Franson Interference Generated by a Two-Level System

We report a Franson interferometry experiment based on correlated photon pairs generated via frequency-filtered scattered light from a near-resonantly driven two-level semiconductor quantum dot. In contrast to spontaneous parametric down-conversion and four-wave mixing, this approach can produce single pairs of correlated photons. We have measured a Franson visibility as high as 66%, which goes beyond the classical limit of 50% and approaches the limit of violation of Bell’s inequalities (70.7%).

Figure 1

(a) Theoretical one-photon spectrum (spectral density) for Rabi frequency $\mathrm{\Omega }/2\pi =1.6\mathrm{GHz}$ and laser detuning $\delta /2\pi =1.0\mathrm{GHz}$. (b) Experimental two-photon spectrum for the same parameters with filter bandwidths ${\mathrm{\Gamma }}_1/2\pi ={\mathrm{\Gamma }}_2/2\pi =\mathrm{\Gamma }/2\pi =0.45\mathrm{GHz}$. The recording time for each frequency pair on the $29\times 29$ point grid was identical and equal to 165 s, which together with various delay times make the total measurement time of the map equal to about 42 hours.

Figure 2

(a) Experimental setup. The split frequency-filtered scattered light from a QD is connected to two unbalanced Mach-Zehnder interferometers, with $L_1=L_2=L=190\mathrm{cm}$ and $S_1=S_2=S=2\mathrm{cm}$. The phase of each interferometer (${\mathrm{\Phi }}_i)$ is controlled by varying the length of their respective short arms. (b) Second-order correlation function for $\mathrm{\Omega }/2\pi =1.6\mathrm{GHz}$, $\delta /2\pi =1.2\mathrm{GHz}$, $({\omega }_1-{\omega }_L)/2\pi =-({\omega }_2-{\omega }_L)/2\pi =2.0\mathrm{GHz}$. (c) One-photon interference (95%) observed at each interferometer during the alignment process, using the pump laser as the interferometer input. The blue line denotes the background level.

Figure 3

Histograms of the normalized coincidence rate for two different phase settings as indicated, (a) minimizing and (b) maximizing the central peak. The measurement time was 600 s for each panel and the bin width was 256 ps. The red and pink shaded areas indicate the coincidences involved in the calculation of the visibility as defined in the text. The dashed black line indicates the accidentals level.

Figure 4

Normalized coincidences in the central peak plotted as a function of the phase ${\mathrm{\Phi }}_1+{\mathrm{\Phi }}_2$ with a postselection window width of (a) 1024 ps and (b) 4096 ps. (c) Franson visibilities for different measurement settings. The red dashed line and the green solid line indicate the classical limit (50%) and the limit at which Bell’s inequalities are violated (70.7%), respectively.