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Andrew Ludlow Martin Boyd -Gretchen Campbell -Sebastian Blatt

An Introduction to Noise in Frequency Stabilization. Michael J. Martin University of Colorado at Boulder, JILA. Andrew Ludlow Martin Boyd -Gretchen Campbell -Sebastian Blatt. Jan Thomsen Matt Swallows Travis Nicholson. The Sr team:. Group leader:. Jun Ye.

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Andrew Ludlow Martin Boyd -Gretchen Campbell -Sebastian Blatt

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  1. An Introduction to Noise in Frequency Stabilization Michael J. Martin University of Colorado at Boulder, JILA • Andrew Ludlow • Martin Boyd • -Gretchen Campbell • -Sebastian Blatt • Jan Thomsen • Matt Swallows • Travis Nicholson The Sr team: Group leader: Jun Ye Ramin Lalezari, Advanced Thin Films Mirror coatings: New approaches: Jeff Kimble, Caltech Uwe Sterr, Fritz Riehle PTB collaborators:

  2. Motivations FWHM: 2.1 Hz • Optical atomic clocks (spectroscopy). • Gravity wave detection. • Quantum Optics. • More…

  3. Error signal Introduction – Noise sources 5-100 Hz Seismic acceleration Fabry-Perot Cavity Laser (Thermal noise) Cavity servo P / Dncav Pound-Drever-Hall Discriminator Contamination of signal (RAM) -For 10 cm ultra-high-finesse cavity, shot noise contributes ~10-16with 10 mW optical power.

  4. Vibrational Sensitivity -Low frequency: Cavity subject to uniform acceleration. Fractional displacement Vs. height -Fractional length change scales linearly with length! L/L0 h Chen et. al. PRA 74, (2006)

  5. Vibrational Sensitivity: Mounting geometry 4 nm Horizontal deflection per g a 0.8 nm/div 0 -Finite element analysis aids in determining vibrational sensitivity. -4 nm • Eg. for 10cm ULE Cavity, sensitivity • is at best 80 kHz/m/s2 @ 698nm. Chen et. al. PRA 74, (2006)

  6. Vibrational Sensitivity: 21 nm Vertical deflection per g 0.5 nm/div 25 nm Mounting geometry Mid-plane Mounting: -Differential motion minimized. -ULE vertical acceleration sensitivity: 30 kHz/m/s2 @ 698 nm. -Short cavity  vibrational insensitivity. M. Notcutt et. al. Optics Letters 30,(2005).

  7. The JILA Sr clock laser -Vibrational contribution: .1 Hz/rtHz @ 1 Hz. -Finesse = 250,000 -Spacer and substrate material: ULE * -Linear drift: <1 Hz/sec -Spacer length = 7cm -System occupies < 1 m3 *Notcutt et. al PRA 73, (2006).

  8. The JILA Sr clock laser -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. -Substrate and coating thermal noise limited. *Numata et. al. PRL 93, 2004.

  9. Thermal noise -With internal dissipation comes thermally driven fluctuations. (in 1 Hz BW) -Most significant thermal contributions typically from mirror substrate and coating, not cavity spacer. -Thermoelastic noise small for low CTE materials. -Generalized coordinate—Gaussian-weighted surface displacement: Callen and Greene. PR 86 (1952) A. Gillespie and F. Raab, PRD (1995) Y. Levin. Physical Review D 57, 659 (1997).

  10. Mirror Thermal noise Complex (lossy) Young’s modulus: -Fractional change scales inversely with length! -ULE cavity has 1.5 times more substrate noise than coating 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).

  11. Cavity 2 Cavity 1 Hz Laser 1 Laser 2 Long-term coherence (>1 s) across the visible spectrum Notcutt et al., Opt. Lett. 30, (2005). Ludlow et al., PRL96, (2006). Beat between two independent lasers

  12. f=1/Q 300 K Frequency fluctuations from thermal noise in Fabry-Perot cavities Notcutt et. al PRA 73, (2006). FP Cavity Thermal reservoir 35mm -> 10mm long spacer FS mirrors -> Zerodur mirrors Measured/calculated ~ 1.8-2.6 K Numata, PRL 93, 250602 (2004)

  13. Comparison of results & theory

  14. JILA Clock laser frequency noise Cavity 1 Cavity 2 Data (dotted) and chirped sine fit (solid) A. D. Ludlow et. al. Opt. Lett. 32, 641 (2007).

  15. Frequency noise S.D. Measurement noise floor Measured freq. noise Thermal noise theory Vibrational contribution Ludlow et al., Opt. Lett. 32, 641 (2007)

  16. Thermal Noise -Can relate fractional frequency stability (Allan Deviation) to frequency noise spectral density with 1/f behavior: Thermal Noise:

  17. Single trace without averaging • Estimated instability FWHM: 2.1 Hz Sr – Yb standards Jan. 2008 Record high precision and stability Q ~ 2.5 x 1014 Quantum projection noise Ludlow et al., Science in press (2008) Boyd et al., Science 314, 1430 (2006) Ludlow et al., Opt. Lett. 32, 641 (2007)

  18. QPN on the horizon -To reach the quantum projection potential we must overcome the dominant thermal noise. 1.5 micron light -Higher substrate Q -Lower temperature -For the future: Si cavity - - Thermal coefficient = 0 @ 120 K - 150 GPa Young’s modulus

  19. Conclusions -Designs trade off between vibrational and thermal sensitivity. -Longer cavities better thermal insensitivity, greater vibrational sensitivity. -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 -New Silicon design will improve both vibrational insensitivity and increase material Q.

  20. Andrew Ludlow • Martin Boyd • -Gretchen Campbell • -Sebastian Blatt • Jan Thomsen • Matt Swallows • Travis Nicholson The Sr team: Group leader: Jun Ye Ramin Lalezari, Advanced Thin Films Mirror coatings: Rainbow from comb New approaches: Jeff Kimble, Caltech Uwe Sterr, Fritz Riehle PTB collaborators:

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