Topologically protected Bell-cat states in a simple spin model

We consider the topological properties of the so-called central spin model that consists of N identical spins coupled to a single distinguishable central spin that arises in physical systems such as circuit-QED and bosonic Josephson junctions coupled to an impurity atom. The model closely corresponds to the Su-Schrieffer-Heeger (SSH) model except that the chain of sites in the SSH model is replaced by a chain of states in Fock space specifying the magnetization. We find that the model accommodates topologically protected eigenstates that are "Bell-cat" states consisting of a Schrödinger cat state of the N spins that is maximally entangled with the central spin, and we show how this state can be adiabatically created and moved along the chain by driving the central spin. The Bell-cat states are visualized by plotting their Wigner function, and we explore their robustness against random noise by solving the master equation for the density matrix. We also explain the essential topological difference between identical spins and the excitations of a bosonic mode.