Controlling parameters of the wave-particle duality of a two-level atom in a double-slit scheme with cavity field

Abstract

A double-slit scheme placed immediately before a standing wave allows one to establish two possible paths for the passage of an atom. Each path matches with a node or antinode of the wave. The atom–field interaction is maximum (null) when the atom crosses an antinode (node), causing a maximum (null) phase shift in the field. Therefore, after the interaction, a proper quadrature measurement on the field can reveal the value of its final phase, and which-path information can be obtained. For a coherent state, the which-path information can be controlled by the amplitude of the field, and partial interference can be observed as it decreases. In this paper, we consider different states of the quantum field (squeezed coherent, cat, and thermal states), and we establish correlations between the internal atomic states and the paths of the double-slit scheme. This allows us to study the relationship among visibility, distinguishability, and concurrence, having in both the field and the atom different controlling parameters of the wave-particle duality.

A double-slit scheme placed immediately before a standing wave allows one to establish two possible paths for the passage of an atom. Each path matches with a node or antinode of the wave. The atom–field interaction is maximum (null) when the atom crosses an antinode (node), causing a maximum (null) phase shift in the field. Therefore, after the interaction, a proper quadrature measurement on the field can reveal the value of its final phase, and which-path information can be obtained. For a coherent state, the which-path information can be controlled by the amplitude of the field, and partial interference can be observed as it decreases. In this paper, we consider different states of the quantum field (squeezed coherent, cat, and thermal states), and we establish correlations between the internal atomic states and the paths of the double-slit scheme. This allows us to study the relationship among visibility, distinguishability, and concurrence, having in both the field and the atom different controlling parameters of the wave-particle duality.