Michael E. Tobar School of Physics University of Western Australia, Perth

1. Frequency Standards and Metrology Testing LI @ Microwave frequencies FSM Michael E. Tobar School of Physics University of Western Australia, Perth Frequency Standards and Metrology Research Group

2. Recent Progress • Testing LLI • ME Tobar, EN Ivanov, PL Stanwix, J-MG le Floch, JG Hartnett, “Rotating odd-parity Lorentz invariance test in electrodynamics,” Phys. Rev. D, vol. 80, 125024, 2009. • ME Tobar, P Wolf, S Bize, G Santarelli, VV Flambaum, “Testing local Lorentz and position invariance and variation of fundamental constants ….” Phys. Rev. D., vol. 81, 022003, 2010. • Hohensee et. al., “Improved Constraints on Isotropic Shift and Anisotropies of the Speed of Light using Rotating Cryogenic Sapphire Oscillators,” arXiv:1006.1376v1 • Technical • Improved Oscillators and Interferometers • C.R. Locke, et. al., P.L. Stanwix, M.E. Tobar, Invited Article Rev. Sci. Instrum., vol. 79, 051301, 2008. • EN Ivanov, METobar, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 56, no. 2, pp. 263-269, 2009. • S Parker, EN Ivanov, METobar, IEEE Trans. UFFC, vol. 56, no. 5, May 2009. • EN Ivanov, ME Tobar, Rev. Sci. Instrum., vol. 80, 044701, 2009.

3. Summary The CSO and Microwave Interferometer UWA Rotating Interferometer Experiment LNE SYRTE Experiment (> 6 year Data) UWA Rotating Michelson-Morley Experiment re-visited

4. Cryogenic Sapphire Oscillator

5. JENNIFER UWA Sapphire Clock: Most Accurate clock to measure 0.1 seconds to a few hours Fundamental Ideas – WG modes • Single crystal Sapphire at cryogenic temperature (4~10K): • Supporting whispering gallery (WG) modes Single crystal Sapphire Resonator (top view)

6. Stability UWA CSOs Paris SYRTE Toulouse CNES Sydney NMI Tokyo NICT Boston Haystack

7. Microwave Interferometers coax waveguide

10. Systematic Effects Data set starts at Sep 14 for 13.2 days Amplitude Standard Error

11. First Operation August 2006 Continuous Since September 2007 For nearly 300 days Blocks of Data Analysed with DLS No. of Rotations for Demodulation: 2 to 7 -0.3±310-7 Improve Phase Noise: High Power Recycling Limit -155-20Log[f] => 20 dB improvement

12. Ultimate Limit Recycled Co-axial interferometer -> 5 x 10-8 Increase rotation frequency to 1.7 Hz -> 10-9 Thermal noise limited -> 10-12

14. Long-term data collection Frequency is sampled every 100 s 212 separate data sets 1 day to 24.5 days (7.6 day av) Spans 2296 days with 71% duty cycle. Veto frequency excursions due to cool down, and frequency jumps. 1. Data is averaged over 95,000 s intervals (1.1 days) to look at long term ~ year 2. Data is averaged over 2,500 s intervals to look at diurnal/sidereal time scales.

15. Long Term Effects over Annual Periods Residuals of the Beat Frequency wrt 12 GHz Residuals between a quadratic and the measured beat frequency with respect to 12 GHz. (susceptible to technical systematics frequency jumps)

16. Derivative of the Beat Frequency wrt 12 GHz Derivative of the experimental data, which filters out systematic jumps between cryogenic refills and relocking of the CSO

17. Sidereal/Diurnal Analysis Average data over 2500 s intervals Residuals between a quadratic and beat frequency with respect to 12 GHz.

18. 377 km/s u CMB RMS: Earth Frame x-y plane -> equatorial Spin at sidereal rate

19. Data KT Lorentz Violation PKT : Frequency Shift due to Boost To find amplitudes C, S, Search (derivative)

20. Data Analysis: Search the Derivative over annual periods Annual frequency = 0.017203 rads/day

21. Data Analysis: Search the Derivative over sidereal periods 8 Sep 02 - Aug 03 ~ Combine annual and Sidereal

22. Local Position Invariance

23. Fortier et. al. PRL 98 070801 Ashby et. al. PRL 98 070802 Compare with other resonator experiments Cs vs Resonator (Superconducting cavity): Limit 1.710-2 Phys. Rev. D 27, 1705 (1983), JP Turneaure, CM Will, BF Farrell, E M Mattison, R F Vessot PRL 88 010401 (2001) I2 vs FP resonator: Limit 410-2 C. Braxmaier, H. Müller, O. Pradl, J. Mlynek, A. Peters, and S. Schiller, This work H-maser vs CSO resonator: Limit ~10-4 With respect to fundamental constants: V. V. Flambaum, et. al., PRD. D 69, 115006 (2004)

24. Boost Dependence of Fundamental Constants? Spacetime-varying coupling constants can be associated with Violations of local Lorentz invariance Time variation of a parameter -> cosmic preferred frame Space and time dependence has been studied What about boost? Redshift due to boost (Doppler shift)

25. Boost wrt Cosmic Frame - CMB

26. arXiv:1006.1376v1

29. Reduce Data Set Through Demodulation

30. Optimised Data Analysis • Search the derivative of the demodulated data around • Optimized the number of rotations (500) to average the value of (ti,dS(ti)/dt) data sets (about 9-10 points in a sidereal day to maximise signal to noise ratio) • Spectral density non-white -> WLS • Previous analysis assumed white noise ->OLS use 40 rotation periods

31. Figure 2*: Amplitude of the time derivative of S(T) for the 17th – 23rd of June 2005. Figure 1*: Amplitude of S(T) for the 17th – 23rd of June 2005. Table 1*: e- in 10-16 o+ in 10-12 Pmm in 10-11 *M.A. Hohensee, P.L. Stanwix, M.E. Tobar, S. R. Parker, D. F. Philips, R. L. Walsworth, arXiv:1006.1376v1 (2010).

32. Stanwix, Tobar et. al. 2005, PRL Herrmann et. al. 2005 Antonini et. al. 2005 Hohensee et. al. Derivative Analysis Hermann et. al. 2009 Eisele et. al Stanwix, Tobar et. al. PHYSICAL REVIEW D 74, 081101(R) (2006)

33. New Experiment -> Berlin New dual cavity design (right) allows for better thermal stability Larger sapphire crystals have a higher quality factor ≈ 2 x 109 (compared to 2 x 108) WGE16 mode is more sensitive to Lorentz violating parameters (S = 0.4567 compared to S = 0.1958) Reduction of noise-inducing systematics (i.e. tilt).

34. THE END