The remaining two pathways are excited-state absorption (ESA) pathways which proceed through the |2⟩⟨1| coherence state. In contrast to typical condensed-phase experiments, the action-detection scheme results in two ESA pathways. Both ESA pathways evolve as e -iω 21 τ and give rise to a signal at the overtone frequency ω21 with intensity proportional to |⟨1|𝜇|0⟩| 2 |⟨2|𝜇|1⟩| 2 . Based on solution-phase experiments of metal carbonyl complexes, overtone features would be expected to fall 10-15 cm -1 lower in energy than the corresponding bleach signals. The two ESA pathways, however, oscillate at different phases. The sign of a Feynman diagram goes as (-1) n where n is the number of interactions with the bra side of the density matrix. This factor results from the nested commutators that arise from the density matrix formulation of time-dependent perturbation theory. ESA1, therefore, oscillates as -e -iω 21 τ while ESA2 oscillates as +e -iω 21 τ . Consequently, the two ESA pathways destructively interfere and cancel, leaving only bleaching signals in nonlinear action spectra. This expectation is consistent with experimental observations by Brixner using fluorescence modulation detection in condensed-phase experiments. ESA1 and ESA2 pathways were observed under certain experimental conditions by Stienkemeier using gas-phase photoionization schemes. In the experiments reported here, only bleaching signals are expected since equal tag loss is expected regardless of the final population state of the system (|1⟩⟨1| or |2⟩⟨2|; i.e., the N2 binding energy is << ħω10).