3D spectroscopy of vibrational coherences in quantum dots: theory.

In semiconductor nanocrystals, called quantum dots (QD), electronic transition energies, phonon frequencies, and electron-phonon coupling strengths are all reported to depend on the size of the crystals. The size dependencies of the transition energies and the mode frequencies are well characterized and understood. At the same time, the electron-phonon coupling dependence on size is controversial-even the sign of the change is not settled. In this article, third-order response functions of a model QD resembling CdSe are calculated. The longitudinal optical (LO) mode is included as a relatively narrow Lorentzian contribution to the spectral density. A novel version of electronic 2D spectroscopy is investigated where a third Fourier transform is taken over a so-called population time, leading to 3D spectral representation. The amplitude and phase of the 2D cuts of the 3D spectral body around the LO mode frequency are analyzed. The analytical power and sensitivity of the cuts in determining the possible Huang-Rhys factor (electron-phonon coupling strength) and the LO mode frequency dependence on the QD size are investigated. Peak structures in the cuts with a tilt relative to the diagonal are identified as sensitive signatures for the size dependencies. The study elucidates the 3D representation of the electronic 2D spectroscopy as a powerful tool for obtaining insight into otherwise hardly accessible characteristics of the system.