Heralded single-photon partial coherence

We study transverse spatial coherence of approximately localized single-photon states. We demonstrate nonlocal control over single-photon spatial coherence via projective measurements of an entangled twin and provide a theoretical interpretation from quantum coherence theory. Our results show that the spatial coherence of a single-photon state behaves similarly to that of a classical optical field, although the coincidence measurement adds a degree of freedom.

Figure 1

A $325$ nm collimated pump undergoes Type-I nondegenerate collinear SPDC at a nonlinear crystal. The crystal face is imaged onto an adjustable-width slit in the idler arm and a computer controlled scanning $50\hspace{0.5em}\mu$m slit in the signal arm. The diffraction pattern from the double slit mask in the signal arm is profiled by the scanning slit. Photons are detected with single-photon counting modules. A PicoHarp coincidence circuit correlates these measurements and provides results to data logging software.

Figure 2

Representative theoretical predictions for heralded single-photon two-point degree of coherence from Eq. (8) for several numbers of birth zones excited by the pump as a function of idler slit width $W$. The only difference between the curves is the birth zone size. Relevant parameters for Eq. (8) are $A=0.22$ mm${}^{-2}$, $B=1.2$ mm${}^{-2}$, $C=9.6$ mm${}^{-2}$, $D=-110$ mm${}^{-2}$, and $x=743\hspace{0.5em}\mu$m. The dotted line is the behavior of a classical incoherent source with the intensity profile of the pump beam, apertured by the slit.

Figure 3

Measured two-point degree of coherence for the heralded photon are shown. The $g^{(1)}(W)$ from Eq. (8) is shown as a dotted line. The expected $g^{(1)}(W)$ with effective idler arm scaling is shown as a solid line.

Figure 4

Detected interference patterns showing characteristics of interest for both heralded single photons (coincidences) and nonheralded photons (singles). Points are experimental data while lines are fits to the data.