Real-time path-integral approach for dissipative quantum dot-cavity quantum electrodynamics: impure dephasing-induced effects

A dissipative quantum dot (QD)-cavity system, where the QD is initially prepared in the excited state with no photon in the cavity, coupled to a longitudinal acoustic (LA) phonon reservoir is studied using a numerically exact real-time path-integral approach. Three distinct dynamical regimes of weak (WC), strong (SC), and coherent coupling (CC) are discussed and more accurate conditions identifying them are presented. Our results show that to have the CC regime, which is characterized by clear vacuum Rabi oscillation (VRO), vacuum Rabi splitting (VRS) should be larger than the sum of the widths of the corresponding peaks. In order to distinguish between contributions of population decay and impure dephasing, induced by LA phonon bath and the dissipations, we propose a two-part phenomenological expression, corresponding to the population decay and impure dephasing, which fits the QD-cavity decay curves perfectly and is used to calculate the corresponding spectra. We demonstrate that the effective population decay rate (the emission rate) increases from the carrier recombination rate to a maximum value, which is the mean of the QD and cavity dissipation rates, with QD-cavity coupling strength. To study the role of the effective impure dephasing rate on the width of the central peak of the spectra we introduce a quantity that can also be applied in determining the distinct coupling regimes. This quantity enables us to identify the onset of the SC regime as the point where the impure dephasing term begins to contribute to the central band of the spectrum significantly, as a result of the existence of VRO with a very small frequency (unclear VRO) at the corresponding decay curve. Its contribution to the width of the central peak increases with the coupling strength up to the onset of the CC regime, then reduces as a result of the appearance of sidebands in the spectra, which originates from clear VRO. The effective population decay and impure dephasing rate contribute solely to the width-of the central and sideband peaks of the triplet spectra respectively-only beyond a very large coupling strength which is the same across the considered temperature range. For higher temperatures, the maximum achievable emission rate can be obtained at larger coupling strengths.