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

21/04/2015 Next Detectors for GWA, Beijing 2015, S. Steinlechner 2

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)


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)


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)


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


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


(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


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


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


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


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


Sagnac configurations for GW detection


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


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


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)


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

21/04/2015 18 Next Detectors for GWA, Beijing 2015, S. Steinlechner

How will we reach these goals?

21/04/2015 19

• 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

Next Detectors for GWA, Beijing 2015, S. Steinlechner

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

20 21/04/2015 Next Detectors for GWA, Beijing 2015, S. Steinlechner

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


Work on suspensions


Auxiliary suspensions

• Input beam

steering

• Small Sagnac

• Double pendulum

• No vertical stage

• Compact design

• Coil actuation on

upper mass

Work on suspensions


ETM suspensions

• 100g mirror

mass

• AEI prototype

design

• Triple

pendulum

• Monolithic last

stage

• Fast ESD

actuation

Work on suspensions


1g suspensions

• Similar to 100g

suspensions, but

scaled down

• Work in progress ?

Parts for auxiliary suspensions arrived

From design to reality


One-gram suspensions


• 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


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

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