Quantum Interference Effects on Josephson Current through Quadruple-Quantum-Dot Molecular Inserted between Superconductors

We study theoretically the Josephson current through a junction composed of quadruple quantum dots (QDs), of which only one is coupled directly to the left and right superconductor leads (denoted by QD1). The other three QDs are side-coupled to QD1 and free from coupling to the leads. It is found that when the energy levels of all the four QDs are identical, the Josephson current varying with energy level of QD1 develops three peaks with two narrow and one wide, showing the typical Dicke lineshape. With increasing inter-dot coupling strength, the triple-peak configuration is well retained and accompanied by an obviously increased current amplitude. The critical current as a function of the energy level of QD1 shows a single resonance peak whose position and height depend on the energy levels of the side-coupled QDs and the inter-dot coupling strengths. We also find that the curve of the critical current versus energy levels of the side-coupled QDs shows a pair of Fano resonances and the same number Fano antiresonances (valleys). When the energy levels of the side-coupled QDs are different from each other, another Fano resonance and antiresonance are induced due to the quantum interference effect. The present results are compared with those in double and triple QDs systems, and may serve as unique means, such as the combination of quantum Dicke and Fano effects, to manipulate the Josehpson currents.