Experimental demonstration of the interferometric complementarity of one- and two-particle interference in a bulk Nuclear Magnetic Resonance ensemble

Abstract

We analyze an interferometric complementarity between one- and two-particle interference in the general case: $V_i^2+V_{12}^2\le 1$ $(i=1$, $2)$, and further examine the relation among one-particle interference visibility $V_i$, two-particle interference visibility $V_{12}$ and the predication $P_i$ of the path of a single particle. An equality $V_i^2+V_{12}^2+P_i^2=1$ $(i=1$, $2)$ is achieved for any pure two-particle source, which implies the condition of the complementarity relation to reach the upper bound and its relation to another interferometric complementarity between path information and interference visibility of a single particle. Meanwhile, the relationships of the complementarities and the entanglement $E$ of the composite system are also investigated. Using nuclear magnetic resonance techniques, the two-particle interferometric complementarity was experimentally tested with the ensemble-averaged spin states, including two extreme cases and an intermediate case.

8 pages, 4 PS figures