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Superconductivity is a result of quantum coherence at macroscopic scales. Two superconductors separated by a metallic or insulating weak link exhibit the AC Josephson effect: the conversion of a DC voltage bias into an AC supercurrent. This current may be used to activate mechanical oscillations in a suspended weak link, acting as an electromechanical resonator. As the DC voltage bias condition is remarkably difficult to achieve in experiments, here the experimentally relevant purely DC current bias case is analyzed thoroughly. It shall be demonstrated that the Josephson effect can be exploited to activate and detect mechanical oscillations, eliminating the need for AC bias conditions that are generally required for nanoelectromechanical systems (NEMS). The coupling between the electronic and mechanical degrees of freedom may be tuned by an external magnetic field, allowing the exploration of the Josephson effect in two distinct coupling regimes. In the weak coupling regime, Shapiro-like plateaus and mechanically induced hysteresis loops develop in the junction's current-voltage (I-V) characteristic which allow for precision measurements of the resonator's resonance frequency by simple DC voltage measurements. In contrast, in the strong coupling regime there are sudden mechanically induced transitions to a zero voltage state which will be explained by energy sharing between the electronic and mechanical degrees of freedom. These transitions are intimately linked to the mechanical damping of the resonator, and may be used to determine the junction's quality factor, again with only DC voltage measurements. It is further revealed that these sudden transitions may be eliminated by using a setup consisting of two suspended weak links connected in parallel forming a superconducting quantum interference device (SQUID), and tuning the external magnetic flux appropriately. Finally, the quantum nature of Josephson junctions is explored more thoroughly by considering Bloch-like oscillations that develop in the junction. These oscillations, when coupled to mechanical vibrations, generate non-classical mechanical states that are intimately linked to the quantum dynamics of the junction.

Josephson junctions (JJs) have become an integral component in superconducting electronics due to their non-linear response, sensitivity to magnetic fields and microwaves and the ability to generate high frequency electromagnetic radiation. This thesis investigates three phenomena of JJ arrays; the ratchet effect, flux flow resonances and Shapiro steps. A simulation model (which is similar to discrete Josephson transmission line) was used extensively to explore what consequence a) multiple array parameters such as the size of the superconducting loops separating the JJs, array spatial asymmetry, number of JJs in the array, structural fluctuations of the array due to imperfections of fabrication or intrinsic inhomogeneity of the Josephson critical current along the array; b) or junction parameters such as junction widths, junction critical currents; c) or finally thermal fluctuations due to the finite temperature of operation have on these three effects, as such this thesis is split into three parts. In the presence of an externally applied magnetic field, ratchet effects have been reproduced numerically in the current voltage characteristics (IVCs) of asymmetric JJ arrays. Firstly, the ratchet efficiency of several arrays was simulated and found that each array design has a unique pattern of efficiency which could be reversed and tuned by changing the applied magnetic field. Larger efficiencies could be achieved with larger numbers of JJs in the array. Larger arrays were able to withstand more amounts of noise than smaller arrays. Flux flow resonances have been reproduced numerically on the IVCs of the JJ arrays for multiple values of applied magnetic field. The derivatives (dI/dV) have been investigated in detail. The spatial asymmetry of the arrays has a large influence on the flux flow resonance produced by the JJ arrays, with each design producing a different pattern of resonances. The number of junctions in an array also has an effect on the resonances, the voltage location of smaller arrays show periodic oscillations with magnetic field whereas larger arrays do not, the resonance voltage and dI/dV locations increases to a maximum and levels out. Simulations also showed that the magnetic field around each insulating loop for larger arrays had distinct distribution around specific holes. Integer and fractional Shapiro steps were reproduced numerically on the IVCs of the JJ arrays. When analysing Shapiro steps, DC and AC magnetic field and / or AC current were applied. The voltage steps appeared in different preferences for steps with positive or negative voltages. It was found that larger steps were a result of the phase difference across the JJs being in phase with each other. An alternating magnetic field was applied to the arrays which produced similar steps caused by the induced current within the array. Combining both AC current and an alternating magnetic field resulted in pumping between the two effects leading to larger steps when the frequencies of both coincide. For the case of ratchet effects and flux flow resonances a detailed qualitive comparison was made with experimental data of JJ arrays made of yttrium barium copper oxide (YBCO).