Superconducting circuits constitute a promising platform for future implementation of quantum processors and simulators. Arrays of capacitively coupled transmon qubits naturally implementthe Bose-Hubbard model with attractive on-site interaction. The spectrum of such many-body systems is characterised by low-energy localised states defining the lattice analog of bright solitons. Here, we demonstrate that these bright solitons can be pinned in the system, and we find that a soliton moves while maintaining its shape. Its velocity obeys a scaling law in terms of the combined interaction and number of constituent bosons. In contrast, the source-to-drain transport of photons through the array occurs through extended states that have higher energy compared to the bright soliton. For weak coupling between the source/drain and the array, the populations of the source and drain oscillate in time, with the chain remaining nearly unpopulated at all times. Such a phenomenon is found to be parity dependent. Implications of our results for the actual experimental realisations are discussed.
Designing the spatial profile of the superconducting gap – gap engineering – has long been recognized as an effective way of controlling quasiparticles in superconductingdevices. In aluminum films, their thickness modulates the gap; therefore, standard fabrication of Al/AlOx/Al Josephson junctions, which relies on overlapping a thicker film on top of a thinner one, always results in gap-engineered devices. Here we reconsider quasiparticle effects in superconducting qubits to explicitly account for the unavoidable asymmetry in the gap on the two sides of a Josephson junction. We find that different regimes can be encountered in which the quasiparticles have either similar densities in the two junction leads, or are largely confined to the lower-gap lead. Qualitatively, for similar densities the qubit’s excited state population is lower but its relaxation rate higher than when the quasiparticles are confined; therefore, there is a potential trade-off between two desirable properties in a qubit.
Heat management and refrigeration are key concepts for nanoscale devices operating at cryogenic temperatures. The design of an on-chip mesoscopic refrigerator that works thanks to theinput heat is presented, thus realizing a solid state implementation of the concept of cooling by heating. The system consists of a circuit featuring a thermoelectric element based on a ferromagnetic insulator-superconductor tunnel junction (N-FI-S) and a series of two normal metal-superconductor tunnel junctions (SINIS). The N-FI-S element converts the incoming heat in a thermovoltage, which is applied to the SINIS, thereby yielding cooling. The cooler’s performance is investigated as a function of the input heat current for different bath temperatures. We show that this system can efficiently employ the performance of SINIS refrigeration, with a substantial cooling of the normal metal island. Its scalability and simplicity in the design makes it a promising building block for low-temperature on-chip energy management applications.