Experimental realization of quantum state engineering with single photons

Fully controlling the transformation of an arbitrary quantum state to a predesigned state is a crucial technology in quantum information processing. Despite numerous efforts in pursuit of this objective, a truly viable method remains elusive. Here we successfully devise an experiment capable of engineering any state on the Bloch sphere to a predetermined target state. To validate our findings, we choose different initial states to evolve and compare the purity and fidelity of the evolved state with the target state. Furthermore, we investigate the relationship between the steering speed and the spectrum of the Liouvillian superoperator, proposing an approach to speed up the steering process. Notably, we observe that setting system parameters at the Liouvillian exceptional point (LEP) leads to the fastest evolution to the steady state. In cases without an LEP, a larger Liouvillian gap corresponds to quicker convergence to the steady state. Our method introduces a different avenue for studying Liouvillian dynamics in open quantum systems and provides a practical means for state manipulation.