How is 2D spectroscopy able to show quantum coherent transport through networks?

Question

For wave-like (quantum coherent) energy transfer in networks (eg. propagation of excitation in photosynthetic protein complexes of algae or FMO complex in plants) 2D electronic (photon echo?) spectroscopy is used (eg. in this article). I have read an article (unfortunately I can't cite it here) about how it works, but I didn't understand it. I know that the off-diagonal peaks in the spectrum mean some kind of coherence in the network but I don't know why. I also don't know what kind of coherence it means. What are meant by electronic eigenstates? What are the so called 'quantum beatings'? It would be very much appreciated if somebody would be so kind as to make these thing clear.

Comments

Have you read the article Two-dimensional infrared spectroscopy in wikipedia? 

Two-dimensional infrared spectroscopy (2DIR) is a nonlinear infrared spectroscopy technique that has the ability to correlate vibrational modes in condensed-phase systems. This technique provides information beyond linear infrared spectra, by spreading the vibrational information along multiple axes, yielding a frequency correlation spectrum. A frequency correlation spectrum can offer structural information such as vibrational mode coupling, anharmonicities, along with chemical dynamics such as energy transfer rates and molecular dynamics with femtosecond time resolution. 2DIR experiments have only become possible with the development of ultrafast lasers and the ability to generate femtosecond infrared pulses.

Coherence means that the phases are known. Lasers deliver coherent beams and can probe coherent states, if their coherence is not lost after the interaction. It means that the states the laser light interacted with also have fixed phases and thus are not incoherent ( thermal states are incoherent for example, because their vibrations and rotations are random as far as phases go).  It seems they succeed with these ultrafast lasers to see whether the probed states are coherent or not .

It needs somebody proficient  in this technique to really  anwer this question, which is a physical chemistry one. Here is a link to an abstract that explains the terms. :

Two-dimensional infrared (2D IR) vibrational spectroscopy is an experimental tool for investigating molecular dynamics in solution on a picosecond time scale. We present experimental and theoretical methods for obtaining a 2D IR correlation spectrum and modeling the underlying microscopic information. Fourier transform 2D spectra are obtained from heterodyne-detected third-order nonlinear signals using a sequence of broad bandwidth femtosecond IR pulses. A 2D IR correlation spectrum with absorptive line shapes results from the addition of 2D rephasing and nonrephasing spectra, which sample conjugate frequencies during the initial evolution time period. The 2D IR spectrum contains peaks with different positions, signs, amplitudes, and line shapes characterizing the vibrational eigenstates of the system and their interactions with the surrounding bath. The positions of the peaks map the transition frequencies between the ground, singly, and doubly excited states of the system and thus describe the anharmonic vibrational potential. Peak amplitudes reflect the relative magnitudes and orientations of the transition dipole moments in the molecular frame, the electrical anharmonicity of the system, and the vibrational relaxation dynamics. The 2D line shapes are sensitive to the system−bath interactions in solution. We illustrate how 2D IR spectra taken with varying polarization conditions and as a function of a variable waiting time can be used to isolate and quantify these spectroscopic observables

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Actually I have just read an article (see §4) which I didn't fully understand, however 2DES just started to make sense. The way I see it, coherent light is able to excite a superposition of electronic eigenstates (I don't fully understand how, and I absolutely don't know why two exciting pulses are used) and a kind of Rabi oscillation starts. Then, after a certain waiting time T (which is varied through the experiment) a third pulse induces emission in the molcelues, whatever the population of the energy levels were. Then the response of the moleclues are recorded, Fourier transformed and the peaks in the response are plotted against the frequency of the exciting pulses. Since the populations of the energy levels change periodically in case of a Rabi oscillation, it may happen, that the exciting frequency was (close to) $\nu_1$, but the emission frequency was close to $\nu_2$. If I plot the excting frequencies vs. the emission frequencies, than this is recorded as an off-diagonal peak, which is a direct evidence of a coherent superposition having been excited. What's your opinion about my theory?