Cooling of many-body systems via selective interactions

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 2N-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.