Second invariant in an excited three-level system

For a three-level atom excited by two laser fields whose amplitudes are sinusoidally modulated with a phase difference of {π}/2, we show that, rather surprisingly, a second (independent) linear constant of motion may be obtained even more directly by the coherence vector method than by the recent density-matrix formulation of Hioe. As a consequence it is found that the two corresponding eigenvectors of the time-independent time-evolution matrix in the degenerate subspace with two zero eigenvalues are orthogonal if a certain relation holds between the laser modulation and Rabi frequencies.