Experimental Aspects of Speed Meters and Sagnac ... · Experimental Aspects of Speed Meters and...

Experimental Aspects of Speed Meters and Sagnac Interferometers

Sebastian Steinlechner

The Next Detectors for Gravitational Wave Astronomy

Beijing, April 2015

The speed meter concept

• Second generation of GW detectors will be limited by radiation-pressure noise at low frequencies

• RPN is back-action noise; a measurement of the test-mass position disturbs the test mass

• This is because current GW detectors are position meters, and 𝑥 𝑡 , 𝑥 𝑡′ ≠ 0

• However, the momentum 𝑝 𝑡 of a free test mass is a conserved quantity, so 𝑝 𝑡 , 𝑝 𝑡′ = 0

• Same then holds true for speed, as the mass is constant → speed meters are back-action noise free

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Early conceptual approaches

• Speed meter concept proposed by Braginsky & Khalili, 1990

• Idea based around weakly coupled resonators, transforming a position signal in one resonator into a velocity signal in the other

• Implementation ideas for actual interferometers appeared around the year 2000

• E.g. coupled cavities by BGKT (2000), sloshing cavity approach by Purdue & Chen (2002)

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Towards experimental realisations

• Signal “sloshes” back and forth between interferometer and sloshing cavity

• This makes the output proportional to signal changes

• Adds significant complexity by introducing another cavity (+ possibly two more for squeezed light injection)

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Bench-top sloshing cavity experiment

Experiment to demonstrate that sloshing cavity setup is indeed sensitive to test-mass speed and that the position signal is cancelled

(classical sensitivity, not a QND experiment)

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Sagnac IFO is a speed meter

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What’s a Sagnac IFO?

• Invented by and named after French physicist Georges Sagnac (1869-1926)

• Originally used to measure rotations instead of displacements

• Beam split in half, travelling CW and CCW through interferometer

• For stationary mirrors, beams travel exact same path, output is dark

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Sagnac IFO measures rotations

• What happens when we rotate the apparatus around its vertical axis?

– say, CW motion

– For CW beam, beam splitter moves further away

– Beam splitter moving towards CCW beam

– Slight difference Δ𝐿 in travelled distance, leading to phase shift Δ𝜙

– Signal proportional to enclosed area A

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(Wikipedia)

Applications of Sagnac IFO

• This rotational sensitivity is exploited e.g. in ring-laser gyros

• Active laser medium inside ring cavity

• In this case, rotation will cause frequency difference between counter-propagating beams

• This can be measured with high precision

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Laser gyro for commercial applications (Wikipedia/Nockson)

Large laser gyro for measuring variations in earth rotation, A = 16m2, Geod. Observatorium Wettzell, Germany

Modifying the Sagnac for our purposes

• Rotational sensitivity proportional to enclosed area

– Make zero-area Sagnac

– Beam encloses two areas of same size, but travels around them in opposite directions

– Easily done by “folding in” the far mirror

• This arrangement immediately looks much more like the conventional Michelson IFOs and would fit into same vacuum envelope

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Why is it a speed meter?

Sagnac interferometer roundtrip phase: 𝜙𝑐𝑤 ∝ 𝑥𝑁 𝑡 + 𝑥𝐸 𝑡 + 𝜏 𝜙𝑐𝑐𝑤 ∝ 𝑥𝐸 𝑡 + 𝑥𝑁 𝑡 + 𝜏

Differential phase is proportional to test-mass speed: Δ𝜙 = 𝑥𝑁 𝑡 − 𝑥𝑁 𝑡 + 𝜏 − 𝑥𝐸 𝑡 − 𝑥𝐸 𝑡 + 𝜏

≈ 𝜏 𝑥 𝐸 𝑡 − 𝑥 𝑁 𝑡

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Sagnac IFO signal transfer function

Contrary to a Michelson IFO, the Sagnac output is always dark for any (stationary) round-trip length 𝐿

– Vanishing displacement sensitivity towards low frequencies

– Inherently stabilised to a dark fringe

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Sun et al., PRL 76, 3053 (1996)

