Absorptive and dispersive responses in a two-level molecule with vibronic coupling: Permanent dipole moments effects

Highlights

• Absorptive and dispersive responses in a two-level molecule with vibronic coupling: Permanent dipole moments effects.

• Permanent dipole moment effects on the nonlinear optical responses in molecular systems with vibronic coupling.

• Intramolecular coupling and permanent dipole moment effect on absorptive and dispersive responses in molecular systems.

• Study of nonlinear optical properties in molecular systems with intramolecular coupling.

Abstract

Profiles of the nonlinear optical properties of a two-level system interacting with a thermal reservoir in Four-wave mixing have been studied. The model is a generalization of the conventional two-level approach, it includes a simplified description of the molecular structure and the explicit consideration of permanent dipole moment. The Born-Oppenheimer electronic energy curves consist of two intercrossing harmonic oscillators potentials, displaced both in their equilibrium minimum position and energy. The critical quantities for this analysis are the transition and permanent dipole moments. Our results show how both nonlinear absorption and dispersion responses, are affected by the vibronic coupling.

Introduction

The dynamic behavior of a molecular system interacting with strong electromagnetic fields in the presence of a thermal reservoir has been the subject of several studies [1], [2], [3], [4], [5]. Four-wave-mixing spectroscopy (FWM) and polarization have been used to determine the parameters associated with the dissipation mechanisms in such molecular systems. These parameters, controlled by the longitudinal and transversal relaxation times T₁ and T₂, have also been validated with experiments and theoretical developments in nonlinear optical. Theoretical and experimental developments in resonant processes of Rayleigh-type Optical Mixing (RTOM) signals, proposed by Yajima and Souma [6], [7]. In another study, Boyd et al [8] characterized a two-level system through the study of parametric interactions in Four-wave Mixing (FWM). Souma et al [9] later performed experiments in resonant wave mixing on Rhodamine 6G, DQCI and Cresyl-violet dyes in ethanol using phase-conjugate configuration. Erskine et al [10] proposed femtosecond studies of the recovery dynamics of Malachite Green in solution. In aqueous solutions, Marcano and García-Golding [11] studied the power effects using polarization spectroscopy. To include phenomenological dephasing constants, these works introduced stochastic modulations of the levels, harmonic oscillators models, or microscopic models of non-Born-Oppenheimer dynamics on multidimensional excited state potential energy surfaces [12]. For pure and mixed states [13], vibronic coupling constants (VCC) and coupling densities (VCD) have been successfully applied as reactivity indices of fullerenes and nanographene. Also, newly emerging vibrational progressions due Herzberg-Teller vibronic coupling that show up in absorption spectra and quantum beats in photon echo signals have been rigorously studied [14].

The presence of intramolecular coupling is of great importance in various physical and chemical processes. Some examples include i) weak transition probabilities forbidden by symmetry in absorption and emission [15], ii) relaxation rates of internal conversion [16], iii) harmonic diabatic potentials studied by femtosecond spectroscopy [17], iv) optical absorption band shape of dimmers [18], and v) resonances in a scattering process [19]. Curve-crossing problems have received special attention in recent years, and they have found applications in various fields of physics, chemistry, and biology [20]. The introduction of a residual perturbation, which may arise from a residual electron–electron correlation and/or spin–orbit coupling terms in the Hamiltonian of the system, may couple the above electronic states, causing a separation of the two curves in agreement with the avoided-crossing rule. The insertion of residual terms allows us to generate a new adiabatic basis, which gives a functional account of the original diabatic states [21], [22]. We evaluate the density matrix elements for both coherence and population difference descriptions, which allows us to express the macroscopic polarization in the FWM spectroscopy. We evaluate the dispersive and absorptive optical properties as a function of the parameters governing the coupling. Our results show the sensitivity of these optical properties with respect to the adiabatic dipole moments. We also demonstrate that at certain frequency detuning regions, the absorption curves display radical changes showing the possibility of generating parametric amplifications tunable to the organic dyes used.