Global stabilization at arbitrary eigenstates of N-dimensional quantum spin systems via continuous feedback

In this paper, we deal with a stabilization problem on quantum spin systems in general dimensions. The spin systems are supposed under continuous measurement by mutual interference with laser beams and a magnetic field is applied for control. The quantum states of spin systems can be estimated by quantum filtering and the intension of the magnetic field is controlled according to the estimation. We show that the global stabilization at arbitrary eigenstates of the spin systems is possible by continuous control inputs. Our proposing control input is the sum of two terms: a term which attracts the quantum states to an objective eigenstate and the other term which draws apart from the other equilibrium points. We also demonstrate the results by a numerical simulation.