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 |ψ (perpindicular)} from |ψ} where {ψ|ψ(perpindicular)}= 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.