Introduction to the absolute brightness and number statistics in spontaneous parametric down-conversion

Abstract

As a tutorial, we examine the absolute brightness and number statistics of photon pairs generated in Spontaneous Parametric Down-Conversion (SPDC) from first principles. In doing so, we demonstrate how the diverse implementations of SPDC can be understood through a single common framework, and use this to derive straightforward formulas for the biphoton generation rate (pairs per second) in a variety of different circumstances. In particular, we consider the common cases of both collimated and focused gaussian pump beams in a bulk nonlinear crystal, as well as in nonlinear waveguides and microring resonators. Furthermore, we examine the number statistics of down-converted light using a non-perturbative approximation (the multi-mode squeezed vacuum), to provide quantitative formulas for the relative likelihood of multi-pair production events, and explore how the quantum state of the pump affects the subsequent statistics of the downconverted light. Following this, we consider the limits of the undepleted pump approximation, and conclude by performing experiments to test the effectiveness of our theoretical predictions for the biphoton generation rate in a variety of different sources.

Towards tailored single-photon sources using continuously-tapered waveguides

“…In both the normal and inverted cases we observe multiple high gain peaks generated away from the central wavelength, indicating that high conversion efficiency can be achieved far from the pump frequency using the PTWtechnique. The spectral band around 750nm in the inverted Gaussian fibre is found to generate approximately 2.79 × 10 9 photons per second after 50 periods, offering photon generation rates close to those found in SPDC schemes [35], which shows the potential for our structures. This number increases to 1.12 × 10 10 photons for 200 periods.…”

Simulating Correlations of Structured Spontaneously Down‐Converted Photon Pairs

“…In this process, momentum conservation dictates that the spontaneously generated photon pairs from a pump beam parallel to the optical axis, are emitted into a cone, concentric with the optical axis, wherein the far‐field pattern corresponds to a circle ( Figure a). The theoretical opening angle θ of the cone is determined by the phase‐matching condition For small pump powers, one may use first‐order perturbation theory to obtain analytically the generated two‐photon state, from which both the intensity pattern, G (1) (since , we omit the indices), and the coincidence rate, G (2) , could be derived . A characteristic feature of these photons is their demonstration of anti‐correlation: they are always emitted into opposite directions on the cone (see Figure b).…”

Entanglement-based quantum key distribution with a blinking-free quantum dot operated at a temperature up to 20 K

“…These sources are commercially available and can be operated in a large temperature range. 11 As a drawback, SPDC sources exhibit approximately Poissonian photon pair emission characteristics, 12 which severely limits their brightness when a high degree of entanglement-and thus a low qubit error rate (QBER)-is demanded. The biexciton-exciton (XX-X) spontaneous decay cascade in epitaxially grown semiconductor quantum dots (QDs) has been demonstrated to be a viable alternative to SPDC sources due to the sub-Poissonian entangled photon pair emission statistics.…”