Interference of Cooper pairs emitted from independent superconductors

We discuss the interference in the two-particle distribution of the electrons emitted from two independent superconductors. It is clarified that, while the interference appearing in the antibunching correlation is due to the Hanbury Brown and Twiss effect, that in the positive correlation due to superconductivity is intrinsically different and is nothing but the first-order interference of Cooper pairs emitted from different sources. This is the equivalent of the interference of two independent Bose-Einstein condensates.

Figure 1

(Color online) Electrons are emitted from two independent superconductors $A$ and $B$ with the phases of the superconducting states ${\varphi }_A$ and ${\varphi }_B$, respectively, and we count coincidences at ${\mathit{r}}_1$ and ${\mathit{r}}_2\left(r_1=r_2=r\right)$. The emitting regions, both of size $w$, are separated by $\mathit{d}$. The directions to the detectors 1 and 2 are specified by the angles ${\theta }_1$ and ${\theta }_2$ measured from the dashed line perpendicular to $\mathit{d}$.

Figure 2

(Color online) Correlation function $\delta Q\left({\theta }_1,{\theta }_2\right)=Q-1$ for different placements of the detectors. The interference pattern in the bunching correlation (indicated by “bunching”) is affected by the relative phase $\Delta \varphi$, while that in the antibunching (indicated by “antibunching”) is not.

Figure 3

(Color online) Interfering processes (solid lines vs dashed) giving rise (a) to the fringes in the antibunching correlation and (b) to those in the bunching one.