Tomography, Control and Characterization of Entanglement in Three level Atomic System

TL;DR

This paper demonstrates efficient quantum state tomography and entanglement characterization for three-level atomic systems emitting two-photon states, revealing exponential reduction in measurements and control via driving fields.

Contribution

It introduces a method for reduced measurement tomography of emitted photons and explores entanglement characterization in mixed states of atomic emission.

Findings

Equivalent atomic and two-photon density matrices facilitate tomography.

Number of measurements reduces from exponential to polynomial in photon number.

Entanglement characterization requires a probability distribution in mixed states.

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 a N photon state, we show that one needs (N+1)^2-1 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 {\it 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.