Leggett-Garg inequalities violation via the Fermi contact hyperfine interaction

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 ²S_1/2 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. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)