Anomalous Weak Values Emerging from Strong Interactions between Light and Matter

Abstract: Some predictions regarding pre- and post-selected states are far-reaching, thereby requiring validation with standard quantum measurements in addition to the customary weak measurements used so far, as well as other advanced techniques. We go further pursuing this goal, proposing two thought experiments which incorporate novel yet feasible validation methods of unconventional light-matter interactions. An excited atom traverses a Mach-Zehnder interferometer (MZI) under a special combination of pre- and post-selection. In the first experiment, photons emitted by the superposed atom, after being hit by two laser beams, are individually counted. Despite the interaction having definitely taken place, the numbers of photons emitted from each arm of the MZI are predicted, at the ensemble level, to be different from those expected with standard stimulated emission. In the second experiment, the atom spontaneously emits a photon while still in the MZI. This photon later serves as a strong measurement of the atom's energy upon hitting a photographic plate. The experiment is repeated to enable an interference effect of the emitted photons. Interestingly, the latter gives the appearance that the photons have been emitted by the atom from a position much farther from the two MZI arms L and R, as if in a "phantom arm" R'. These experiments also emphasize the key role of anomalous weak values in determining light-matter interactions. In fact, they present a straightforward realization of an entity we term counter-particles, namely pre- and post-selected states acting as if they have negative physical variables such as mass and energy. The novel verification methods we suggest for testing these predictions resemble weak measurements in some aspects, yet result from definite atomic transitions verified by the detected photons.