Criteria for generalized macroscopic and mesoscopic quantum coherence

Abstract

We consider macroscopic, mesoscopic and "S-scopic" quantum superpositions of eigenstates of an observable, and develop some signatures for their existence. We define the extent, or size $S$ of a superposition, with respect to an observable \hat{x}, as being the range of outcomes of \hat{x} predicted by that superposition. Such superpositions are referred to as generalized $S$-scopic superpositions to distinguish them from the extreme superpositions that superpose only the two states that have a difference $S$ in their prediction for the observable. We also consider generalized $S$-scopic superpositions of coherent states. We explore the constraints that are placed on the statistics if we suppose a system to be described by mixtures of superpositions that are restricted in size. In this way we arrive at experimental criteria that are sufficient to deduce the existence of a generalized $S$-scopic superposition. The signatures developed are useful where one is able to demonstrate a degree of squeezing. We also discuss how the signatures enable a new type of Einstein-Podolsky-Rosen gedanken experiment.

15 pages, accepted for publication in Phys. Rev. A

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• Quantifying the mesoscopic quantum coherence of approximate NOON states and spin-squeezed two-mode Bose-Einstein condensates
• Creation, storage and retrieval of an optomechanical cat state
• Two-mode squeezed states as Schrodinger-cat-like states
• Demonstrating mesoscopic superpositions in double-well Bose-Einstein condensates
• Full multipartite steering inseparability, genuine multipartite steering and monogamy for continuous variable systems
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• Testing macroscopic local realism using cat-states and Bell inequalities in time
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• General measure for macroscopic quantum states beyond "dead and alive"
• Weak versus deterministic macroscopic realism, and Einstein-Podolsky-Rosen's elements of reality
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• Macroscopic quantumness of optically conditioned mechanical systems