Macroscopicity of quantum superposition

Abstract

In this paper, we define a universal measure of macroscopicity ${\hat{I}}^2$ in the form of, ({\em experimentally observed coherence time})/({\em characteristic time required to repeatably distinguish the components of a quantum superposition state}), to divide the quantum/classical (Q-C) boundary. The analysis shows that, for a matter-wave interferometer, covering systems from electron to macromolecular, the measure of its macroscopicity is expressed by ${\hat{I}}^2=p\hat{I}¸d/8\hslash$, and it consistently yields ${\hat{I}}^2<1$ by investigating the coherence data reported in the literature. The result implies that limited advancement has been made toward exploring the Q-C boundary in such experiments. Additionally, for a Ramsey-like interferometer, the measure of its macroscopicity is expressed as ${\hat{I}}^2=8\ddot{I}{€}^3\hat{I}\pm \hat{I}{½}_0{r}_s^2\hat{I}{½}_s^{2}T/(9c^2)$. After analyzing the reported experimental data, we find that a maximum value of ${\hat{I}}^2\sim 300$ is achieved in the vertical atomic fountain experiments. Therefore, searching the Q-C boundary in the atomic fountain may be a more proper direction.

18 pages, 3 figures, 2 tables