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 Ô = Ŝz ⊗ ̂n1 ⊗ ̂n2, in which Ŝz is the atom operator, and ̂n1 and ̂n2 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.