Flux ramp modulation for Microwave SQUID Multiplexing

Microwave SQUID multiplexing ($\mu$MUXing) based on non-hysteretic rf-SQUIDs appears to be the most suitable multiplexing technique to read out metallic magnetic calorimeter (MMC) arrays. The intrinsically fast signal rise time of MMCs, for example, can be maintained by providing sufficient bandwidth per channel. However, since rf-SQUIDs are intrinsically non-linear devices due to their periodic flux-to-voltage characteristic, the almost ideal linear detector response of MMCs is degraded unless suitable counter-measures are applied. Standard feedback techniques such as flux-locked loop can't be adapted for a microwave SQUID multiplexer since individual feedback lines would have to be routed to each pixel. In contrast, modulation techniques such as flux ramp modulation provide a conceptually easy solution for linearizing the output signal of the multiplexer. In this contribution, we will first introduce the basic concept of flux ramp modulation. We will then discuss proof-of-principle as well as comprehensive characterization measurements for which we used customized dc-SQUIDs as well as a microwave SQUID multiplexer. Finally, we will outline present challenges as well as other applications where flux ramp modulation might significantly simplify the SQUID based readout.