Spectral Filtering as a Tool for Two-Dimensional Spectroscopy: A Theoretical Model

Abstract

Two-dimensional optical spectroscopy is a powerful technique for the probing of coherent quantum superpositions. Recently, the finite width of the laser spectrum has been employed to selectively tune experiments for the study of particular coherences. This involves the exclusion of certain transition frequencies, which results in the elimination of specific Liouville pathways. The rigorous analysis of such experiments requires the use of ever more sophisticated theoretical models for the optical spectroscopy of electronic and vibronic systems. Here we develop a nonimpulsive and non-Markovian model, which combines an explicit definition of the laser spectrum, via the equation of motion-phase matching approach (EOM-PMA), with the hierarchical equations of motion (HEOM). This theoretical framework is capable of simulating the 2D spectroscopy of vibronic systems with low frequency modes, coupled to environments of intermediate and slower time scales. In order to demonstrate the spectral filtering of vibronic coherences, we examine the elimination of lower energy peaks from the 2D spectra of a zinc porphyrin monomer upon blue-shifting the laser spectrum. The filtering of Liouville pathways is revealed through the disappearance of peaks from the amplitude spectra for a coupled vibrational mode.

Rapid multiple-quantum three-dimensional fluorescence spectroscopy disentangles quantum pathways

“…As further shown in Supplementary Note 5 and Supplementary Fig. 7 and discussed in a similar scenario 61 , the filtering effect by the laser spectrum removes from the complete manifold a number of pathways that involve the transition between | e 0 〉 and | g 1 〉, also in the nonrephasing 1Q–0Q–1Q contribution. This simplifies the interpretation.

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“…3b), where the wavy arrows pointing to the right (left) denote the laser fields, interacting with a phase of + φ (− φ ). The sign of the 0Q coherence frequency determines whether the coherence oscillates positively, e.g., | e 1 〉〈 e 0 | ∝ exp(− iω 0Q T ), or negatively with | e 0 〉〈 e 1 | ∝ exp(+ iω 0Q T ) 29,61 . As previously demonstrated, analyzing these oppositely signed signatures has proven to be a powerful tool to decipher the origin of the underlying quantum coherences 62,63 .…”

Biomimetic Nanoarchitectures for Light Harvesting: Self-Assembly of Pyropheophorbide-Peptide Conjugates

“…The beating analysis reveals several oscillating components, all corresponding to vibrational modes also detected in Raman spectra. The amplitude distribution of each beating component along the two frequency axes, plotted in the so-called Fourier maps, confirms the vibrational nature of the oscillating signals. − Panels g–l of Figure exemplify this analysis for a mode beating at 823 cm –1 . A further investigation of the sign of the oscillation frequency at specific positions in rephasing and non-rephasing spectra allows an assessment of whether a particular vibrational coherence is evolving in the ground state or the excited state. , For the PPh- ap monomer, it was determined that the frequency components contributing to the beating pattern in 2D maps can be mainly attributed to ground state vibration (Supporting Information).…”

Quantifying non-Markovianity in underdamped versus overdamped environments and its effect on spectral lineshape

“…37 The hierarchy is terminated using a convergence parameter, ξ, beyond which the evolution is assumed to be within the Markovian limit. 36,41 The convergence parameter determines the number of Matsubara frequencies via,…”