Tracking phase entanglement during propagation of downconverted photons

Abstract: High-dimensional entanglement in the form of transverse spatial correlation between a pair of photons generated via spontaneous parametric downconversion is not only a valuable resource in many academic and real-life applications but also provides access to several intriguing quantum phenomena. One such non-intuitive phenomenon is phase entanglement, in which the biphoton state is correlated in the complex phase of its wavefunction. This state, which emerges during the propagation of the biphoton wavefunction, exhibits neither position nor momentum correlation, yet retains full entanglement. In this work, we experimentally explore this state in two distinct ways. The first is by tracking the vanishing spatial photon number correlation over propagation distances lying in $\left[0,\infty\right)$, folded into a finite range using single-lens imaging. These observations show excellent agreement with our theoretical predictions based on the Double Gaussian (DG) approximation of the biphoton state. The second approach involves performing a two-photon interference experiment using a double slit and this state, which reveals the correlated phase front. We show, both theoretically and experimentally, that the observed two-photon interference structure is markedly different from that produced by position-correlated photons, as confirmed by computing the joint probability distribution of photons (JPD) and related metrics. Such interference using phase-entangled light has not been attempted before and opens avenues for advanced experiments and applications in the field of spatial entanglement.