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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Signatures for generalized macroscopic and S-scopic superpositions

M. D. Reid, Eric G. Cavalcanti

Published Jun 1, 2007• 0 citations
Publisher

Abstract

We develop experimental signatures for generalized macroscopic, mesoscopic and S-scopic quantum superpositions. We also examine the extent to which current experiments confirm their existence, and propose new measurements to further signify them. The size S of a quantum superposition (or pure state), with respect to the observable X, is defined as the maximum range in predictions for the observable X. We also define and consider generalized 5-scopic superpositions of coherent states.

DOI
10.1109/cleoe-iqec.2007.4386774

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We develop experimental signatures for generalized macroscopic, mesoscopic and S-scopic quantum superpositions. We also examine the extent to which current experiments confirm their existence, and propose new measurements to further signify them. The size S of a quantum superposition (or pure state), with respect to the observable X, is defined as the maximum range in predictions for the observable X. We also define and consider generalized 5-scopic superpositions of coherent states.
We consider macroscopic, mesoscopic, and ``SSS-scopic'' quantum superpositions of eigenstates of an observable and develop some signatures for their existence. We define the extent, or size SSS of a superposition, with respect to an observable $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{x}$, as being the range of outcomes of $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{x}$ predicted by that superposition. Such superpositions are referred to as generalized SSS-scopic superpositions to distinguish them from the extreme superpositions that superpose only the two states that have a difference SSS in their prediction for the observable. We also consider generalized SSS-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 SSS-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.
Recent experiments claiming the formation of quantum superposition states in near-macroscopic systems raise the question of how the sizes of general quantum superposition states in an interacting system are to be quantified. We propose here a measure of size for such superposition states that is based on what measurements can be performed to probe and distinguish the different branches of the state. The measure allows the comparison of the effective size for superposition states in very different physical systems. It can be applied to a very general class of superposition states and reproduces known results for near-ideal cases. Comparison with a prior measure based on analysis of coherence between branches indicates that significantly smaller effective superposition sizes result from our measurement-based measure. Application to a system of interacting bosons in a double-well trapping potential shows that the effective superposition size is strongly dependent on the relative magnitude of the barrier height and interparticle interaction.
I present the motivation for experiments which attempt to generate, and verify the existence of, quantum superpositions of two or more states which are by some reasonable criterion ‘macroscopically’ distinct, and show that various a priori objections to this programme made in the literature are flawed. I review the extent to which such experiments currently exist in the areas of free-space molecular diffraction, magnetic biomolecules, quantum optics and Josephson devices, and sketch possible future lines of development of the programme.
I present the motivation for experiments which attempt to generate, and verify the existence of, quantum superpositions of two or more states which are by some reasonable criterion `macroscopically' distinct, and show that various a priori objections to this programme made in the literature are flawed. I review the extent to which such experiments currently exist in the areas of free-space molecular diffraction, magnetic biomolecules, quantum optics and Josephson devices, and sketch possible future lines of development of the programme.