Fig. 4: Frequency mixing and two-photon interference.
From: Programmable frequency-bin quantum states in a nano-engineered silicon device
a Schematic of the effect of modulation on the generated idler (red) and signal (blue) frequency bins. The frequency mixing produces maps each of the signal and idler states in a superposition of three frequency components: the outermost ones are reminiscent of the probability amplitude proportional to \({\left|0\right\rangle }_{{{{{{{{\rm{s}}}}}}}},{{{{{{{\rm{i}}}}}}}}}\) or \({\left|1\right\rangle }_{{{{{{{{\rm{s}}}}}}}},{{{{{{{\rm{i}}}}}}}}}\), while the “central” bin results in a superposition of the two. Each frequency-shifted bin also acquires a phase ± φs,i due to the modulation. The superposition of the generated bins is regulated by the modulation frequency, and the overlap is ideally maximized when fm = Δ/2, when perfect indistinguishability of the generated bins is achieved. b Two-photon correlation \({G}_{1,2}^{(2)}\) of the frequency-mixed bins as a function of the detuning fm − Δ/2. The experimental points (black dots) were obtained by counting coincidences between frequency-mixed bins at varying modulation frequency, while keeping fixed the modulation phase, and normalizing. Error bars (light gray) were estimated assuming Poissonian statistics. Blue curve represents the best-fit of the curve according with Eq. (2), showing good agreement (c) with theoretical predictions.
