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 $|ψ_\perp>$ from $|ψ>$ where $<ψ|ψ_\perp> = 0$, which does not require significant a priori knowledge of the input state. We illustrate how to achieve orthogonalization using the Jaynes-Cummings or beam-splitter interaction, which permits realization in a number of 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.

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