Anomalous switching curves in a dc SQUID phase qubit

We have measured switching curves (s-curves), Rabi oscillations (T'$\sim $160ns) and relaxation (T$_{1}\sim $280ns) in a dc SQUID phase qubit with an LC filter that provides good isolation from the bias leads at the operating frequency (3.5 GHz). The device is built on sapphire and has a 2 $\mu $m$^{2}$ Al/AlO$_{x}$/Al qubit junction shunted by a low-loss SiN$_{x}$ capacitor. To measure an s-curve, we apply microwaves to pump to a specific state and then find the probability that the device switches to the voltage state after a short ($\sim $2ns) current pulse is applied. As expected, the switching probability increases with the amplitude of the current pulse, is smallest in the ground state $\vert $0$>$ and largest in the excited state $\vert $1$>$. However, the s-curves for superposition states of $\vert $0$>$ and $\vert $1$>$ are anomalous - they are not the weighted sum of the $\vert $0$>$ and $\vert $1$>$ s-curves and the probability to switch is not linear in the excited state probability. Instead, the s-curves shift continuously along the current axis as the amplitude to be in $\vert $1$>$ increases. We will discuss the likely cause of this behavior and its implication for measurements in phase qubits.