Frequency Standards and Metrology Testing LI Microwave frequencies

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

Recent Progress • Testing LLI • Tobar, Wolf, Bize, Santarelli, 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, ” Physical Review D, vol. 82, 076001, 2010. • Parker et. al. , “Cavity Bounds on Higher-Order Lorentz. Violating Coefficients, ” submitted, on the Archive

Summary 1. The Cryogenic Sapphire Oscillator 1. UWA rotating Michelson-Morley experiment re-visited 2. LNE SYRTE Experiment (> 6 year Data)

Cryogenic Sapphire Oscillator

UWA Sapphire Clock: Most precise device to measure 0. 1 seconds Fundamental Ideas JENNIFER to a few hours– WG modes ØSingle crystal Sapphire at cryogenic temperature (4~10 K): ØSupporting whispering gallery (WG) modes Single crystal Sapphire Resonator (top view)

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 the prior experiment) allows better frequency stability WGE 16, 0, 0 mode is more sensitive to Lorentz violating parameters (S = 0. 4567 compared to S = 0. 1958) -> over all near two orders of magnitude improvement. Reduction of noise-inducing systematics (i. e. tilt) use Berlin system.

Weighted Least Squares to Estimate Amplitudes of LV Coefficients

SME Parameters • Search the derivative of the demodulated data around • Optimized the number of rotations (500) to average the values of (ti, d. S(ti)/dt) • There is about 9 -10 points in a sidereal day to maximise signal to noise ratio) • Spectral density non-white -> WLS • 2 -4 times better than Previous analysis assumed white noise -> OLS use 40 rotation periods

Prior analysis -> Minimal SME (renormalizable in flat space-time) This analysis -> d ≥ 4 camoflauge coefficients

Camoflauge coefficients non-birefringent and non-dispersive to first order Dispersive Coefficients n: characterizes frequency dependence of coefficient: j m: usual angular momentum quantum numbers

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)

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

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

Data Analysis: Search the Derivative over annual periods Annual frequency = 0. 017203 rads/day

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

Local Position Invariance

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) I 2 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 Fortier et. al. PRL 98 070801 Ashby et. al. PRL 98 070802 With respect to fundamental constants: V. V. Flambaum, et. al. , PRD. D 69, 115006 (2004)