Previous experiments

• The Sagnac interferometer topology for GW detection has been investigated in the late 90s, e.g. in Stanford and at the ANU

• Found no significant improvement over more mature Michelson, but some technical challenges

• Speed-meter nature of Sagnac only discovered after experiments stopped

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Sagnac configurations for GW detection

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M. Wang, PhD thesis

• Requires large cavity optics because of 45deg AOI

• Possible issue of small-angle scattering coupling the two directions

• Requires high-quality polarising optics, probably far beyond current technologies

Example: beam splitter requirements

• For a (lossless) Michelson IFO, the beam splitter does not need to be perfectly balanced (although there’s a requirement due to differential radiation pressure)

• In a Sagnac however, any imbalance immediately leads to imperfect overlap and reduced sensitivity

• Also, tilt has to be controlled to higher precision in Sagnac

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Phase readout

• Can we use beam splitter asymmetry to provide a dark-fringe offset (local oscillator) for DC readout?

• No! The quadrature orientation is wrong.

• Need signal + LO aligned so that 𝐼 = 𝐸2 ≈ 𝐸𝐿𝑂2 + 𝐸𝐿𝑂𝛿𝜙

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Phase readout, done right

• So how do we get a local oscillator? Some options:

– Use non-zero area + earth rotation

– Use PBS leakage light (for polarising Sagnac)

– Use external LO, balanced homodyne detection (well-established in quantum optics, but not demonstrated for suspended interferometry)

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The Glasgow Sagnac Speed Meter Experiment

The Glasgow Sagnac Speed Meter experiment is an European Research Council funded project with three major goals:

1. Create an ultra-low noise speed meter testbed which is dominated by radiation pressure noise

2. Demonstrate the back-action noise cancellation of the Sagnac topology

3. Explore speed meter technology for future GW detectors, such as ET

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How will we reach these goals?

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• Show that Sagnac configuration can beat the equivalent Michelson configuration

• Need low-mass optics and high laser powers so that Michelson would be backaction-noise limited

• Aim for 2-3x better sensitivity between 100Hz and 1kHz

• Assume Michelson is understood well enough

– Won’t actually build it

– Go straight for Sagnac

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Conceptual approach

• In-vacuum operation, passive multi-stage seismic pre-isolation (+ maybe active as well)

• Triangular arm cavities with monolithically suspended mirrors

• 1g ITMs, 100g ETMs

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Target displacement sensitivity:

better than 10-18 m/√Hz at 1kHz

• Approx. 2.8m cavity round trip length,

20ppm – 30ppm loss per round trip

• Approx. 1kW of intra-cavity power

• Large laser beam spots to reduce

coating Brownian thermal noise

• In vacuum suspended balanced

homodyne detector

ITM ETMs

BHD

Seismic isolation platform • Bridge structure on top of seismic

isolation stack rigidly connects breadboards inside the two vacuum tanks for LF stability

• Filled with Silastic rubber compound to dampen resonances

• Had cleanliness issues, now solved

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Work on suspensions

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Auxiliary suspensions

• Input beam

steering

• Small Sagnac

• Double pendulum

• No vertical stage

• Compact design

• Coil actuation on

upper mass

Work on suspensions

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ETM suspensions

• 100g mirror

mass

• AEI prototype

design

• Triple

pendulum

• Monolithic last

stage

• Fast ESD

actuation

Work on suspensions

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1g suspensions

• Similar to 100g

suspensions, but

scaled down

• Work in progress ?

Parts for auxiliary suspensions arrived

From design to reality

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One-gram suspensions

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• Extensive modelling underway

• Investigating and optimising parameters such as

– Mirror size and geometry

– Suspension options (number of fibres, attachment points)

– Fibre diameter and length

• Identified possible parameter set giving us 100Hz to 1kHz window

Future plans

• Prototype scale

– Glasgow 10m prototype will switch to Sagnac configuration

– Investigate control issues

– Maybe get acquainted with 1550nm and Silicon optics

• ET

– It’s in the design study as an alternative configuration

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