Dissipation-Assisted Steady-State Entanglement Engineering based on Electron Transfer Models

We propose a series of dissipation-assisted entanglement generation protocols that can be implemented on a trapped-ion quantum simulator. Our approach builds on the single-site molecular electron transfer (ET) model recently realized in the experiment [So et al. Sci. Adv. 10, eads8011 (2024)]. This model leverages spin-dependent boson displacement and dissipation controlled by sympathetic cooling. We show that, when coupled to external degrees of freedom, the ET model can be used as a dissipative quantum control mechanism, enabling the precise tailoring of both spin and phonon steady state of a target sub-system. We derive simplified analytical formalisms that offer intuitive insights into the dissipative dynamics. Using realistic interactions in a trapped-ion system, we develop a protocol for generating $N$-qubit and $N$-boson $W$ states. Additionally, we generalize this protocol to realize generic $N$-qubit Dicke states with tunable excitation numbers. Finally, we outline a realistic experimental setup to implement our schemes in the presence of noise sources.