Noise limits for dc SQUID readout of high-$Q$ resonators below 300 MHz

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We present the limits on noise for the readout of cryogenic high-$Q$ resonators using dc Superconducting Quantum Interference Devices (SQUIDs) below 300 MHz.

• This analysis uses realized first-stage SQUIDs (previously published), whose performance is well described by Tesche-Clarke (TC) theory, coupled directly to the resonators.
• We also present data from a prototype second-stage dc SQUID array designed to couple to this first-stage SQUID as a follow-on amplifier with high system bandwidth.
• This analysis is the first full consideration of dc SQUID noise performance referred to a high-$Q$ resonator over this frequency range, and is presented relative to the standard quantum limit.