(a) Structure of APC trimer in which blue and red are respectively used to represent and pigments. Also shown is the energy level diagram discussed in Ref. 32. (b) Structure of CPC trimer in which red, blue, and green are respectively used to represent the , , and pigments. Also shown is the energy level diagram presented in Ref. 33. Structural representations for APC and CPC are generated using PDB files 1ALL (Ref. 4) and 1GH0 (Ref. 8). X-ray data for both systems are obtained using proteins isolated from Spirulina platensis.
(a) Pulse sequence for IECS. Experimentally controlled delays are denoted by and , where for all measurements in this paper. High (blue) and low (green) frequency laser pulses initiate electronic and nuclear coherences in the delay, . The polarization evolves in interband coherences in and . Experimental laser spectra overlaid on absorbance spectra of (b) APC and (c) CPC.
Feynman diagrams for dominant terms in transient grating and intraband electronic coherence spectroscopies. The dummy indices and are used for single exciton states, whereas is reserved for the double exciton manifold. Terms in the first two rows yield the largest contributions in intraband electronic coherence spectroscopy. The superscript “IC” in the third row denotes incoherent population transfer. The excited state absorption terms, , , , and do not enter the model response function for CPC (Ref. 33).
Absolute value of transient grating signal fields measured for (a) APC and (b) CPC under the ZZXX polarization condition in which the pump and probe pulses have orthogonal polarizations. Delay times, , are given in the figure legend. Excitation is achieved with 20 fs pump pulses centered at .
Absolute value IECS signals measured for [(a) and (c)] APC; [(b) and (d)] CPC. Panels [(a) and (b)] use the ZZZZ polarization condition, whereas [(c) and (d)] are ZXZX (see Sec. II). Signals in all panels are normalized to 1.0. Panels [(e) and (f)], respectively, represent the ZZZZ and ZXZX tensor elements of IECS signals measured at for (black) APC and (red) CPC. Contour lines in panels [(a)–(d)] are linearly spaced.
Absolute value IECS signals calculated for [(a) and (c)] APC; [(b) and (d)] CPC using Eq. (1). Panels [(a) and (b)] use the ZZZZ polarization condition, whereas [(c) and (d)] are ZXZX. Signals in all panels are normalized to 1.0. Panels [(e) and (f)], respectively, represent the ZZZZ and ZXZX tensor elements of IECS signals measured at for (black) APC and (red) CPC. Contour lines in panels [(a)–(d)] are linearly spaced.
(a) Experimental (solid) and calculated (dash-dotted) ZZZZ/ZXZX ratios of absolute value IECS signals emitted at . Black and red lines, respectively, correspond to APC and CPC. (b) Calculated absolute value IECS signals for APC radiated at . The parameter, , tunes the amount of correlation characteristic of fluctuations at the and pigment sites; uncorrelated and fully correlated fluctuations are found at and , respectively. These calculations remove all nuclear coherences in from the response function to isolate effects of intraband exciton dephasing between and .
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