Controlled engineering of desired pure and mixed atomic quantum states is a problem of central interest for knowing the fundamental limits to control quantum systems as well as for practical applications in measurements and in quantum computing with mixed states. We will discuss a method for engineering arbitrary pure and mixed quantum states using a special combination of coherent and incoherent lights. The method is deterministic and realizes the strongest possible degree of quantum state control --- complete density matrix controllability meaning the ability to steer arbitrary pure and mixed initial states into any desired pure or mixed state.

Reference: A.N. Pechen, Engineering arbitrary pure and mixed quantum states. Phys. Rev. A, 84, 042106 (2011).