First demonstration of a TES based cryogenic Li$_2$MoO$_4$detector for neutrinoless double beta decay search

Cryogenic calorimetric experiments to search for neutrinoless double-beta decay ($0\nu\beta\beta$) are highly competitive, scalable and versatile in isotope. The largest planned detector array, CUPID, is comprised of about 1500 individual Li$_2^{100}$MoO$_{4}$ detector modules with a further scale up envisioned for a follow up experiment (CUPID-1T). In this article, we present a novel detector concept targeting this second stage with a low impedance TES based readout for the Li$_2$MoO$_{4}$ absorber that is easily mass-produced and lends itself to a multiplexed readout. We present the detector design and results from a first prototype detector operated at the NEXUS shallow underground facility at Fermilab. The detector is a 2-cm-side cube with 21$\,$g mass that is strongly thermally coupled to its readout chip to allow rise-times of $\sim$0.5$\,$ms. This design is more than one order of magnitude faster than present NTD based detectors and is hence expected to effectively mitigate backgrounds generated through the pile-up of two independent two neutrino decay events coinciding close in time. Together with a baseline resolution of 1.95$\,$keV (FWHM) these performance parameters extrapolate to a background index from pile-up as low as $5\cdot 10^{-6}\,$counts/keV/kg/yr in CUPID size crystals. The detector was calibrated up to the MeV region showing sufficient dynamic range for $0\nu\beta\beta$ searches. In combination with a SuperCDMS HVeV detector this setup also allowed us to perform a precision measurement of the scintillation time constants of Li$_2$MoO$_{4}$. The crystal showed a significant fast scintillation emission with O(10$\,\mu$s) time-scale, more than an order below the detector response of presently considered light detectors suggesting the possibility of further progress in pile-up rejection through better light detectors in the future.