, the Advanced LIGO detector has been successfully locked and brought to an operating point where detecting gravitational-waves becomes feasible.

Radiative thermal noise for transmissive optics in gravitational-wave detectors

Radiative losses have traditionally been neglected in the calculation of thermal noise of transmissive optical elements because for the most commonly used geometries they are small compared to losses due to thermal conduction. We explore the use of such transmissive optical elements in extremely noise-sensitive environments such as the arm cavities of future gravitational-wave interferometers. This drives us to a geometry regime where radiative losses are no longer negligible. In this paper we derive the thermo-refractive noise associated with such radiative losses and compare it to other known sources of thermal noise.