Probing Cooper pairs with Franson interferometry

A setup based on the Franson optical interferometer is analyzed, which allows us to detect the coherence properties of Cooper pairs emerging via tunneling from a superconductor in contact with two one-dimensional channels. By tuning the system parameters we show that both the internal coherence of the emitted Cooper pairs, which is proportional to Pippard's length, and the de Broglie wavelength of their center-of-mass motion can be measured via current-current correlation measurements.

Figure 1

Schematics of the Franson interferometer (optical implementation). The EPR-like state (2) is injected by the source $S$ along the two optical paths $L$ and $R$, while the coincidence counts are recorded at the detectors, e.g., $(L,-)$ and $(R,-)$, to reveal the two-photon coherence of the emitted biphoton state.

Figure 2

Four interfering processes: (a) long-long (LL) (solid lines) and short-short (SS) (dashed lines), (b) long-short (LS) (solid lines) and short-long (SL) (dashed lines).

Figure 3

The pair wave function ${\left|\Phi \left(x\right)\right|}^2$ [normalized by ${(AeV/|\Delta \left|\right)}^2$] as a function of $x$ and $eV$, on the basis of the numerical integration of Eq. (49). The parameters are $\left|\Delta \right|=150\mu \mathrm{eV}$, ${\lambda }_F=2\pi /k_F=0.36\mathrm{nm}$, ${\mu }_S=11.6\mathrm{eV}$, $d=150\mathrm{nm}$, and $\xi =2.8\mu \mathrm{m}$ for an Al superconductor.[32]