We propose a model describing $N$ spin-1/2 systems coupled through $N$-order homogeneous interaction terms, in the presence of local time-dependent magnetic fields. This model can be experimentally implemented with current technologies in trapped ions and superconducting circuits. By introducing a chain of unitary transformations, we succeed in exactly converting the quantum dynamics of this system into that of $2^{N-1}$ fictitious spin-1/2 dynamical problems. We bring to light the possibility of controlling the unitary evolution of the $N$ spins generating Greenberger-Horne-Zeilinger states under specific time-dependent scenarios. Moreover, we show that by appropriately engineering the time dependence of the coupling parameters, one may choose a specific subspace in which the $N$-spin system dynamics takes place. This dynamical feature, which we call time-dependent selective interaction, can generate a cooling effect of all spins in the system.

• Received 1 August 2018

DOI:https://doi.org/10.1103/PhysRevA.98.042330