Tomography, control, and characterization of entanglement in a three-level atomic system

Abstract

We study the quantum correlations of the radiation emitted by three-level atoms (cascade type) interacting with two driving fields. In the linear regime, and in the Weisskopf-Wigner approximation, we show that the atomic and the two-photon density matrix are equivalent to each other. This facilitates the tomography of the two-mode state to be realized by measurements on either the atomic system or the emitted fields. While, in general, one needs ${4}^{N}$ measurements for the tomography of an $N$-photon state, we show that one needs $(N+1){}^{2}\ensuremath{-}1$ observables for the tomography of photons emitted by an atomic system. Thus there is an exponential reduction in the number of observables for the reconstruction of the class of $N$-photon states emitted by atoms. We show that the driving field strengths and detunings provide the control parameters for the preparation of a specific target state. Finally, we study the characterization of entanglement of the two-photon state. We observe that a characterization of entanglement in terms of a single parameter is not possible when the system is in a mixed state; therefore, we provide a description in terms of the newly introduced probability distribution for entanglement, in various regimes of interest.