Shaul Mukamel (UC Irvine) gave the last talk at conference, Coherent nonlinear optical spectroscopy of biological complexes: from nmr to x-rays. It contained several really new and stimulating ideas. A nice overview is in this recent Accounts of Chemical Research paper.

Heterodyne-detected four wave mixing produces a signal S(t1,t2,t3).

There are three time differences between the four pulses t1, t2, and t3.

Experiments will soon be done in UV and X-ray part of the spectrum.

Joke: Translating Othello into Yiddish with great improvement!

Two-dimensional correlation peaks S(omega1,t2,omega3) gives a direct handle on coupling of modes, and on diagonal fluctuations and noise from lineshapes.

Recent experiments on Helical J-aggregrates reveal the pattern of energy flow.

There are TWO alternative and equivalent theoretical descriptions of these experiments. Eigenstate vs. Quasiparticle (oscillator) description of nonlinear response of excitons.

Same effective Hamiltonian for excitons, and several other systems.

H = site energies + hopping +

two-particle interactions (K coupling is a measure of anharmonicity).

Schrodinger picture. Eigenstates.

Third-order measurements probe single and double excitons.

Feynman diagrams and associated rules greatly help visualisation of the essential physics and aid derivation of equations.

Alternative approach: quasi-particles. Write Heisenberg equations of motion.

If they are linear (because there are no interactions) there is no non-linear spectroscopy. Add bath and solve equations of motion. Response function looks very different from the eigenstate picture. How do we relate the two?

Bethe-Saltpeter equation.

Oscillator picture has advantage numerically since it scales with N, whereas the eigenstate picture scales with N^2. The latter also involves massive cancellations of terms which obscures the physics.

For the FMO complex 7 excitons, 21 double exciton states.

New idea for new experiments. 1.

Measure Double quantum coherence. S(t3,omega2,omega1) shows a picture of which single excitons contribute to the two-exciton wavefunction. This is sensitive to electron correlations.

Greg Scholes has done the first experiment. Photon echo technique is not sensitive to these correlations.

Derive Lindblad equation from a modified Redfield equation.

There are features in some of Flemings spectra which are evidence for 3 exciton correlations.

New idea for new experiments. 2.

Non-linear spectroscopy with entangled pairs of photons.

Possibility of selecting between pathways/diagrams. Different scaling with intensity. (seen in Boston experiments). Control entanglement time can be varied with femtosecond resolution.

Provides a new spectroscopic tool which will work at low intensities.

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