Abstract
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.
Highlights
We introduce a method that can orthogonalize any pure continuous variable quantum state, i.e., generate a state jc ?i from jc i where hc jc ?i 1⁄4 0, which does not require significant a priori knowledge of the input state
In this Letter, we introduce a method for quantum state orthogonalization for continuous variable quantum systems
Our method is readily extended to generate an arbitrary superposition of the initial state and an orthogonal counterpart to allow the encoding of quantum information
Summary
We introduce a method that can orthogonalize any pure continuous variable quantum state, i.e., generate a state jc ?i from jc i where hc jc ?i 1⁄4 0, which does not require significant a priori knowledge of the input state. Our method is readily extended to generate an arbitrary superposition of the initial state and an orthogonal counterpart to allow the encoding of quantum information. Optical [8] or microwave [9] fields in a cavity, or the motional state of trapped ions [10] can be orthogonalized by appropriately setting A and B.
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