Testing for reality with atomic cascades

Oleksandr V. Marchukov, Maxim Olshanii

In this article, we are interested in situations where the existence of a contiguous cascade of quantum resonant transitions is predicated on the validity of a particular statement in number theory. The setting is a tailored one-atom one-dimensional potential with a prescribed spectrum under a weak periodic perturbation. The former is, by now, an experimental reality [Cassettari et al., PNAS Nexus 2, pgac279 (2022)]. As a case study, we look at the following trivial statement: “Any power of 3 is an integer.” Consequently, we “test” this statement in a numerical experiment where we demonstrate an unimpeded upward mobility along an equidistant ln (3)-spaced subsequence of the energy levels of a potential with a log-natural spectrum under a frequency ln (3) time-periodic perturbation. We further show that when we “remove” 9 from the set of integers—by excluding the corresponding energy level from the spectrum—the cascade halts abruptly.

Richard A. Holt

Emilio Santos

The proposal is made of replacing the usual auxiliary assumptions needed for the derivation of testable Bell inequalities by an assumption resting only on symmetry considerations. It is shown that reliable atomic cascade tests of symmetric local hidden-variables theories should combine high statistics, cascades of type 0\ensuremath{\rightarrow}1\ensuremath{\rightarrow}0, and calcite polarizers. The three conditions have been achieved in experiments already performed, but never before simultaneously.

Nelson Frederick Beeler, Franklyn Mansfield Branley

Angel L. Sanz, J. L. Sánchez‐Gómez

We compute the probability, P , that the second photon of an atomic-cascade experiment, performed to test Bell inequalities, undergoes rescattering. In the case of the experiments of Aspect et al. , we find P ≃ 0.1; hence, the possibility that photon rescattering be a "loophole" in the experimental refutation of local hidden-variable theories is ruled out.