We’ve just published a quick guide to “Tailoring nonlinear processes for quantum optics with temporal mode encodings,” online now at Optica and on the arXiv. A big congratulations and thanks to my co-authors in Paderborn (Vahid Ansari and Christine Silberhorn) and Oxford (Benni Brecht).
The review collects a lot of information that’s become “conventional wisdom” to an extent in the community, but still can be difficult to talk straight about. Maybe the best starting point for the quantum-optics community is from the joint-spectral-intensity picture of spontaneous parameter downconversion. Many of us have waved our hands around to explain why, when a pump photon splits into a signal and idler pair, they generally have frequency anti correlations (because energy conservation demands it so) and time correlations (because they must have been created at the same time). However, when pulsed broadband pumps get involved, the energy conservation concerns become relaxed. When the group-velocities of the fields involved differ (which is the same statement, to first order, as saying that phasematching becomes restrictive), those timing arguments also change. There are still very physical ways to motivate the results of, for example, extended-phasematching for pure photon sources, but increasingly the continuous time/frequency picture limits its usefulness.
By switching to a time-frequency mode picture, we not only get the fundamental answer to questions like “how entangled is our photon pair?” or “what is the useful dimensionality of our photon?”, but we also can find new ways to engineer particular states of light by selecting specific group-velocity relationships to tailor the phasematching. Not only is this useful for downconversion, but we can invert the problem for sum-frequency generation: instead of generating a photon pair in a single pulsed temporal mode, we want to upconvert a photon if and only if it exists in a specific pulsed temporal mode. Mode-selective upconversion, called a quantum pulse gate to emphasize the SPDC analogy, has recently become something of a hot topic in the sub-sub-community, and here we outline (from the basics) how to make it work, how well its working so far, and what’s left to do to really make it sing.