Einstein-Podolsky-Rosen correlations from colliding Bose-Einstein condensates

We propose an experiment which can demonstrate quantum correlations in a physical scenario as discussed in the seminal work of Einstein, Podolsky, and Rosen. Momentum-entangled massive particles are produced via the four-wave mixing process of two colliding Bose-Einstein condensates. The particles’ quantum correlations can be shown in a double–double-slit experiment or via ghost interference.

Figure 1

Schematic of the double–double-slit experiment (not drawn to scale). Pairs of atoms collide at height $H$ and fall under gravity through the double slits onto the detector. See main text for details.

Figure 2

Schematic of the double–double-slit experiment (top view, not drawn to scale). Pairs of atoms, A and B, are emitted from source points ${\mathbf{r}}_{\text{S}}$ within the BEC, pass double slits, and arrive at detectors at positions ${\mathbf{r}}_{\text{A}}$ and ${\mathbf{r}}_{\text{B}}$. See main text for details.

Figure 3

Two-particle probability distribution $|{\psi }_{\text{AB}}^{\text{(dds)}}{|}^2$ for the double–double-slit experiment for different source sizes. The slit distance $d=100$ $\mu$m, source-slit distance $L_1=5$ mm, and slit-detector distance $L_2=25$ mm are kept fixed, resulting in a constant fringe distance $d_f\simeq 271$ $\mu$m. For a very small source (top left, $S_x=25$ $\mu$m) the momentum spread of each individual particle is large, and one obtains a product of two one-particle patterns of the form ${\cos }^2\left(\pi \frac{x_{\text{A}}}{d_f}\right){\cos }^2\left(\pi \frac{x_{\text{B}}}{d_f}\right)$. If the source is larger than the slit distance (bottom right, $S_x=$ 200 $\mu$m), two two-particle patterns together wash out again into a factorizable pattern. An intermediate source size (top right, $S_x=50$ $\mu$m) fulfills all conditions for two-particle interference and shows a distribution of the unfactorizable form ${\cos }^2\left(\pi \frac{x_{\text{A}}-x_{\text{B}}}{d_f}\right)$.

Figure 4

Schematic of the ghost interference experiment (top view, not drawn to scale). Pairs of atoms, A and B, are emitted from source points ${\mathbf{r}}_{\text{S}}$ within the BEC and arrive at detectors at positions ${\mathbf{r}}_{\text{A}}$ and ${\mathbf{r}}_{\text{B}}$. Only atom A passes through a double slit. See main text for details.

Figure 5

Two-particle probability distribution $|{\psi }_{\text{AB}}^{\text{(gh)}}{|}^2$ for the ghost interference experiment for different source sizes. The source-slit distance $L_1=5$ mm and slit-detector distance $L_2=25$ mm are the same as in Fig. 3. The slit distance $d=50$ $\mu$m is smaller now, leading to larger fringe distances $d_f^{\text{(A)}}\simeq 542$ $\mu$m and $d_f^{\text{(B)}}\simeq 758$ $\mu$m at sides A and B, respectively. A very small source (top left, $S_x=50$ $\mu$m) results in a product of two one-particle patterns. Large sources (bottom, $S_x=200$ and 400 $\mu$m) show two-particle interference and produce a pattern of the unfactorizable form ${\cos }^2\left(\pi \frac{x_{\text{A}}+x_{\text{B}}}{d_f}\right)$.