Quantum State Orthogonalization and a Toolset for Quantum Optomechanical Phonon Control

TL;DR

This paper presents a versatile method for orthogonalizing any pure continuous variable quantum state and demonstrates its application in optomechanical systems for advanced quantum state engineering.

Contribution

It introduces a general orthogonalization technique applicable to various quantum systems and develops a set of phonon operations for mechanical oscillator state control.

Findings

Orthogonalization method does not require prior knowledge of the input state.

Application of the method to cavity optomechanics enables control over mechanical quantum states.

The approach allows transformation of any pure state into any target state.

Abstract

We introduce a method that can orthogonalize any pure continuous variable quantum state, i.e. generate a state $|\psi_\perp>$ from $|\psi>$ where $<\psi|\psi_\perp> = 0$, 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.