Time-optimal processes for interacting spin systems

Reversible adiabatic processes connecting thermal equilibrium states are usually considered to be infinitely slow. Recently, fast reversible adiabatic processes for quantum systems have been discussed. Here we present time-optimal processes for a paradigmatic ensemble of two interacting spin-1/2 systems in an external magnetic field, which previously had been employed as working fluid in a quantum refrigerator. These processes are realized by appropriate bang-bang or quasi-bang-bang controls of the external magnetic field. Explicit control protocols including the necessary times for a transition connecting thermal equilibrium states depending on the limiting conditions on the magnetic field strength are presented.