Capturing Open Quantum System Dynamics with Cavity Dressed Hamiltonians

We present an extension of the reaction-coordinate (RC) polaron transform [PRX Quantum 4, 020307 (2023)], a non-perturbative method for the study of strongly coupled open quantum systems via a combination of reaction coordinate and generalized polaron transforms, to the cavity dressed Hamiltonian (CDH) method via the inclusion of higher reaction-coordinate levels. Our method converges faster than a pure RC approach, and more accurately captures elements of the system dynamics such as phase and characteristic frequency at lower levels. We benchmark the method with the spin-boson model, demonstrating improved performance across the intermediate and strong coupling regimes, as well as extensions to larger systems of spins interacting through a common bath. These highlight the advantage of the CDH method, which can produce accurate dynamics while keeping overall system size small.