Efficient Simulation of Polariton Spectra under the Collective Coupling Regime

We outline two general theoretical techniques to simulate polariton quantum dynamics and optical spectra under the collective coupling regimes described by a Holestein-Tavis-Cummings (HTC) model Hamiltonian. The first one takes the advantage of sparsity of the HTC Hamiltonian, which allows one to reduce the cost of acting polariton Hamiltonian onto a state vector to the linear order of the number of states, instead of the quadratic order. The second one is applying the well-known Chebyshev series expansion approach for quantum dynamics propagation and applying them to simulate the polariton dynamics in the HTC system, allowing one to use a much larger time step for propagation and only requires a few recursive operations of the Polariton Hamiltonian acting on state vectors. These two theoretical approaches are general and can be applied to any trajectory-based non-adiabatic quantum dynamics methods. We use these two techniques with our previously developed Lindblad-Partially Linearized Density Matrix (L-PLDM) approach to simulate the linear absorption spectra of the HTC model system, with both inhomogeneous site energy disorder as well as dipolar orientational disorders. Our numerical results agree well with the previous analytic and numerical work. Further, we vectorize our algorithm also to reduce the computational cost of simulating the 2D electronic spectroscopy of many molecule exciton-polariton systems and demonstrate the effects of collective behavior on the 2D lineshapes.