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Humboldt-Universität zu Berlin - Faculty of Mathematics and Natural Sciences - Optical Metrology

Optical test of Lorentz invariance

M. Nagel, K. Möhle, K. Döringshoff, E. V. Kovalchuk, A. Peters

The Lorentz invariance as a fundamental principle in modern physics is tested in several experiments. In our group we perform a modern Michelson-Morley experiment testing the isotropy of the speed of light by comparing the resonance frequency of two orthogonal cavities rotated on a turntable. In our previous experiments a possible anisotropy of c could be restricted under a level of 5 · 10-16. Our current setup shows an improvement of more than one order of magnitude and provides SME-parameters at the level of 10-17.


Basic idea


The well-known concept of the experiment implemented by A. A. Michelson and E. W. Morley in the year 1887 (a) is modified by replacing the interferometer arms by optical high-finesse cavities (b).

Basics


Two lasers are stabilized to the resonators in order to read out their resonance frequencies. Assuming a constant length L of the cavities a change in the resonance frequency ν0 can be directly connected to a change of the speed of light c using the relation ν0 ~ c/L.

While the cavities are continuously rotated on a turntable, the stabilized laser frequencies are compared to each other by a beat measurement. An anisotropy of the speed of light would then lead to a modulation of the beat frequency at twice the rotation rate:

Formula 1

The amplitudes of this modulation in turn would be modulated by the Earth’s rotation and orbital motion.


Our Realization


The orthogonal cavities are implemented in a single block of fused silica as shown below. The fused silica mirror substrates of both cavities are coated with a high-reflectivity dielectric coating leading to a finesse of almost 400 000 and a linewidth of 7 kHz.

Resonator
photography (c) by Ernst Fesseler


The resonators are set up in a custom-made vacuum chamber featuring several stages of thermal insulation and a good mechanical stability. To isolate the cavities from ambient vibrations, the vacuum chamber is placed on an active vibration isolation system. Two Nd:YAG lasers at 1064 nm are stabilized to the cavities according to a modified Pound-Drever-Hall method reaching a relative frequency stability close to 1 x 10-15 at an integration time of 20s. The whole setup so far described is mounted on a precision air bearing turntable that can be rotated continuously. Electrical connections are made via a slip ring feedthrough, an optical feedthrough along the rotation axis of the turntable is installed in order to measure the beat signal in the non-rotating laboratory frame.

Setup
photography (c) by Ernst Fesseler


Active rotation of the setup gives rise to systematic effects that compromise a possible anisotropy signal. Slowly varying tilt of the rotation axis against the vertical axis is reduced to better than 1µrad by an active stabilization. To minimize systematics arising from centrifugal forces an active stabilization of the rotation rate (45s) is performed. Further measures to reduce systematic frequency variations include balancing the center of mass of the table and shielding the lasers and optics outside the vacuum chamber against air currents, temperature gradients etc.


Test theory and data analysis


The beat signal between the two stabilized lasers is examined with regard to a possible violation of the Lorentz invariance using the Lorentz-violating Standard-Model Extension (SME) as a test theory. In the photonic sector the extension of the Standard-Model is given by

Formula 2

The tensor kF possesses the symmetries of the Riemann tensor and thus is left with 19 independent components. Ten of these describe polarization dependent effects and have been restricted to values below 2 x 10-32 by astrophysical observations. Eight of the remaining nine parameters can be determined by our experiment.


Results


Data were taken intermittent from April 2007 to May 2008 with a total of about 130 000 useable turntable rotations at a rate of 45 seconds. We could place an upper limit of

Δc/c= (0.6 ± 1.2) · 10-17


for the anisotropy of the speed of light in vacuum and we could set bounds on the magnitude of 8 parameters of the SME in the 10-17 level.


Publications


Current results can be found in the following article:

Rotating optical cavity experiment testing Lorentz invariance at the 10-17 level
S. Herrmann, A. Senger, K. Möhle, M. Nagel, E. V. Kovalchuk, A. Peters
Phys. Rev. D 80, 105011 (2009)
[ Link ]

Previous results and further details of the experimental setup and the test theory can be found in the following publications:

Tests of Relativity by Complementary Rotating Michelson-Morley Experiments
H. Müller, P.L. Stanwix, M.E. Tobar, E. Ivanov, P. Wolf, S. Herrmann, A. Senger, E. Kovalchuk, A. Peters
Phys. Rev. Lett. 99, 050401 (2007)
[ Link ]

Test of the Isotropy of the Speed of Light Using a Continuously Rotating Optical Resonator
S. Herrmann, A. Senger, E. Kovalchuk, H. Müller, A. Peters
Phys. Rev. Lett. 95, 150401 (2005)
[ Link ]

Modern Michelson-Morley Experiment using Cryogenic Optical Resonators
H. Müller, S. Herrmann, C. Braxmaier, S. Schiller, A. Peters
Phys. Rev. Lett. 91, 020401 (2003)
[ Link ]

For further publications on this experiment, see our complete publications list.