Soliton versus single-photon quantum dynamics in arrays of superconducting qubits

Abstract

Superconducting circuits constitute a promising platform for future implementation of quantum processors and simulators. Arrays of capacitively coupled transmon qubits naturally implement the Bose-Hubbard model with attractive on-site interaction. The spectrum of such many-body systems is characterized by low-energy localized 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 or drain and the array, the populations of the source and drain oscillate in time; for chains of even length, their population remains low at all times, while it can reach half the number of total bosons in odd chains. Implications of our results for actual experimental realizations are discussed.