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Journal of Modern Optics

Revival Time Estimation in the Process of Down Conversion

Igor Jex

Published Sep 1, 1993• 2 citations
Publisher

Abstract

We analyse the collapse-revival phenomenon in the process of k-photon down conversion with quantized pump for initial Fock states. We give an explanation for the appearance of the revivals by analysing the decomposition of the initial state into the interaction Hamiltonian eigenvectors. A quantitative estimation of the revival times is given as well.

DOI
10.1080/09500349314551771

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Journal of Modern Optics•Feb 1, 1997•10 citations
We analyse the collapse-revival phenomenon in the process of k-photon down conversion with quantized pump for initial Fock states. We give an explanation for the appearance of the revivals by analysing the decomposition of the initial state into the interaction Hamiltonian eigenvectors. A quantitative estimation of the revival times is given as well.
Abstract In this paper the interaction of a three-level atom in V -configuration with a two-mode quantized field in cavity optomechanics is studied. To achieve the purpose, we first deduce the effective Hamiltonian and evaluate the explicit time-dependent form of the state vector of the whole system by choosing special initial conditions for atom, field and the oscillatory mirror. Interestingly, we can obtain the time evolution of atomic linear entropy, population inversion, quantum statistics and squeezing, both analytically and numerically. The results show that the entanglement between the atom and the subsystem of field and mirror, and all above-mentioned physical quantities can be appropriately controlled by the initial atom-field state condition, the parameters of cavity optomechanics as well as atom-field coupling strengths. In particular, the appearance of collapse-revival phenomenon in the entanglement and quantum photon statistics, also the full sub-Poissonian statistics in the two modes of field as well as in the mechanical mode of optomechanical system are noticeable features of the work.
We study entanglement between field modes in the process of nondegenerate two-photon down-conversion with quantized pump. We show that due to the quantum nature of the dynamics, strong entanglement between the pump and the signal-idler subsystems can be observed. We find that the higher the initial intensity of the pump mode the stronger the entanglement between the pump and the signal-idler subsystem is established during the first instants of the time evolution. We also show that the signal and the idler modes are strongly entangled (correlated). This entanglement is much stronger than the entanglement between the pump and the signal-idler subsystem. Correlation between the signal and the idler modes leads to a high degree of two-mode squeezing, which can be observed during the first instants of the time evolution when the pump mode is still approximately in a pure state. On the other hand, the back action of the signal-idler subsystem on the pump mode leads to a strong single-mode squeezing of the pump mode. At the time interval during which squeezing of the pump mode can be observed the pump mode is far from being in the minimum uncertainty state. We also analyze the long-time behavior of the quantum-optical system under consideration and we show that the interesting collapse-revival effect in the time evolution of the mean photon number and of the purity parameters of field modes can be observed. Finally, we show that the degree of entanglement between modes in the nondegenerate quantum-optical down-conversion strongly depends on the initial state of the system.