Spectrally controlled dissipation in a target subsystem

We present a microscopic Hamiltonian time-evolution on an ancilla+target system that evolves the target to a steady state. Using this description, we demonstrate the potential of a spectrally controllable dissipator: Depending on the energy scale of the target, the subsystem reaches the intended steady state or remains partially trapped in the initial state. For a steady state which is pure, this protocol can function as an autonomous qubit reset. We can also choose a mixed steady state so that this functions as a tunable mixed-state preparation. With a particular dissipative condition, we guarantee the equilibration to the steady-state with spectral measure theory. This type of spectral control over dissipation is not present in the common Lindblad description of open systems. Our construction establishes a new design principle for engineered dissipation and opens a pathway toward tunable autonomous quantum control.