[Paper Review] Towards an ultra-stable optical sapphire cavity system for testing Lorentz invariance

Moritz Nagel, Achim Peters|arXiv (Cornell University)|Dec 15, 2011

Noncommutative and Quantum Gravity Theories1 references3 citations

TL;DR

This paper presents a cryogenically cooled sapphire optical cavity system designed to achieve fractional frequency stability below $1 \times 10^{-16}$ at 1-second integration time, using finite element method (FEM)-optimized mechanical mounting and low-noise materials. The system enables a laboratory test of Lorentz invariance at the $10^{-20}$ level via a rotating Michelson-Morley configuration, representing a 100-fold improvement over existing experiments.

ABSTRACT

We present a design for an ultra-stable cryogenically cooled sapphire optical cavity system, with fractional frequency stability better than 1 x 10^-16 at one second integration time. We plan to use such ultra-stable cavities to perform a test of the isotropy of light propagation at the 10^-20 level.

Motivation & Objective

• To develop an ultra-stable optical cavity system for high-precision tests of Lorentz invariance.
• To overcome thermal noise limitations in room-temperature optical cavities by cooling to 4.2 K.
• To reduce mechanical coupling to vibrations through FEM-optimized sapphire cavity mounting structures.
• To improve long-term stability by replacing Ta₂O₅/SiO₂ mirror coatings with monocrystalline AlₓGa₁₋ₓAs coatings.
• To achieve a sensitivity to Lorentz violation at the $10^{-19}$ to $10^{-20}$ level using a rotating cavity setup.

Proposed method

• Design and finite element method (FEM) simulation of a sapphire cavity with enhanced thermal contact and reduced mechanical coupling to vibrations.
• Cooling the cavity to 4.2 K to suppress thermal noise, the dominant instability source in room-temperature resonators.
• Implementation of a high-precision, low-noise granite turntable to continuously rotate the cavity system over 10–100 second periods.
• Use of a Michelson-Morley interferometric configuration with two orthogonally aligned cavities to detect anisotropies in light propagation.
• Integration of ultra-stable cryogenic microwave whispering gallery resonators from the University of Western Australia for multi-band signal detection.
• Planned replacement of Ta₂O₅/SiO₂ mirror coatings with monocrystalline AlₓGa₁₋ₓAs coatings to reduce thermal noise by over an order of magnitude.

Experimental results

Research questions

• RQ1 Can a cryogenic sapphire optical cavity achieve fractional frequency stability below $1 \times 10^{-16}$ at 1-second integration time?
• RQ2 To what extent can FEM-optimized mechanical mounting reduce vibration-induced path length fluctuations in cryogenic cavities?
• RQ3 Can a rotating cavity system detect Lorentz invariance violations at the $10^{-20}$ level?
• RQ4 How much improvement in stability is achievable by replacing amorphous Ta₂O₅/SiO₂ coatings with monocrystalline AlₓGa₁₋ₓAs coatings?
• RQ5 Can co-rotating microwave and optical cavities jointly enhance sensitivity to Lorentz-violating signals?

Key findings

• The theoretical frequency stability of the cryogenic sapphire cavity at 4.2 K is predicted to be an order of magnitude better than the best room-temperature resonator systems.
• FEM simulations show that the optimized cavity design reduces vertical and horizontal vibration coupling by minimizing mechanical deformation, even when deformation is scaled up by $10^{10}$.
• The system is projected to achieve a relative frequency stability below $1 \times 10^{-16}$ over long integration times, enabling high-precision Lorentz invariance tests.
• The planned use of monocrystalline AlₓGa₁₋ₓAs coatings is expected to reduce thermal noise by more than an additional order of magnitude compared to Ta₂O₅/SiO₂ coatings.
• The rotating Michelson-Morley setup is expected to achieve sensitivity to Lorentz violation in the $10^{-19}$ to $10^{-20}$ range, surpassing current experiments by over 100-fold.
• The addition of cryogenic microwave whispering gallery resonators will allow simultaneous detection of multiple types of Lorentz-violating signals.