Quantum State Orthogonalization and a Toolset for Quantum Optomechanical Phonon Control

We introduce a method that can orthogonalize any pure continuous variable quantum state, i.e., generate a state vertical bar psi(perpendicular to)> from vertical bar psi > where = 0, which does not require significant a priori knowledge of the input state. We illustrate how to achieve orthogonalization using the Jaynes-Cummings or beamsplitter interaction, which permits realization in a number of physical systems. Furthermore, we demonstrate how to orthogonalize the motional state of a mechanical oscillator in a cavity optomechanics context by developing a set of coherent phonon level operations. As the mechanical oscillator is a stationary system, such operations can be performed at multiple times providing considerable versatility for quantum state engineering applications. Utilizing this, we additionally introduce a method how to transform any known pure state into any desired target state. DOI: 10.1103/PhysRevLett.110.010504