## Experimental Concept

What's the basic idea of GravNet? Which technologies are used?

## The Basic Idea of GravNet

The experimental concept of the HFGW detection at GravNet is very similar to the cavity based search for axion-like particles (ALPs), e.g. at the SUPAX experiment, however, with two crucial differences:

- The HFGW signal sweeps through the frequency space, hence it is in principle sufficient to be sensitive at one frequency and wait until a signal is seen. This is very different to ALPs searches, where the signal is expected to be present only at one specific frequency, that corresponds to the rest mass of the axion. Hence those experiments need to have tunable cavities.
- Second, and more important for GravNet, the HFGW signal is expected to appear correlated across earth. Hence the data of several cavity based experiments across the globe can be correlated and analysed together, allowing for a significant improvement of the signal to noise ratio. This is the basic idea of GravNet: Developing the tools for an ultra sensitive global network for cavity based experiments for the hunt of high frequency gravitational waves.

To achieve this goal, we are currently developing new techniques on different fronts.

## Theory Modeling and Data Analysis

For the search for tiny signals, it is extremely important to have a well understood theory modelling of the signal in order to allow for an optimized subsequent data analysis. One should keep in mind that one expects maybe one signal with a duration not longer than fractions of a second within one year of data-taking. Interestingly, the effect of Earth's rotation and motion around the Sun also has to be taken into account.

As the PBH merger happen, their GW signal frequency sweeps through a frequency band in a predictable way. This generates a unique pattern in time for the different excitation of modes of increasing frequency resonating within the cavity. Hence one needs to understand the expected signal at these modes since they may allow us to increase the SNR significantly by applying methods inspired by the matched-filtering techniques. Furthermore, the direction of the source impacts the couplong for different modes of the same frequency or different cavity orientations. By computing this for a multi-cavity/multi-mode setup, we can use this information to find the direction of the wave, but also to increase the SNR and confirm that the source of the signal is a GW (as opposed to an axion).

## Cavity Design and Construction

Since the cavity shape has a direct impact on the coupling coefficient of the HFGW, it needs to be optimized in the context of the available magnet infrastructure. Moreover, an optimal value of the quality factor has to be found: While ultra high quality factors increase the signal enhancement, they reduce the actual time in which the cavity is sensitive.

The shape of the cavities defines their base resonance frequencies, their higher resonance modes, and also their coupling to HFGWs. Moreover, a trade-off between the volume of the cavities and the available volume of the magnetic field has to be made. Given that the construction processes for large cavities with volumes of several liters is significantly different than for smaller cavities, we define three different objectives: the design and construction of the FLASH cavity to be placed in the FINUDA magnet, the shape optimization for the small GHz cavities and their construction.

## Cavity Readout

An extremely good signal over noise ratio is necessary to be able to probe the most prominent sources and models that predict HFGWs. Hence we need to test several optimized readout approaches, starting from simple electronic commercial schemes, over SQUID based approaches to single photon counting detectors. The readout scheme for a typical cavity-based axion search experiment is built around a real-time spectrum analyzer yielding time-series data within a bandwidth in the MHz regime, centered around the resonance frequency in the GHz range, to a readout computer. As a baseline approach, we foresee to enhance the signal-to-noise ratio by employing quantum amplifiers, such as SQUIDs or Josephson Parametric Amplifiers (JPA), which introduce noise levels close to the Quantum Limit (QL).

While a readout scheme based on linear amplifiers such as SQUIDs is optimal for operation frequencies below 1 GHz, at higher frequencies, the quantum limit (QL) increases, diminishing the advantages of working with a dilution refrigerator. To circumvent the limits imposed by quantum mechanics, significant efforts are underway to leverage quantum squeezing, quantum metrology, and quantum sensing to derive optimal measurement strategies for axion dark matter.