A microwave SQUID multiplexing concept for macro-cryogenic calorimeter arrays

Abstract

Massive cryogenic calorimeters read out by transition-edge sensors (TES) can reach eV-scale baseline resolution, but the single-channel dc-SQUID readout conventionally used in rare-event searches, with one amplifier chain and several wires per detector, limits practical arrays to a few tens of channels. We propose to apply microwave SQUID multiplexing ($\mu$MUX), developed for fast X-ray and neutrino-mass microcalorimeters, to massive BGO (Bi${}_4$Ge${}_3$O${}_{12}$) calorimeters operated at $\simeq 20$~mK; sapphire and TeO${}_2$ absorbers are covered by the same framework. Using the established thermal and noise model for massive TES calorimeters, we derive a noise model for the multiplexed readout, including the HEMT, two-level-system and SQUID contributions, and its scaling with the multiplexing factor $N_{\mathrm{mux}}$. Since the slow thermal signals require only about a kHz of sampling per channel, the limiting requirement is not bandwidth but an input-coil sensitivity of $(0.1$ to $1)\mu$A$/{\Phi }_0$, a factor of $10$ to $30$ beyond current $\mu$MUX devices, matched to the detector current noise of ($9$ to $10$)~pA$/\sqrt{\mathrm{Hz}}$, which is independent of the absorber mass. With a total flux noise of $\simeq$$1.2\mu {\Phi }_0/\sqrt{\mathrm{Hz}}$, the readout degrades the baseline resolution by less than $2\%$ up to $N_{\mathrm{mux}}=1000$, negligible compared with the TES-limited resolution. These results are implemented in a single-tower design: 52 BGO crystals of 100~g each and one HEMT amplifier. The tower is the unit of a multi-tower array of several kilograms aimed at CE$\nu$NS and dark matter searches.