Polariton Spectra under the Collective Coupling Regime. II. 2D Non-linear Spectra

In our previous work [Ref.~\citenum{MondalJCP2024paper1}], we developed several efficient strategies to simulate exciton-polariton dynamics described by the Holestein-Tavis-Cummings (HTC) Hamiltonian under the collective coupling regime. Here, we incorporated these strategies into the previously developed $\mathcal{L}$-PLDM approach for simulating 2D Electronic Spectroscopy (2DES) spectra of exciton-polariton under the collective coupling regime. In particular, we apply the efficient quantum dynamics propagation scheme developed in Paper I to both the forward and the backward propagations in the PLDM, and develop an efficient important sampling scheme and GPU vectorization scheme that allow us to reduce the computational costs from $\mathcal{O}(\mathcal{K}^2)\mathcal{O}(T^3)$ to $\mathcal{O}(\mathcal{K}) \mathcal{O}(T^0)$ for the 2DES spectra simulation, where $\mathcal{K}$ is the number of states and $T$ is the number of time steps of propagation. We further simulated the 2DES spectra for an HTC Hamiltonian under the collective coupling regime and analyzed the signal from both rephasing and non-rephasing contributions of the ground state bleaching (GSB), excited state emission (ESA), and stimulated emission (SE) pathways.