Quantum mechanical rotations, information transfer and decoherence in the converter limit of parametric processes

Abstract

In classical three-wave interaction there is a regime where only the phases move but no energy is exchanged. This is strictly valid for classical trajectories with sharp amplitudes and phases. Quantum mechanically, such a phase motion regime can be realized only approximately if all three waves start in coherent states because the states deform due to their initial uncertainties during rotation. In the limit of a strong signal or idler wave, what amounts to frequency conversion, we show that exact rotations of coherent states become possible. This completes our understanding of three-wave interaction. Different initial quantum states are exchanged periodically if the strong wave is treated classically and undepleted. This limit is investigated by numerical diagonalization of the exact Hamiltonian via nonclassical states in the pump and coherent states in the signal and idler. Classical phase motion turns out to be very helpful to understand the strong demands for the converter limit. In the converter, we consider the impurity of the two modes and show that the coherent state in one mode, which enables the no-energy transfer regime, has no influence on the impurity of the other wave and can be substituted by a vacuum state. Thus, the impurity in such a regime behaves exactly as under simple one-photon losses although the energy can be held constant. The different rotations are illustrated by calculating the Wigner functions via classical trajectories. In addition, we also consider the equivalent emission from a prepared atomic system (squeezed atoms) into one mode.