Non-Hermitian Hamiltonian Approach for Two-Dimensional Coherent Spectra of Driven Systems

Abstract: Two-dimensional coherent spectroscopy (2DCS) offers significant advantages in terms of high temporal and frequency resolutions and signal-to-noise ratio. Until now, the response-function (RF) formalism has been the prevalent theoretical description. In this study, we compare the non-Hermitian Hamiltonian (NHH) method with the RF formalism in a three-level system with a constant control field. We obtain the signals from both approaches and compare their population dynamics and 2DCS. We propose the quasi-Green functions for the NHH method, which allows all dominant Liouville paths to be inferred. We further simulate the 2DCS of Rh(CO)$_2$C$_5$H$_7$O$_2$ (RDC) dissolved in hexane with the NHH method, which is in good agreement with the previous experiments. Although the NHH method overestimates relaxations, it provides all important paths by analytical solutions, which are different from the four paths used in the RF formalism. Our results demonstrate that the NHH method is more suitable than the RF formalism for investigating the systems including relaxation and control fields via the 2DCS.