TOPOCIRCUS · Simulations of Topological Phases in Superconducting Circuits

Simulations of Topological Phases in Superconducting Circuits

The goals of the TOPOCIRCUS project is to view a superconducting circuit as a playground where novel topological phases of matter can be engineered and simulated. A topological phase is characterized by a Hamiltonian whose typically low energy eigenstates has a non-local character, so that they are insensitive to local perturbations. Objective i) Simulation of topological phases in two-terminal Josephson circuits Objective ii) Search for new fermions in multi-terminal Josephson junctions One of the main ideas of the present Marie Curie action proposal is to simulate topological states of matter with superconducting circuits. In the proposed Objectives i) and ii) of the present TOPOCIRCUS project specific mention is made of the possibility to engineer the spectrum of a superconducting circuits in such a way that it contains bulk topologically non-trivial features. The achievement of such a goal had to go through singling out what are the possible players that can be exploited for engineering the Josephson potential. Any superconducting circuit is generically described by a charging energy, that is a quadratic form in the charges on the islands, and the Josephson potential, that is periodic on the phase. All properties of superconducting circuits depends on the details of the Josephson potential. The main change of speed in the project occurred when realizing that some complicate circuits can effectively show a π-periodicity with respect to the typical 2π-periodicity in the phase difference, that opened up completely novel possibilities. We managed to accomplish the goals of Objective i) and ii) in an excellent way by showing how groups of flat bands can be engineered by tailoring the Josephson potential and exploiting the achievement to enhance coherence. The TOPOCIRCUS project ended mid September 2022. The main result of the project is the identification of π-periodic Josephson junction as a novel element in superconducting circuits that allows augmented freedom of manipulation of the Josephson potentials and enhanced coherence of superconducting qubits. Coupling to Majorana qubit shows also full versatility of parity-protected superconducting qubits based on π-periodic Josephson junction. In addition the spectrum of a π-periodic qubit realizes a SSH topological model, that is one of the main goals of the present TOPOCIRCUS projects.

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