Determining the state of a three-level atom by interaction with two radiation fields

An unknown state of a quantum system S is usually determined by repeatedly measuring a set of non-commuting observables. The state can also be obtained from the repeated measurements of a single separable observable when the system S interacts with an assistant system A in a known state. In this paper, we study the quantum state tomography of a three-level atom (the system S) interacting with two radiation fields as the assistant system A. We obtain the initial state of S by repeatedly measuring a separable observable A" = Ae (z) aSu I,n (1) aSu I,n (2), in which Ae (z) is the atom operator, and I,n (1) and I,n (2) are the photon number operators of the two radiation fields. We achieve the one-to-one mapping M between the initial density matrix of the system S and the measured results of the single separable observable. We also give a concrete numerical example.