Overcoming non-Markovian dephasing in single-photon sources through postselection

We study the effects of realistic dephasing environments on a pair of solid-state single-photon sources in the context of the Hong-Ou-Mandel dip. By means of solutions for the Markovian or exact non-Markovian dephasing dynamics of the sources, we show that the resulting loss of visibility depends crucially on the timing of photon detection events. Our results demonstrate that the effective visibility can be improved via temporal postselection, and also that time-resolved interference can be a useful probe of the interaction between the emitter and its host environment.

Figure 1

(Color online) Visibility against ${\omega }_c\tau$ for an Ohmic bath with ${\Gamma }_{n=1}\left(\tau \right)=A\ln (1+{\omega }_c^2{\tau }^2)+A\ln [\sinh (\pi \tau ∕\beta )∕(\pi \tau ∕\beta )]$ (blue, solid line); a super-Ohmic bath with ${\Gamma }_{n=3}\left(\tau \right)=A{\omega }_c^2{\tau }^2(3+{\omega }_c^2{\tau }^2)∕{(1+{\omega }_c^2{\tau }^2)}^2+A[{\pi }^2∕3{\left({\omega }_c\beta \right)}^2-1∕{\left({\omega }_c\tau \right)}^2+{\pi }^2{\mathrm{csch}}^2(\pi \tau ∕\beta )∕{\left({\omega }_c\beta \right)}^2]$ (yellow, dashed line); and Markovian dephasing of rate ${\Gamma }_M\left(\tau \right)=A\pi \tau ∕\beta$ (red, dotted line). Parameters: $A=0.5$, ${\omega }_c\beta =10$. Inset: Schematic of the interference setup. Two photons incident on a 50:50 beam splitter (BS) interfere such that they are always detected at the same output, provided the photons themselves and the paths they take are identical. The resulting absence of coincidence counts between the detectors is known as the HOM dip. Its visibility measures the indistinguishability of the incident photons.

Figure 2

(Color online) Visibility against ${\omega }_c\Delta$ for the Ohmic (blue, solid line), super-Ohmic (yellow, dashed line), and Markovian (red, dotted line) baths. Parameters are as in Fig. 1, with $\gamma ∕{\omega }_c=0.01$.