Signatures for Generalized Macroscopic Superpositions

We develop criteria sufficient to enable detection of macroscopic coherence where there are not just two macroscopically distinct outcomes for a pointer measurement, but rather a spread of outcomes over a macroscopic range. The criteria provide a means to distinguish a macroscopic quantum description from a microscopic one based on mixtures of microscopic superpositions of pointer-measurement eigenstates. The criteria are applied to Gaussian-squeezed and spin-entangled states.

Figure 1

Probability distribution for a measurement $O$ which gives three distinct regions of outcome: 0, $-1$, and $+1$.

Figure 2

Violation of (9) [and (10)] for single- (and two-mode) squeezed minimum uncertainty states. Inset shows behavior for general Gaussian-squeezed states. The maximum $S/\Delta x$ giving violation of (9) [and (10)] is plotted versus $\Delta x\Delta p$ (replace $\Delta p$ with ${\Delta }_{\inf }p$ for the two-mode case).