Leggett–Garg inequalities violation via the Fermi contact hyperfine interaction

Abstract

In this paper we examine theoretically how the spin–spin interaction between a nuclei and an electron in the atom affects violation of the Leggett–Garg inequalities. We consider the simplest case of atoms in the state that in the valence shell have just a single electron and the evolution in time of the spin is dictated only by the Fermi contact hyperfine interaction. We found that for special initial conditions and a particular measured observable the high spin nucleus couple to the valence electron such that violation of Leggett–Garg inequalities increases with total spin of states. Consequently, our results show that for the Hydrogen, the smallest atom in Nature, the violation of the Leggett–Garg inequalities is the smallest whereas for the largest atom, the Cesium, the violation is the largest. Moreover, this violation does not depend on a principal quantum number, thus our model can be used for Rydberg atoms in order to test macrorealism for ‘almost macroscopic’ objects.