Protocols for cooling with reservoirs strongly coupled to a system

In conventional theories of reservoirs coupled to systems, the reservoir is infinitely large and couples with an infinitesimally small coupling to the system. This allows it to exchange energy without modifying the properties of the system, ultimately leading to thermal equilibrium. In quantum computing, we would like to design cooling qubits that rapidly cool a system. But, because we only have a small number of qubits available, we must couple the reservoir strongly to the system. An ion-trap simulator is ideal for examining this behavior. We consider the ions at the end as the reservoir and the ions in the center as the system. It is a transverse-field Ising model with long-range interactions, which creates a strongly coupled reservoir-system. Our protocol is to start the bath sites in a low-energy state, wait, and then reset them back to a low-energy state at specific times. We show that this procedure makes the middle system reach close to its ground state. The efficiency of such cooling strongly depends on the reset rate and the strength of the system-bath coupling. By looking into the average of the spin, both along the Ising coupling direction and along the field direction, we can optimally predict the reset times in order to evolve the system closer to the ground state.