Single-photon indistinguishability: influence of phonons

Recent years have demonstrated that the interaction with phonons plays an important role in semiconductor based cavity QED systems [2], consisting of a quantum dot (QD) coupled to a single cavity mode [Fig. 1(a)], where the phonon interaction is the main decoherence mechanism. Avoiding decoherence effects is important in linear optical quantum computing [1], where a device emitting fully coherent indistinguishable single photons on demand, is the essential ingredient.

In this contribution we present a numerically exact simulation of the effect of phonons on the degree of indistinguishability of photons emitted from a solid-state cavity QED system. Our model rigorously describes non-Markovian effects to all orders in the phonon coupling constant, being based on an exact diagonalization procedure accounting for the time evoluiton of one-time and two-time photon correlation funcitons.

We compare to standard approaches for treating the phonon interaction, namely the Markovian Lindblad formalism and the long-time limit of the non-Markovian timeconvolution-less (TCL) approach, and find large quantitative and qualitative differences [3]. Figures 1(b) and (c) show the calculated indistingusihability as a function of the QD-cavity coupling strength for light emitted from the QD and the cavity, respectively, for all the employed methods.

Both the Lindblad and TCL theories deviate significantly from our exact results, where, importantly, the exact results predict a pronounced maximum in the degree of indistinguishability, absent in the approximate theories. The maximum arises due to virtual processes in the highly non-Markovian short-time regime, which dominate the decoherence for small QD-cavity coupling, and phonon-mediated real transitions between the upper and lower polariton branches in the long-time regime, dominating the decoherence for large QD-cavity coupling.

Our method captures the physics of the regime of small and as well as large QD-cavity coupling, both corresponding to experimentally relevant situations. Importantly, the commonly used Lindblad formalism fails completely in describing the variations of the indistinguishability predicted by the two other models.