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Using wave-packet interferometry to monitor the external vibrational control of electronic excitation transfer
19.P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University Press, Cambridge, 1991).
20.S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford University Press, New York, 1995).
21.M. Cho, Two-Dimensional Optical Spectroscopy (CRC, Boca Raton, 2009).
22.An approach somewhat similar to ours is taken in a recent paper on the two-dimensional optical spectroscopy of molecular dimers;
27.G. S. Engel, T. R. Calhoun, E. L. Read, T. K. Ahn, T. Mancal, Y. C. Cheng, R. E. Blankenship, and G. R. Fleming, Nature (London) 446, 782 (2007).
29.M. Cho, Bull. Korean Chem. Soc. 27, 1940 (2006).
35.J. D. Biggs and J. A. Cina, J. Chem. Phys. 131, 224302 (2009).
41.N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochín, J. A. Cina, G. R. Fleming, and S. A. Rice, J. Chem. Phys. 95, 1487 (1991).
65.For present purposes this pulse should perhaps be regarded as preresonant with the and transitions so that effects of interactions with higher-lying electronic states that are absent from our model Hamiltonian can safely be neglected.
68.The nuclear degrees of freedom governed by the may comprise any number of molecular and environmental modes. The pure state may, in particular, describe the energy-transfer complex in thermal equilibrium with a surrounding medium at any temperature such that is much smaller than the monomer electronic excitation energies. For an interesting discussion on this point in a larger context, see Refs. 69 and 70.
71.This choice of observable differs from that of Ref. 42, where the population of the acceptor state was monitored for an oriented complex. If the similarity in emission frequency from the two- and one-exciton states were to make discrimination between them difficult, the theoretical treatment would have to be modified to calculate the expected number of “stored photons,” .
72.Under stronger EET coupling, when the time scale for energy transfer may be less than or on the order of pulse durations, vibrational periods, or both, it can be advantageous to frame the treatment in terms of delocalized exciton states, rather than site states. See Ref. 29 and Sec. III.C of Ref. 30.
73.In the analogous matrix elements for a transition, , and is the component of along .
74. is an exception, however. Because energy transfer during the pulse is presumed negligible, this amplitude involves a single excitation pathway.
75.Another possibility would be to set , , and all parallel to each other and the delay time equal to one-quarter of the vibrational period for the mode in question. In this case the ground nuclear state of the donor-excited electronic state is preferentially populated and excited-state nuclear motion is essentially quenched.
79.A. Migani and M. Olivucci, in Conical Intersections: Electronic Structure, Dynamics, and Spectroscopy, edited by W. Domcke, D. R. Yarkony, and H. Köppel (World Scientific, Singapore, 2004), Chap. 6.
85.For another example of calculations involving the orientational average of sixfold products of transition-dipole directions, see A. Tokmakoff, J. Chem. Phys. 105, 13 (1996).
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