Effects of Current-Phase Relationship on SFQ Pulses

The Current-Phase Relation (CΦR) of Josephson junctions (JJs) is typically assumed to be sinusoidal, but this is not always the case. For any type of JJ, the CΦR is only required to be 2π periodic and an odd function of phase. Therefore, physics allows many possible non-sinusoidal CΦRs. We will show that incorporating JJs with non-sinusoidal CΦRs into an SFQ circuit changes the shape and timing of the pulses. Therefore, understanding the CΦR and its effects on junction behavior is necessary for accurate modeling of SFQ circuits. For JJs with tunable barrier parameters, such as the Nb_xSi_1-x barriers used at NIST, this could eventually lead to the optimization of the CΦR to improve circuit performance. We are performing indirect measurements of the CΦR of JJs with insulating and normal-metal barriers by incorporating the test junction into an RF-SQUID coupled via mutual inductance to a DC-SQUID magnetometer. By measuring the CΦR, it is possible to use this information to optimize the bias current and circuit parameters of single flux quantum (SFQ) circuits.