Experimental Demonstration of Direct Path State Characterization by Strongly Measuring Weak Values in a Matter-Wave Interferometer

A method was recently proposed and experimentally realized for characterizing a quantum state by directly measuring its complex probability amplitudes in a particular basis using so-called weak values. Recently, Vallone and Dequal [Phys. Rev. Lett. 116, 040502 (2016)] showed theoretically that weak measurements are not a necessary condition to determine the weak value. Here, we report a measurement scheme used in a matter-wave interferometric experiment in which the neutron path system’s quantum state was characterized via direct measurements, using both strong and weak interactions. Experimental evidence is given that strong interactions outperform weak ones for tomographic accuracy. Our results are not limited to neutron interferometry, but can be used in a wide range of quantum systems.

Figure 1

Schematic drawing of the neutron interferometer setup implementing spin polarization.

Figure 2

Interference fringes of the weak measurement ($\alpha =15°$) on the left side and those of the strong measurement ($\alpha =90°$) on the right side. The directions of spin analysis $\pm x$, $\pm y$, and $\pm z$ are shown in the top, middle, and bottom rows, respectively. The solid and dashed lines show the least square fits for the $+$ and—analysis directions, respectively. The error bars show one standard deviation. The background has already been subtracted from all interferograms.

Figure 3

Measurement results for the path state vector for both the weak ($\alpha =15°$) and the strong measurement ($\alpha =90°$) cases: The error bars show one standard deviation. The solid lines are the theoretical predictions.