Mobile Topological Su-Schrieffer-Heeger Soliton in a Josephson Metamaterial

Circuits involving arrays of Josephson junctions have emerged as a new platform for exploring and simulating complex bosonic systems. Motivated by this advance, we develop and theoretically analyze a one-dimensional bosonic system with sublattice symmetry, a bosonic Su-Schrieffer-Heeger (SSH) model in this work. The system features electrostatically controlled topological mid-gap states that we call soliton states. We propose spectroscopy to detect the presence of these states using local spectroscopy or admittance. We develop a protocol to adiabatically shuttle the position of these topological soliton states using local electrostatic gates. We demonstrate a nearly perfect fidelity of soliton shuttling for timescales within experimental reach. The fast and efficient manipulation of soliton defect states can be utilized for implementing robust mesoscopic qubits and racetrack-type quantum memories.