Violation of Bell’s Inequality with Photons from Independent Sources

We report a violation of Bell’s inequality using one photon from a parametric down-conversion source and a second photon from an attenuated laser beam. The two photons were entangled at a beam splitter using the postselection technique of Shih and Alley [Phys. Rev. Lett. 61, 2921 (1988)]. A quantum interference pattern with a visibility of $91\%$ was obtained using the photons from these independent sources, as compared with a visibility of $99.4\%$ using two photons from a central parametric down-conversion source.

Figure 1

An overview of the Shih-Alley technique [8] used to violate Bell’s inequalities. In our experiment, one of the input photons is heralded from a down-conversion pair, while the second input photon is postselected from an auxiliary weak coherent state.

Figure 2

A simplified schematic of the experiment used to postselect two-photon entanglement from independent sources. Details and symbols are described in the text.

Figure 3

Experimental results of a two-photon Hong-Ou-Mandel test [20] using the apparatus of Fig. 2. The data shows coincidence counts between detectors $D_1$ and $D_2$ as a function of relative optical delay between the down-converted beams when fibers $A$ and $B$ were used as the inputs to the $50/50$ beam splitter. The solid line is a least-squares fit to a simple Gaussian function with a visibility of $(99.4\pm 0.1)\%$.

Figure 4

Observation of a highly nonclassical three-photon quantum interference dip [19, 20]. The data shows the threefold coincidence counts (i.e., gated two-photon events) as a function of the relative optical delay between a heralded single photon and a single photon postselected from a weak coherent state. The solid line is a least-squares fit to a simple Gaussian function with a visibility of $(90.8\pm 1.7)\%$.

Figure 5

Experimental signature of the polarization entangled state of Eq. (1) postselected from independent sources. The data shows the accumulation of three-photon (i.e., gated two-photon) coincidence counts as a function of the setting of ${\theta }_1$. The solid line is a least-squares fit to a Sine-squared function with a visibility of $(86.4\pm 3.2)\%$. This high visibility represents the main result of this paper.