Photon exchange and entanglement formation during transmission through a rectangular quantum barrier

When a quantum particle traverses a rectangular potential created by a quantum field both photon exchange and entanglement between particle and field take place. We present the full analytic solution of the Schrödinger equation of the composite particle–field system allowing investigation of these phenomena in detail and comparison to the results of a classical field treatment. Besides entanglement formation, remarkable differences also appear with respect to the symmetry between energy emission and absorption, resonance effects and if the field initially occupies the vacuum state. - Highlights: • Full analytic solution for the transmission through a rectangular quantum barrier. • Transition from classical to quantum field is illustrated. • Entanglement as a unique feature of the quantized field treatment is emphasized. • Non-trivial entanglement between position and photon number for coherent fields. • Interaction with vacuum state peculiar to the quantized field treatment