Temporal coherence and indistinguishability in two-photon interference effects

We show that temporal two-photon interference effects involving the signal and idler photons created by parametric down-conversion can be fully characterized in terms of the variations of two length parameters—called the biphoton path-length difference and the biphoton path-asymmetry-length difference—which we construct using the six different length parameters that a general two-photon interference experiment involves. We perform an experiment in which the effects of the variations of these two parameters can be independently controlled and studied. In our experimental setup, which does not involve mixing of signal and idler photons at a beam splitter, we further report observations of Hong-Ou-Mandel- (HOM-)like effects both in coincidence and in one-photon count rates. As an important consequence, we argue that the HOM and the HOM-like effects are best described as observations of how two-photon coherence changes as a function of the biphoton path-asymmetry-length difference.

Figure 1

(Color online) Schematic representation of two-photon interference using two-photon path diagrams. Alternatives $a$ and $b$ are the two pathways by which a pump photon is down-converted and the down-converted photons are detected at single-photon detectors $D_A$ and $D_B$ in coincidence.

Figure 2

(Color online) Schematic of the experimental setup and the corresponding two-photon path diagrams. In alternative $a$, the pump photon gets down-converted in the forward pass while in alternative $b$, it gets down-converted in the backward pass. $F$ is an interference filter with $10\mathrm{nm}$ bandwidth, centered at $727.6\mathrm{nm}$; ID is an iris diaphragm.

Figure 3

(Color online) Measured (a) coincidence count rate $R_{AB}$, (b) count rate $R_A$, and (c) count rate $R_B$ as a function of the idler mirror position. Measured (d) coincidence count rate $R_{AB}$, (e) count rate $R_A$, and (f) count rate $R_B$ as a function of $\mathrm{\Delta }{L}^{\prime }$ for various fixed values of $\mathrm{\Delta }L$. Solid lines are the theoretical best fits.