Deterministic ratchet effect in asymmetric d.c. SQUIDs

The dynamical equations for the superconducting phase differences of a conventional d.c. SQUID in the presence of small structural asymmetry and coupling energy inhomogeneity can be studied by means of a reduced two-junction interferometer model. In this context, the resulting dynamics can be described by a single first-order nonlinear differential equation, in which adjustable parameters are present. As a consequence, a ratchet-like potential can be obtained for a convenient choice of parameters. We show, in a zero thermal noise case, that asymmetric d.c. SQUIDs can operate as voltage rectifiers under an external deterministic a.c. signal. Average voltage quantization in the I-V characteristics of the device can be observed as an effect of phase-locking mechanisms. Analytic expressions for the constant voltage steps appearing in the I-V characteristics can be found as a function of the bias current and of the a.c. amplitude of the forcing term.