Vibrational response functions for multidimensional electronic spectroscopy: from Duschinsky rotations to multimode squeezed coherent states

Multidimensional spectroscopy unveils the interplay of nuclear and electronic dynamics, which characterizes the ultrafast dynamics of various molecular and solid-state systems. In a widely used class of models used for the simulation of such dynamics, field-induced transitions between electronic states result in linear transformations (Duschinsky rotations) between the normal coordinates of the vibrational modes. Here we present an approach for the calculation of the response functions, based on the explicit derivation of the vibrational state. This can be shown to coincide with a multimode squeezed coherent state, whose expression we derive within a quantum-optical formalism, and specifically by the sequential application to the initial state of rotation, displacement and squeeze operators. This approach potentially simplifies the numerical derivation of the response function, avoiding the time integration of the Schr\"odinger equation or the Hamiltonian diagonalization, combined with the sum over infinite vibronic pathways. Besides, it quantitatively substantiates in the considered models the intuitive interpretation of the response function in terms of the vibrational wave packet dynamics.