-andrew ludlow -martin boyd -gretchen campbell -sebastian blatt -jan thomsen - matt swallows -travis...
TRANSCRIPT
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-Andrew Ludlow-Martin Boyd
-Gretchen Campbell
-Sebastian Blatt
-Jan Thomsen
- Matt Swallows
-Travis Nicholson
The Sr team:
Group leader: Jun Ye
New approaches: Jeff Kimble, Caltech
Mirror coatings: Ramin Lalezari, Advanced Thin Films
An Introduction to Noise in Frequency StabilizationMichael J. MartinUniversity of Colorado at Boulder, JILA
PTB collaborators: Uwe Sterr, Fritz Riehle
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Motivations
• Optical atomic clocks (spectroscopy).
FWHM:2.1 Hz
• Gravity wave detection.
• More…
• Quantum Optics.
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Introduction – Noise sources
LaserFabry-Perot Cavity
Pound-Drever-Hall
Discriminator
Cavity servo
Contamination of signal (RAM)
5-100 Hz
Seismic acceleration
Erro
r sig
nal
P / cav
-For 10 cm ultra-high-finesse cavity, shot noise contributes ~10-16 with 10 W optical power.
(Thermal noise)
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h/L0
L
(h)/
L0
Vibrational Sensitivity
-Low frequency: Cavity subject to uniform acceleration.
Chen et. al. PRA 74, (2006)
Fractional displacementVs. height
-Fractional length change scales linearly with length!
h
L/L
0
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4 nm
-4 nm
0.8 nm/div aHorizontaldeflection
per g0
Mounting geometry
Chen et. al. PRA 74, (2006)
-Finite element analysis aids in determining vibrational sensitivity.
-Eg. for 10cm ULE Cavity, sensitivity is at best 80 kHz/m/s2 @ 698nm.
Vibrational Sensitivity:
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Mid-plane Mounting:
M. Notcutt et. al. Optics Letters 30, (2005).
-ULE vertical acceleration sensitivity: 30 kHz/m/s2 @ 698 nm.
-Differential motion minimized.
Mounting geometryVibrational Sensitivity:
-Short cavity vibrational insensitivity.
Verticaldeflection
per g
21 nm
25 nm
0.5 nm/div
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The JILA Sr clock laser
-Finesse = 250,000
-Spacer length = 7cm
-Spacer and substrate material: ULE *
-Linear drift: <1 Hz/sec
-System occupies < 1 m3
*Notcutt et. al PRA 73, (2006).
-Vibrational contribution: .1 Hz/rtHz @ 1 Hz.
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-Mirror technology:
- 40 layers of Ta2O5 and SiO2 ¼ wave
dielectric stacks *.
-Deposited via ion beam sputtering.
-Surface flatness and reflectivity support finesse of 250,000.
The JILA Sr clock laser
*Numata et. al. PRL 93, 2004.
-Substrate and coating thermal noise limited.
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Thermal noise-With internal dissipation comes thermally driven fluctuations.
(in 1 Hz BW)
-Generalized coordinate—Gaussian-weighted surface displacement:
A. Gillespie and F. Raab, PRD (1995)
-Most significant thermal contributions typically from mirror substrate and coating, not cavity spacer.
Y. Levin. Physical Review D 57, 659 (1997).
Callen and Greene. PR 86 (1952)
-Thermoelastic noise small for low CTE materials.
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Mirror Thermal noise
K. Numata et. al. PRL 93, (2004).G. M. Harry et. al. Class. Quant. Grav. 19, (2002).
N. Nakagawa et. al. PRD 65, (2002).
Complex (lossy) Young’s modulus:
-ULE cavity has 1.5 times more substrate noise than coating noise.
-Fractional change scales inversely with length!
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Long-term coherence (>1 s) across the visible spectrum
Hz
Notcutt et al., Opt. Lett. 30, (2005).Ludlow et al., PRL 96, (2006).
Laser 2
Cavity 2 Cavity 1
Laser 1
Beat between two independent lasers
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Frequency fluctuations from thermal noise in Fabry-Perot cavities
Loss angle
Zerodur 3e-4
Fused Silica 1e-6
Coating 4e-4
6
10-14
2
4
6
10-13
2
4
Alla
n d
evi
atio
n
0.001 0.01 0.1 1 10 100
Integration time [s]
35 mm zerodur spcr/ FS mirrors 35 mm zerodur spcr/ zerodur mirrors 10 mm zerodur spcr/ zerodur mirrors
300 K=1/Q
FP Cavity Thermal reservoir
FS mirrors -> Zerodur mirrors
35mm -> 10mm long spacer
Measured/calculated ~ 1.8-2.6K Numata, PRL 93, 250602 (2004)
Notcutt et. al PRA 73, (2006).
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Comparison of results & theory
CaseCalculatedAllan-dev.
MeasuredLowest Point
A-dev
RatioMeasured/Calc
MeasuredDisplacement
Noise
(m/rtHz)
FS Subs 2.8×10-15 5.0×10-15 1.8
Zerodur Subs 1.3×10-14 2.0×10-14 1.6 1.0×10-15
698 nm cavity 9.4×10-15 2.5×10-14 2.7 1.2×10-15
10 mm w/ Zer 3.8×0-14 1.0×10-13 2.7 1.0×10-15
10mm w/ FS 7.1×10-15 3.0×10-14 4.2 2.7×10-16
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JILA Clock laser frequency noise
A. D. Ludlow et. al. Opt. Lett. 32, 641 (2007).
Cavity 1 Cavity 2
Data (dotted) and chirped sine fit (solid)
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Frequency noise S.D.
Measurementnoise floor
Thermal noisetheory
Measured freq. noise
Vibrationalcontribution
Ludlow et al., Opt. Lett. 32, 641 (2007)
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Thermal Noise
-Can relate fractional frequency stability (Allan Deviation) to frequency noise spectral density with 1/f behavior:
ThermalNoise:
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Record high precision and stability
Boyd et al., Science 314, 1430 (2006)
• Single trace without averaging
• Estimated instability /102~)( 15
FWHM:2.1 Hz
Ludlow et al., Opt. Lett. 32, 641 (2007)
Q ~ 2.5 x 1014Sr – Yb standards
Jan. 2008
Ludlow et al., Science in press (2008)
Quantum projectionnoise
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QPN on the horizon
-To reach the quantum projection potential we must overcome the dominant thermal noise.
-Higher substrate Q
-Lower temperature
-For the future: Si cavity-- Thermal coefficient = 0 @ 120 K- 150 GPa Young’s modulus
1.5 micron light
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Conclusions
-Thermal noise in substrate/coatings is currently largest noise source.
-Higher Q substrate can reduce this contribution.-Possible coating noise cancellation schemes? (Jeff Kimble)-Lower temperatures help, but only as
-Designs trade off between vibrational and thermal sensitivity.
-Longer cavities better thermal insensitivity, greater vibrational sensitivity.
.T
-New Silicon design will improve both vibrational insensitivity and increase material Q.
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Rainbow from comb
-Andrew Ludlow-Martin Boyd
-Gretchen Campbell
-Sebastian Blatt
-Jan Thomsen
- Matt Swallows
-Travis Nicholson
The Sr team:
Group leader: Jun Ye
New approaches: Jeff Kimble, Caltech
Mirror coatings: Ramin Lalezari, Advanced Thin Films
PTB collaborators: Uwe Sterr, Fritz Riehle