Strong coupling, weak impact: Phonon coupling versus pure dephasing in the photon statistics of cooperative emitters

Realising scalable quantum networks requires a meticulous level of understanding and mitigating the deleterious effects of decoherence. Many quantum device platforms feature multiple decoherence mechanisms, often with a dominant mechanism seemingly fully masking others. In this paper, we show how access to weaker dephasing mechanisms can nevertheless be obtained for optically active qubits by performing two-photon coincidence measurements. To this end we theoretically investigate the impact of different decoherence mechanisms on cooperatively emitting quantum dots. Focusing on the typically dominant deformation-potential coupling to longitudinal acoustic phonons and typically much less severe additional sources of pure dephasing, we employ a numerically exact method to show that these mechanisms lead to very different two-photon coincidence signals. Moreover, surprisingly, the impact of the strongly coupled phonon environment is weak and leads to long-lived coherences. We trace this back to the superohmic nature of the deformation-potential coupling causing inter-emitter coherences to converge to a nonzero value on a short timescale, whereas pure dephasing contributions cause a complete decay of coherence over longer times. Our approach provides a practical means of investigating decoherence processes on different timescales in solid state emitters, and thus contributes to understanding and possibly eliminating their detrimental influences.