Vibrational superposition states without rotating wave approximation

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Abstract
We propose a scheme to generate superpositions of coherent states for the vibrational motion of a laser-cooled trapped ion. It is based on the interaction with a standing wave making use of the counter-rotating terms, i.e. not applying the rotating wave approximation. We also show that the same scheme can be exploited for quantum state measurement, i.e. with the same scheme non-classical states may be reconstructed.
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