The frequency stability of todays' most stable lasers is based on the length stability of well-isolated Fabry Perot Cavities (FPCs), e.g., a 50 cm long cavity with ultralow expansion glass spacer, reaching 6×10^-17 fractional frequency stability, or a 21 cm cavity with silicon spacer at 124 K with 4×10^-17 stability, limited by the fundamental Brownian thermal fluctuations of the cavity. Novel cavity designs based on e.g., metamaterial mirrors, are being developed to reduce the instability due to Brownian thermal noise by a factor of 5 to around 1×10¹⁷. Alternative references based on spectral hole burning that are less sensitive to thermal noise and environmental fluctuations are expected to reduce the current instability level by at least an order of magnitude to a few 10^-17 or below. 

Using dedicated sensors and multiple-in multiple-out servo loops pioneered for Gravitational Waves (GW) detectors, the vibrations acting on the frequency references will be reduced below the level of currently available commercial systems to the micro g level also at lower frequencies.

The project will set up and investigate dedicated cryostats down to sub-kelvin temperatures that allows reliable low noise operation of ultrastable lasers with fractional frequency instability in the 10^-18 decade. The target is to identify and mitigate the limits in the transfer of frequency stability from the ultrastable lasers to the target wavelengths via optical frequency combs, which mainly originate from detection and uncontrolled path length fluctuations in wavelength conversion modules.

As a proof of the improvements obtained, ultrastable lasers from this project will be applied for tests of fundamental physics, where lower present bounds will be produced e.g. on potential violation of Lorentz invariance.

Results

Novel low-thermal noise cavity designs (Objective 1):

Microstructured metamirrors based on silicon nano-grating structures on fused silica substrates with plane phase profile were combined with dielectric coatings on the rear side of the substrate to form highly reflecting “meta etalons”. Optical ring-down measurements show overall reflectivities of 99.97%. These results are very promising for setting up high finesse ultra-stable cavities. Focusing metamirrors with curved phase profile on planar substrates were designed with the help of deep-learning algorithms. Fabrication and firsts tests to optically contact these structures to cavities have started.
Investigations on crystalline low-Brownian mirrors based on GaAs/AlGaAs Bragg reflectors at 124 K indicate excess noise above the Brownian noise. So far, the physical noise mechanism is not understood and further investigations on its temperature dependence and spatial correlations are in progress.
Large mode diameters also reduce the influence of thermal Brownian mirror noise. A simulation code for systematic studies of cavity geometries and mirror configurations was developed and configurations, that both provide large mode sizes on the mirrors and are largely insensitive to manufacturing tolerances have been identified and will be produced. 
As an alternative to optical cavities, spectral hole burning in europium-doped crystals is being investigated. Samples of the crystals were prepared for mechanical loss measurements. In a single pass geometry, excitation and simultaneous interrogation by up to 9 separate modes was implemented to reduce the noise. Another crystal has been fabricated, characterised, and is being prepared to realise a slow-light cavity. The crystal surface was machined to create a constant optical thickness independent of local variations of refractive index.

Improved vibration isolation systems at low frequency (Objective 2):

Acceleration and tilt sensors at low frequencies (1 mHz – 100 Hz) suitable for integration with the room-temperature vibration-isolation systems were identified. With these sensors, suppression of the low-frequency vibrations below 2 Hz in the vertical direction by about one order of magnitude could be achieved.
The frequency dependent response of the cavity resonance frequency on accelerations was measured. This information will be used to predict the actual vibration-induced frequency fluctuations in real-time. To strongly suppress their influence, the predicted fluctuations will be subtracted from the laser frequency in a feed-forward scheme, using frequency agile frequency sources that are currently developed.

Integration of closed-cycle cooling for continuous cryogenic operation of SHB and optical cavities at 124 K, 4 K and below (Objective 3):

For a 124 K Silicon cavity, a cold He-gas circulation system with a closed-cycle heat exchanger was designed, and preparations have started for its realisation. Vibrations will be decoupled from the cavity by flexible hoses that are damped at intermediate positions.
With a closed-cycle dilution cryostat for a sub 1-K silicon cavity a minimum temperature of 15 mK was reached and stabilised operation at 20 mK was achieved. Similarly sub 2-K cryostats for the spectral-hole burning setups have been installed for first tests. Temperatures of 1.5 K and 80 mK have been achieved. Next, vibrational levels and temperature stability will be investigated, and the mechanical decoupling optimized to enable stable optical references from cavities and spectral holes at the 10^-17 level.

Making ultrahigh stability available to clocks (Objective 4):

The use of ultrastable lasers very often requires the transfer of stability to other wavelengths, using optical frequency combs with low added noise. The electronics and digital signal processing chains to generate low-noise signals from optical frequency combs were designed. Concepts for fully digital signal processing using Field Programmable Gate Arrays (FPGAs) were developed between the partners.
By electrically gating the detected beat notes of stable continuous-wave (cw) lasers with a femtosecond comb the signal-to-noise ratio could be improved by 12 dB, improving the stability for frequency transfer at short averaging times by the same amount.
Next the FPGA hardware and the gated detection will be further characterized to demonstrate a frequency transfer with added electronic and detection noise well below the targeted laser instability of 10-17 for averaging times down to at least 1s. To identify the fundamental noise limits of the spectral transfer by femtosecond frequency combs, the noise added by nonlinear processes in the spectral broadening will be investigated. The partners are improving their comb setups to enable systematic studies of contributions at a level of 10^-17 and below, e.g., by adding additional amplitude modulation.

Application for tests of fundamental physics (Objective 5):

A three-dimensional data analysis method has been developed for correlating data from multiple clocks that takes into account geometrical configuration of the clocks to investigate dark-matter coupling to the fine-structure constant from observations of three clocks and distinguish it from technical noise. A correlation analysis of join data of local comparisons between cavities and atomic clock transitions from up to 7 systems distributed between USA, Europe and Asia is ongoing.
The response of a cavity made of two mirrors connected by a solid elastic spacer to gravitational waves was analysed theoretically. The theory for Weber-bar mechanical resonators was applied to optical resonators. It indicates that for spacers made of typical materials like ULE or fused silica, with mechanical resonances in the kHz range, a sensitivity competitive to already existing mechanical detectors can be achieved. A complete noise budget is now set up.