Optical reconstruction of the collective density matrix of a qutrit

Reliable tomography of a quantum state of atoms in room-temperature vapors offers interesting applications in quantum-information science. To step toward the applications, here, we theoretical investigate a technique of reconstruction of a collective density matrix of atoms in a state of a total angular momentum equal to unity. By studying transformation of density matrix due to magnetic-field pulses and deriving explicit relations between optical signals and specific density-matrix elements, we demonstrate full reconstruction of quantum states. Numerical simulations allow us to demonstrate that the reconstruction fidelity of pure and mixed states may exceed 0.95 and that the technique is robust against noise and uncertainties.