Symmetry restoring and ancilla-driven entanglement for ultra-cold spin-1 atoms in a three-site ring

The spin-change dynamics of a model with ultra-cold hyperfine-spin-1 atoms confined in an optical superlattice is discussed. First, the disturbance of the two-site dynamics by coupling the dimer to a spin-1 ancilla is analyzed. When the dimer is coupled to the ancilla, even by a weak coupling, the significant changes in the system’s time-evolution processes are observed. Next, we show that for the two-particle case the total hyperfine-spin-singlet state is generated by exploiting a quadratic Zeeman shift with realistic values of the strength of external magnetic field and evolution period of time. Moreover, even in a weak coupling regime, the proper choice of the additional ancilla–dimer interaction results in generating the wave function which is characteristic of the homogeneous three-site ring. In consequence, such wave function exhibits translational invariance symmetry despite the strong asymmetry of the lattice. Furthermore, we present our proposal for extracting various kinds of maximally entangled states (MES) for three-site spin-1 systems, starting from initial product states. In particular, we show that the type of generated MES can be unambiguously recognized by the measurement performed on the ancilla.