We present a simple model for multiphoton transitions between the quasi-bound states of a current-driven Josephson junction. The transitions are induced by applying an ac voltage with controllable frequency and amplitude across the junction. The voltage induces transitions when the ac frequency equals n times the splitting between the ground and first excited quasi-bound state of the junction. We calculate the transition matrix elements as functions of the dc bias current I, and the frequency and amplitude of the ac voltage, for representative junction parameters. We also calculate the frequency-dependent absorption coefficient by solving the relevant Bloch equations when the ac amplitude is sufficiently small. In this regime, the absorption coefficient is a sum of Lorentzian lines centered at the n-photon absorption frequency, of strength proportional to the squared matrix elements. For fixed ac voltage amplitude, the n-photon transition rate usually decreases with increasing n. We also find a characteristic even-odd effect: The absorption coefficient typically increases with I for n even but decreases for n odd. Our results agree qualitatively with recent experiments.Comment: 15 pages, 13 figures, accepted for publication in Physical Review

We present a model to describe an underdamped long Josephson junction coupled to a single-mode electromagnetic cavity, and carry out numerical calculations using this model in various regimes. The coupling may occur through either the electric or the magnetic field of the cavity mode. When a current is injected into the junction, we find that the time-averaged voltage exhibits self-induced resonant steps ͑SIRSs͒ due to coupling between the current in the junction and the electric field of the cavity mode. These steps are similar to those observed and calculated in small Josephson junctions. When a soliton is present in the junction ͑corresponding to a quantum of magnetic flux parallel to the junction plates͒, the SIRSs disappear if the electric field in the cavity is spatially uniform. If the cavity mode has a spatially varying electric field, there is a strong coupling between the soliton and the cavity mode. This coupling causes the soliton to become phase locked to the cavity mode, and produces steplike anomalies on the soliton branch of the I-V characteristics. If the coupling is strong enough, the frequency of the cavity mode is greatly redshifted from its uncoupled value. We present simple geometrical arguments which account for this behavior.

Very anisotropic cuprate superconductors, such as BiSr 2 Ca 2 CuO 8ϩx , when driven by currents parallel to the c axis, behave like stacks of underdamped Josephson junctions. Here, we analyze the possibility that such a stack can be caused to phase lock, to exhibit self-induced resonant voltage steps ͑SIRS's͒, and hence to radiate coherently when placed in a suitable resonant electromagnetic cavity. We analyze this possibility using equations of motion developed to describe such SIRS's in stacks of artificial Josephson junctions. We conclude that such steps might be observable with a suitably chosen cavity and resonant frequency.

A zigzag boundary between a d x 2 −y 2 and an s-wave superconductor is believed to behave like a long Josephson junction with alternating sections of 0 and π symmetry. We calculate the fielddependent critical current of such a junction, using a simple model. The calculation involves discretizing the partial differential equation for the phase difference across a long 0-π junction. In this form, the equations describe a hybrid ladder of inductively coupled small 0 and π resistively and capacitively shunted Josephson junctions (RCSJ's). The calculated critical critical current density J c (H a ) is maximum at non-zero applied magnetic field H a , and depends strongly on the ratio of Josephson penetration depth λ J to facet length L f . If λ J /L f ≫ 1 and the number of facets is large, there is a broad range of H a where J c (H a ) is less than 2% of the maximum critical current density of a long 0 junction. All of these features are in qualitative agreement with recent experiments. In the limit λ J /L f → ∞, our model reduces to a previously-obtained analytical superposition result for J c (H a ). In the same limit, we also obtain an analytical expression for the effective field-dependent quality factor Q J (H a ), finding that Q J (H a ) ∝ J c (H a ). We suggest that measuring the field-dependence of Q J (H a ) would provide further evidence that this RCSJ model applies to a long 0-π junction between a d-wave and an s-wave superconductor.

We show numerically that, in a Josephson ladder with periodic boundary conditions and subject to a suitable transverse magnetic field, a vortex excitation can spontaneously breakup into two or more fractional excitations. If the ladder has N plaquettes, and N is divisible by an integer q, then in an applied transverse field of 1/q flux quanta per plaquette the ground state is a regular pattern of one fluxon every q plaquettes. When one additional fluxon is added to the ladder, it breaks up into q fractional fluxons, each carrying 1 / q units of vorticity. The fractional fluxons are basically walls between different domains of the ground state of the underlying 1 / q lattice. The fractional fluxons are all depinned at the same applied current and move as a unit. For certain applied fields and ladder lengths, we show that there are isolated fractional fluxons. It is shown that the fractional fluxons would produce a time-averaged voltage related in a characteristic way to the ac voltage frequency.