Asking Neutrons where they have been

Abstract

Based on the results of Vaidman’s photonic three-path interferometer experiment with weak path marking [A. Danan, D. Farfurnik, S. Bar-Ad, and L. Vaidman, Phys. Rev. Lett. 111, 240402 (2013)] the authors claim that the photons have discontinuous particle trajectories. Here, we present a neutron optical version of the experiment by Danan et al., where in various beam paths of the interferometer the energy of the neutrons is slightly shifted. This is achieved by using resonance-frequency spin-rotators (SR) operating at different frequencies. The which-way information is derived from the time-dependent intensity, which is considered to result from the interfering cross terms between the stationary main component and the energy-shifted which-way signals. Our statements are based on a simple theoretical model, following the time evolution of the wave function of the neutrons, which clarifies the observation in the framework of standard quantum mechanics and reveals the multifold presence of the neutron’s wave function in the interferometer.