What dynamics can be expected for mixed states in two-slit experiments?

• The dynamics associated with mixture states in investigated by means of two simple Young’s two-slit models.
• The models are prepared to be easily implemented and tested in the laboratory by means of weak measurements.
• Bohmian mechanics has been generalized to encompass statistical mixtures.
• Even for conditions of maximal mixedness numerical simulations show that the dynamics is strongly influenced by both slits.
• Accordingly, weak measurements are unable to discriminate how mixedness arises in an experiment.

Weak-measurement-based experiments (Kocsis et al., 2011) have shown that, at least for pure states, the average evolution of independent photons in Young’s two-slit experiment is in compliance with the trajectories prescribed by the Bohmian formulation of quantum mechanics. But, what happens if the same experiment is repeated assuming that the wave function associated with each particle is different, i.e., in the case of mixed (incoherent) states? This question is investigated here by means of two alternative numerical simulations of Young’s experiment, purposely devised to be easily implemented and tested in the laboratory. Contrary to what could be expected a priori, it is found that even for conditions of maximal mixedness or incoherence (total lack of interference fringes), experimental data will render a puzzling and challenging outcome: the average particle trajectories will still display features analogous to those for pure states, i.e., independently of how mixedness arises, the associated dynamics is influenced by both slits at the same time. Physically this simply means that weak measurements are not able to discriminate how mixedness arises in the experiment, since they only provide information about the averaged system dynamics.

Figure optionsDownload as PowerPoint slide