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 LorentzViolating 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
Single crystal
Sapphire at cryogenic
temperature (4~10K):
Supporting 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
WGE16,0,0 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 2 R
• Optimized the number of rotations (500) to average the
values of (ti,dS(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
-12
Derivative Residual [1/day]
1.5 10
09 Sept 02 - 22 Dec 08
-12
1 10
-13
5 10
0
-13
-5 10
-1 10-12
-12
-1.5 10
4
4
5.3 10
5.4 10
Modi fied Juli an Day
Residuals between a quadratic and beat frequency with respect to 12 GHz.

Data Analysis: Search the Derivative over annual periods
1.7 10-13
C
S
-14


10-13
8.5 10
10-14
0
-8.5 10
i
2
i
2
C  S
i
i
-16
10
-13
-1.7 10
C2  S2
-15
10
-14
0.5
1
1.5
2
2.5
Frequency [1/year]
3
0.5

1
1.5
2
2.5
Frequency [1/year]
 iC i Sin[ i (t  to )] i S i Cos[ i (t  to )]
i
C = -2.7(2.1)10-14
S = -5.4(2.4)10-14
PKT of -2.3(1.0)10-7



Annual frequency = 0.017203 rads/day
3
Data Analysis: Search the Derivative over sidereal periods
-16
3 10
-16
8 10
-16
-16
6 10
-16
4 10
2 10
-16
1 10
-16
2 10
0
0
-16
-16
-2 10
-16
-4 10
-1 10
-16
-2 10
-3 10-16
0.5
C
S

1
1.5
2
2.5
3
Frequency [1/sidereal day ]
-16
-6 10
-16
-8 10
C   = -1.7(1.0)10-16
S = 0.56(1.0)10-16
~
i
S

-1.5 -1 -0.5 0
0.5 1
1.5
Of f set f requency f rom sidereal [1/y ear]
Combine annual and Sidereal
PKT = -4.8(3.7)10-8
-8
PKT = -1.7(4.0)10
C
8
Sep 02 - Aug 03
Local Position Invariance
http://aa.usno.navy.mil/data/docs/EarthSeasons.php .
y = -899.327 + 0.01720292x R= 0.9999992
Annual Phase [Rads]
40
35
30
25
20
15
10
5
0
4
4
5.3 10
5.4 10
Modified Julian Day
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
Fortier et. al.
PRL 98 070801
Hg  Cs  2(3.5) 106
Ashby et. al.
PRL 98 070802
HMaser  Cs  0.1(1.4) 106

With respect to fundamental constants: V. V.
Flambaum, et. al., PRD. D 69, 115006 (2004)