On the control of interference and diffraction of a 3-level atom in a double-slit scheme with cavity fields

A double cavity with a quantum mechanical and a classical field is located immediately behind of a double-slit in order to analyse the wave-particle duality. Both fields have common nodes and antinodes through which a three-level atom passes after crossing the double-slit. The atom-field interaction is maximum when the atom crosses a common antinode and path-information can be recorded on the phase of the quantum field. On other hand, if the atom crosses a common node, the interaction is null and no path-information is stored. A quadrature measurement on the quantum field can reveal the path followed by the atom, depending on its initial amplitude $\alpha$ and the classical amplitude $\varepsilon$. In this report we show that the classical radiation acts like a focusing element of the interference and diffraction patterns and how it alters the visibility and distinguishabilily. Furthermore, in our double-slit scheme the two possible paths are correlated with the internal atomic states, which allows us to study the relationship between concurrence and wave-particle duality considering different cases.