Abstract
We develop a theory to address the non equilibrium dynamics of phonons in a one-dimensional finite size trapped ion system for non linear ramp and periodic protocols. Our analysis, which is based on our earlier proposal of dynamics-induced cooling and entanglement generation between phonons in these systems when subjected to a linear ramp protocol [], identifies the optimal protocol within the above-mentioned classes, which minimizes both the cooling and entanglement generation time. We also introduce single-/two-site addressing to achieve cooling/entanglement, which is expected to lead to simpler implementation of these protocols. Finally, we discuss the effect of noise due to the fluctuation of the intensity of the laser used to generate the trap on entanglement generation. We also discuss realistic experimental setups that may serve as test beds for our theory.
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