Fluxon-Based Quantum Simulation in circuit QED

Long-lived fluxon excitations can be trapped inside a superinductor ring, which is realized by a long array of Josephson junctions, one of which offers the “input/output” path for the magnetic flux [1]. The ring can be separated into smaller loops by a periodic sequence of Josephson junctions in the quantum regime, thereby allowing fluxons to tunnel between neighboring sites of this Josephson ladder. By tuning the Josephson couplings, and implicitly the fluxon tunneling probability amplitudes, a wide class of 1D tight-binding lattice models could be implemented and populated with a stable number of fluxons. We illustrate the use of this quantum simulation platform by discussing the Su-Schrieffer-Heeger model [2] in the 1-fluxon subspace, which hosts a symmetry protected topological phase with fractionally charged bound states at the edges. This pair of localized edge states could be used to implement a superconducting qubit increasingly decoupled from decoherence mechanisms.
[1] N. A. Masluk et al., Phys. Rev. Lett. 109, 137002 (2012).
[2] W. P. Su et al., Phys. Rev. Lett. 42, 1698 (1979).