experimental aspects of speed meters and sagnac ... · experimental aspects of speed meters and...
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Experimental Aspects of Speed Meters and Sagnac Interferometers
Sebastian Steinlechner
The Next Detectors for Gravitational Wave Astronomy
Beijing, April 2015
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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)
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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
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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)
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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
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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
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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
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Work on suspensions
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ETM suspensions
• 100g mirror
mass
• AEI prototype
design
• Triple
pendulum
• Monolithic last
stage
• Fast ESD
actuation
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Work on suspensions
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1g suspensions
• Similar to 100g
suspensions, but
scaled down
• Work in progress ?
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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
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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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