Soliton versus single photon quantum dynamics in arrays of superconducting qubits

TL;DR

This paper explores the dynamics of bright solitons versus single-photon transport in superconducting qubit arrays, revealing how solitons can be pinned and move while maintaining shape, with implications for quantum simulation.

Contribution

It demonstrates the existence and behavior of bright solitons in superconducting qubit arrays and contrasts their dynamics with photon transport, providing new insights into many-body quantum states.

Findings

Bright solitons can be pinned and move maintaining their shape.

Soliton velocity scales with interaction strength and number of bosons.

Photon transport occurs via extended states with higher energy than solitons.

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 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.