Cavity Modified Dissipative Dynamics of the Two‐Spin Spin‐Boson Model

We investigate the dynamics of two spins that are simultaneously coupled to a high‐Q cavity and an Ohmic phonon bath using the Dirac–Frenkel time‐dependent variational principle together with two types of the multiple Davydov ansatz. In our framework, the cavity mode can either be treated as part of the bath modes within the multi‐D 2 ansatz or regarded together with the spins as a dressed composite system within the multi‐D 1 ansatz. Although both approaches yield consistent results for the spin, cavity, and phonon observables, the multi‐D 1 ansatz proves to be numerically much more efficient than the multi‐D 2 ansatz. In the regime of relatively weak spin‐bath coupling, we find that the cavity induces intricate beat patterns in the spin population dynamics as well as multipeaked phonon spectra. These cavity‐related features can also be reproduced by a polaron‐like transformed Nakajima–Zwanzig master equation, where the multipeaked phonon spectra arise from transitions between dressed states. By contrast, under relatively strong spin‐bath coupling, both the beat patterns and the multipeaked phonon spectra become suppressed. Furthermore, even with strong spin‐cavity coupling, sufficiently strong spin‐bath interaction leads to spin localization, reminiscent of the single‐spin spin‐boson model. Overall, our results reveal how spin‐bath and spin‐cavity couplings compete to shape the dissipative dynamics.