Near-Quantum-Limited SQUID Amplifier

The SET (Single-Electron Transistor), which detects charge, is the dual of the SQUID (Superconducting QUantum Interference Device), which detects flux. In 1998, Schoelkopf and co-workers introduced the RFSET, which uses a resonance circuit to increase the frequency response to the 100-MHz range. The same year saw the introduction of the Microstrip SQUID Amplifier$^{1}$ (MSA) in which the input coil forms a microstrip with the SQUID washer, thereby extending the operating frequency to the gigahertz range. I briefly describe the theory of SQUID amplifiers involving a tuned input circuit with resonant frequency f. For an optimized SQUID at temperature T, the power gain and noise temperature are approximately G = f$_{p}$/$\pi $f and T$_{N}$ = 20T(f/f$_{p})$, respectively; f$_{p}$ is the plasma frequency of one of the Josephson junctions. Because the SQUID voltage and current noise are correlated, however, the optimum noise temperature is at a frequency below resonance. For a phase-preserving amplifier, T$_{N}$ = ($\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} $ + A)hf/k$_{B}$, where Caves' added noise number A = $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} $ at the quantum limit. Simulations based on the quantum Langevin equation (QLE) suggest that the SQUID amplifier should attain A = $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} $. We have measured the gain and noise of an MSA in which the resistive shunts of the junctions are coupled to cooling fins to reduce hot electron effects. The minimum value A = 1.1 $\pm $ 0.2 occurs at a frequency below resonance. On resonance, the value A = 1.5 $\pm $ 0.3 is close to the predictions of the QLE, suggesting that this model may fail to predict the cross-correlated noise term correctly. Indeed, recent work suggests that a fully quantum mechanical theory is required to account properly for this term$^{2}$. This work is in collaboration with D. Kinion and supported by DOE BES. $^{1}$M. Mueck, \textit{et al}., \textit{Appl. Phys. Lett.} \textbf{72}, 2885 (1998). $^{2}$A. Clerk, \textit{et al.,} http://arxiv.org/abs/0810.4729.