Viabilidad y sostenibilidad

At the 2017 Einstein Telescope Design Update Workshop, plans for ET underwent review, with the aim of both renewing interest in the project and updating the design itself to reflect progress in the field post-detection. There, it was suggested that the xylophone configuration may not be necessary to achieve ET’s initial science goals. The xylophone configuration is a means of avoiding the conflicting design requirements necessary to achieve good sensitivity at both high and low

aLIGO (QN)

Figure 4.2: Sensitivity curves for the High-Frequency and Low-Frequency interferometers proposed in the 2011 Einstein Telescope Design Study, reproduced from Figure 7 of [12]. These include pro- jected noise contributions from all known sources. The ET-HF (red) and ET-LF (blue) curves together give the final curve for ET, which has an order of magnitude overall sensitivity improve- ment when compared to Advanced LIGO. The total broadband sensitivity of ET is also significantly wider than that of the Advanced LIGO design. The quantum-noise-limited sensitivity curve of the Advanced LIGO design is shown for reference.

gravitational wave frequencies: for example high laser power is required to improve the detector sensitivity at high frequencies, but this will increase the thermal noise of the test masses. Using a xylophone configuration means that a lower optical power and cryogenic cooling can be used at lower frequencies where thermal noise is limiting, while at high frequencies, where the detector is quantum-limited, a high optical power can be used.

The development of the LIGO Voyager design [67], a proposal to upgrade the current LIGO facilities including cryogenically cooling the test masses to 123 K, has shown that some of these compromises are less constraining than initially believed. As such, the idea emerged that the Voyager design could be adapted to an ET-scale (10 km) facility, resulting in a interferometer with sensitivity similar to the xylophone design. The resulting design is therefore dubbed ‘ET-Voyager’, or ‘ET- 120K’.

The ET-120K design is still very much in development. Table4.1lists suggested parameters for the core interferometer in this new design, as well as the corresponding values for both Voyager, and ET-HF and -LF. Figure4.3depicts the resulting quantum-limited sensitivity curve, alongside the equivalent curves for the xylophone configuration. ET-120K can be viewed as a ‘warmer ET-LF’ or ‘long Voyager’. The optical layout is thus largely identical to ET-LF. The circulating power of 3 MW is higher than that proposed for ET-LF, and is designed to improve ET-120K’s sensitivity

at higher frequencies.

Like LIGO, ET-120K will be based on the dual-recycled Michelson with Fabry-Perot arms (DRF- PMi) described in chapter1. Figure4.4shows a schematic of the proposed layout of the core optics. Assuming that ET-120K retains the triangular configuration, the two arms of each interferometer will be angled at 60◦ to each other rather than the 90◦ depicted here, and additional folding may be required to fit the input and output optics into the site (see figure4.1for how this may work). However, for the purpose of this study we consider the simplified layout depicted in figure4.4. ET uses a similar naming convention to LIGO. The Fabry-Perot X- and Y-arm cavities are identical and 10 km long, formed by the Input- and End Mirrors (I- and ETMs). The radius of curvature for the I- and ETMs is designed so that the beam spot size on the mirrors is as large as possible, which helps reduce coating thermal noise. The upper limit to the spot size is set primarily by the maximum mirror substrate sizes anticipated to be available, and then by the geometric stability of the arm cavities. Due to the 10 km arm length, I have taken the recycling cavity design in my model from the original ET study, while the mirror transmissions, losses and materials are those proposed for Voyager. Test mass curvatures are based on the ET study, however with adjustments due to the projected clipping losses in the original design (see section 4.4). Since ET-120K is proposed to make use of technologies developed for LIGO Voyager, I assume a laser wavelength of 2 µm and identical test mass properties.

