Two-Dimensional (2D) Spectroscopy
Absorptive 2D electronic spectrum of a coupled dimer: exciton splitting √(Δ² + 4J²), bleach, stimulated-emission and excited-state-absorption peaks, energy transfer during the waiting time and homogeneous vs inhomogeneous lineshapes.
Exciton Energies E₋ / E₊
12358.6 / 12641.4 cm⁻¹
809.15 / 791.05 nm
Splitting √(Δ² + 4J²)
282.8 cm⁻¹
mixing angle θ = 22.5°
Dipole Strengths |μ₀₋|² / |μ₀₊|²
0.646 / 1.35
in monomer units; sum = 2
Homogeneous FWHM 1/(πcT₂)
53.09 cm⁻¹
after T_w: P(E₋ | excited E₊) = 0.00
Dimer: sites ν₀ ∓ Δ/2 coupled by J form excitons E∓ = ν₀ ∓ ½√(Δ² + 4J²) with tan 2θ = 2J/Δ; the doubly excited state lies at 2ν₀ = E₋ + E₊.
Absorptive spectrum S(ω₁, T_w, ω₃), the sum of rephasing and non-rephasing signals: ground-state bleach and stimulated emission (positive, red) at (Eₐ, E_b), excited-state absorption (negative, blue) at (Eₐ, 2ν₀ − E_b), weighted by the isotropic ⟨μμμμ⟩ for parallel pulse polarisations and by the population transfer P(b|a) during T_w.
Lineshape: Lorentzian with FWHM 1/(πcT₂) across the diagonal, stretched along it by static inhomogeneous broadening. With J = 0 and T_w = 0 the cross peaks vanish: bleach and excited-state absorption cancel; at T_w > 0 the model's transfer (an input rate, not derived from J) still builds a cross peak.
Not included: inter-exciton coherences (quantum beats) during T_w, spectral diffusion, ground-state recovery, biexciton binding and vibronic structure. Uphill transfer follows detailed balance at the given temperature.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Excitonic dimer of two-level chromophores, population pathways only (coherences dephased), isotropic parallel polarisations, Lorentzian homogeneous and static correlated Gaussian inhomogeneous broadening.
- Hamm P., Zanni M. (2011). Concepts and Methods of 2D Infrared Spectroscopy. Cambridge University Press. doi:10.1017/CBO9780511675935
- Jonas D. M. (2003). Two-dimensional femtosecond spectroscopy. Annu. Rev. Phys. Chem. 54, 425–463. doi:10.1146/annurev.physchem.54.011002.103907