Parametric Down-Conversion

 

The process known as parametric down-conversion(PDC) is a  consequence of a non-linear interaction between light and certain types of crystals, called non-linear crystals. The process is sketched in Fig. 1.

 

 

A pumping laser shines the non-linear crystal. The crystal is almost transparent for the laser, but some photons are converted into pairs of new photons. It is possible to see with naked eye (using only color filters to prevent against excessive pump laser radiation) the light produced in the process.  It looks like the rainbow cone sketched in Fig. 1. Within the light cone it is possible to find twin photons, if one searches in the directions defined by the phase matching conditions, which are basically given by energy and momentum conservation:

where the indexes p,s and I mean pump, signal and idler respectively.

 

In general, a laser is used to pump the non-linear crystal, because the conversion efficiency is low. h  ~ 10-6 is a typical value. It depends on the non-linear crystal and on the wavelengths involved. For the purpose of generating entangled photons, BBO(barium beta-borate)  and LiIO3(Lithium Iodate)  are the most used nonlinear crystals. Even though the conversion efficiency is an important parameter, the choice of the wavelengths for the pump laser and down-converted signal and idler photons is dominated by the availability of photon counting detectors with high detection efficiency and availability of  pumping lasers in the corresponding wavelength. For instance, if one uses silicon avalanche photon counters, the best efficiencies associated with low dark counts are found around the wavelength  l = 700nm. In this case, the best choice is to use an Argon laser to pump with l = 351nm and to detect twin photons, both with wavelength l = 702nm. However,  a much less expensive solution in terms of  pump laser can be found with gas lasers like He-Cd(l = 442nm) and solid state lasers(l ~ 400nm). The down-converted wavelength shifted to l ~ 800 to 900nm can still be detected with efficiencies of  h  ~  35 to 45%, enough to several applications.

 

PDC occurs spontaneously, induced by vaccum fluctuations, Fig.1 a). It can also be stimulated by an external intense field, Fig. 1 b). An auxiliary laser can be aligned with a down-conversion mode having the same wavelength. This auxiliary laser field stimulates the emission in the down-conversion mode and its conjugate indirectly. The coherence properties of the signal and idler fields are also affected  and tend to those of a coherent field in the limit of very intense stimulating field.

 

Coincidence Detection

 

 

Fig. 2 shows a typical coincidence detection scheme. Signal and idler photons from the parametric down-conversion(PDC) are detected with single photon detectors. Ideally, each photon gives rise to an electronic pulse, even though in practice some of the photons are lost due to non ideal quantum efficiency of the detectors. The electronic pulses are then sent to devices that count the single photon events and coincidence. There are several devices that can be used in this task. The main requirement is that they are fast enough to distinguish between the arrival of two consecutive pulses and fast enough to implement the coincidence within the time window required. Typical single photon counting rates are not higher than 106 s-1, therefore the mean time separation between pulses is usually higher than 1ms. Even if one has a higher photon flux, the time between consecutive pulses is limited by the dead time of the detector, which is typically not smaller than 50ns. The dead time is the time interval  after one photon is detected, required to prepare the detector for another detection event. For the coincidences,  the electronic requirements depend on the coincidence window. The coincidence window is the maximal time interval between the arrival of the pulses generated by a signal and an idler photon. Typical values range between 1 to 10ns. Therefore, the electronic devices are required to be fast enough to count a pulse triggered(conditioned) by another one within a time window of a few nanoseconds.