Unlike LIGO, where curved folding mirrors are used in the recycling cavities to ensure that they

Figure 4.3: Quantum-noise-limited sensitivity curves for a possible ‘ET-120K’ design (black), com- pared to the quantum-limited curves of ET-HF and ET-LF. All curves are the result of plane-waves models and computed using Finesse; models of ET-HF and -LF were provided by V. Adya.

input optics output optics BS PRM SRM ITMX ETMX ITMY ETMY laser lensIMY lensIMX

Figure 4.4: Optical layout of the ET-120K interferometer design, depicting the core optics only. While the core design is again a dual-recycled Michelson with Fabry-Perot arms, ET plans to incor- porate focusing elements (‘lensIMX/Y’) directly into the input test masses rather than including telescopes in the recycling cavities, as used at LIGO.

are geometrically stable, the arm and recycling cavity lengths in ET can be designed to ensure geometric stability. ET will still require focusing elements, since without these the beamsplitter substrate would need to be significantly larger than would be available. The design study proposes geometrically symmetric recycling cavities, and incorporating focussing lenses into the ITMs, which are then further from the beamsplitter compared to the aLIGO design. This would allow the beamsplitter and recycling mirrors to be significantly smaller than the test masses. This means that the power and signal recycling cavities, formed by the Power- and Signal-Recycling Mirrors (P- and SRMs) and the arm cavities respectively, are linear except for the central beamsplitter, and do not introduce astigmatism to the beam. However, this does reduce the number of pick-off points that could be used for monitoring control signals from the interferometer.

ET-120K is also expected to use frequency-dependant squeezing (‘FDS’) [68,69,70,71]. Squeezers are currently being installed at LIGO; full deployment of FDS is expected to increase the BNS range by 30% [72]. It may also employ balanced homodyne readout [73,74,75]. This is currently under investigation for the LIGO A+ design [60] and LIGO Voyager due to the reduction in readout noise compared to DC readout, and tuneable readout angle. In the long-term, it is foreseen that

ET could be further upgraded to incorporate elements such as optomechanical filters (see chapter5

and [13]) and other technologies designed to optimise the quantum-limited detector response. In this study of parametric instabilities we focus on the core optics of the DRFPMi. The behaviour here should be understood, and the design modified to minimise PIs if necessary, before considering the effects of further input and output optics on PIs.

LIGO Voyager ET-120K ET-LF ET-HF

Arm Power 2.82 MW 3 MW 18 kW 3 MW

Laser wavelength 2 µm 2 µm 1550 nm 1064 nm

Beam Shape HG00 HG00 HG00 LG33

Readout Scheme Homodyne Homodyne DC Homodyne

Additional QN elements FDS: FDS FDS: FDS: 1 x 300 m FC - 2 x 10 km FCs 1 x 300 m FC Arm Cavities Arm Length 4 km 10 km 10 km 10 km Temperature 123 K 120 K 10 K 290 K TM RoC - 6690 m* 5580 m 5690 m – ITM 1798 m - - - – ETM 2492 m - - - ITM Transmission 3000 ppm 3000 ppm* 7000 ppm 7000 ppm ETM Transmission 5 ppm 5 ppm 6 ppm 6 ppm

TM Scatter loss per surface 10 ppm 10 ppm 37.5 ppm 37.5 ppm

TM Material Silicon Silicon Silicon Fused Silica

TM Mass 200 kg 200 kg 211 kg 200 kg

TM diameter ∼45 cm 45 cm >45 cm 60 cm

TM thickness ∼55 cm 55 cm ∼ 50 cm 30 cm

Central Interferometer

Optic material Fused Silica Fused Silica Fused Silica Fused Silica

Recycling Cavity Length 310 m* 310 m 310 m

– Length ITM-BS 300 m* 300 m 300 m

– Focusing element - in/near ITM; in/near ITM; in/near ITM;

f = 303 m f = 303 m f = 303 m

Temperature room temp. room temp. room temp. room temp.

PRM Transmission 3.3% 3.3% 4.6 % 4.6 %

SRM Transmission 2.7% 2.7%* 20 % 10 %

SRC Tuning RSE RSE detuned RSE

Table 4.1: Comparison: parameters of the core optics in my ET-120K design files versus the earlier ET xylophone configuration [12] and proposed LIGO Voyager [67] designs. All acronyms are as listed in the glossary. Starred (*) values in the ET-120K design indicate parameters whose values I explore in this study. While the eventual design for ET-120K is likely to use Homodyne readout and Frequency-Dependent Squeezing, my model only considers the core optics of the interferometer. Sensitivity curves are therefore shown with DC readout and no squeezing.