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Study of decoherence in models for hard-core bosons coupled to optical phonons

Understanding coherent dynamics of excitons, spins, or hard-core bosons (HCBs) has tremendous scientific and technological implications for light harvesting and quantum computation. Here, we study decay of excited-state population and decoherence in two models for HCBs, namely: an infinite-range HCB model governed by Markovian dynamics and a two-site HCB model with site-dependent strong potentials and subject to non-Markovian dynamics. Both models are investigated in the regimes of antiadiabaticity and strong HCB-phonon coupling with each site providing a different local optical phonon environment; furthermore, the HCB systems in both models are taken to be initially uncorrelated with the environment in the polaronic frame of reference. For the infinite-range model, we derive an effective many-body Hamiltonian that commutes with the long-range system Hamiltonian and thus has the same set of eigenstates; consequently, a quantum-master-equation approach shows that the quantum states of the system do not decohere. In the case of the two-site HCB model, we show clearly that the degree of decoherence and decay of excited state are enhanced by the proximity of the site-energy difference to the eigenenergy of phonons and are most pronounced when the site-energy difference is at resonance with twice the polaronic energy; additionally, the decoherence and the decay effects are reduced when the strength of HCB-phonon coupling is increased. Even for a multimode situation, the degree of decoherence and decay are again dictated by the nearness of the energy difference to the allowed phonon mode eigenenergies.