Expanding the Capability of Microwave Multiplexed Readout for Fast Signals in Microcalorimeters

Abstract

Microwave SQUID multiplexing has become a key technology for reading out large arrays of X-ray and gamma-ray microcalorimeters with mux factors of 100 or more. The desire for fast X-ray pulses that accommodate photon counting rates of hundreds or thousands of counts per second per sensor drives system design toward high sensor current slew rate. Typically, readout of high current slew rate events is accomplished by increasing the sampling rate, such that rates of order 1 MHz may be necessary for some experiments. In our microwave multiplexed readout scheme, the effective sampling rate is set by the frequency of the flux-ramp modulation ($f_\mathrm{r}$) used to linearize the SQUID response. The maximum current slew rate between samples is then nominally $\varPhi _0 f_\mathrm{r}/2M_\mathrm{in}$ (where $M_\mathrm{in}$ is the input coupling) because it is generally not possible to distinguish phase shifts of $> \pi$ from negative phase shifts of $< -\pi$. However, during a pulse, we know which direction the current ought to be slewing, and this makes it possible to reconstruct a pulse where the magnitude of the phase shift between samples is $>\pi$. We describe a practical algorithm to identify and reconstruct pulses that exceed this nominal slew rate limit on the rising edge. Using pulses produced by X-ray transition-edge sensors, we find that the pulse reconstruction has a negligible impact on energy resolution compared to arrival time effects induced by under-sampling the rising edge. This technique can increase the effective slew rate limit by more than a factor of two, thereby either reducing the resonator bandwidth required or extending the energy range of measurable photons. The extra margin could also be used to improve crosstalk or to decrease readout noise.