## SPONTANEOUS PARAMETRIC DOWN CONVERSION (SPDC)

 Figure 10: Principle of type-II parametric down conversion. An incident pump photon can spontaneously decay into two photons which are entangled in momentum and energy. Each photon can be emitted along a cone in such a way that two photons of a pair are found opposite to each other on the respective cones. The two photons are orthogonally polarized. Along the directions where the two cones overlap, one obtains polarization-entangled pairs. In the figure, it is assumed that a filter already selects those photons which have exactly half the energy of a pump photon.

The early experiments with entangled photons were inefficient as many photons belonging to an entangled pair were lost. This is because photons generated by a source consisting of an excited atom could be emitted in any direction and if a detector happened to register one photon of an entangled pair, there was no guarantee that its twin would be detected as well.

In fact, one of the pressing challenges in applied quantum communication is to build a robust and wide-spread communication network based on quantum protocols that require a bright source of high quality entangled photon pairs meeting the criteria: high brightness, meaning large rate of photon pairs, and high quality of entanglement, meaning large violation of a Bell inequality. Photon is a rational choice of carrier of information since it hardly interacts with the environment thus can survive against decoherence (see page 18). Moreover, single photons can be readily manipulated using current photonic technology.

But how are these entangled photons generated? Is there a way to deterministically prepare and manipulate entangled particles? The answer is yes and we will now explore how entangled photons are generated.

The phenomenon of spontaneous parametric down-conversion is an excellent way of making a source of single photons. Described as early as 1970 by D. C. Burnham and D.L. Weinberg, SPDC occurs when a non-linear and birefringent crystal is used to spontaneously split photons into pairs of daughter photons following the laws of conservation of energy and momentum. The incident photon in SPDC is referred to as the “pump” while the outgoing photons are called the “signal” and “idler”. The photons are generated spontaneously inside the crystal and hence the term spontaneous. “Down-conversion” refers to that fact that the signal and idler fields always have a lower frequency (higher wavelength) than the pump, but it occurs in accordance with conservation laws: the signal and the idler photons have combined energy and momentum equal to the energy and momentum of the original photon.

Each photon is emitted into a cone, and the photon on the top cone is vertically polarized while its exactly opposite partner in the bottom cone is horizontally polarized. The signal and idler photons in SPDC are also entangled and emerge polarized orthogonally to each other. Along the directions where the two cones intersect, their polarizations are undefined; all that is known is that they have to be different, which results in polarization entanglement between the two photons in beams. However, the conversion efficiency is very low—one pair per $10^{12}$ incoming photons. But if one of the pair, say the “signal”, is detected at any time then its partner, the “idler”, is guaranteed to be present.

SPDC is the current state of the art method for the efficient generation of high-quality and high-flux polarization-entangled photons. But how can we prove that the signal and idler photons really are entangled?

Various research groups have shown that these photons do display nonclassical correlations as they were used in the tests of Bell’s inequalities. I will now review one such experiment performed by Paul G. Kwiat and team (Kwiat, Waks, White, Appelbaum, & Eberhard, 1999) who were able to generate a “bright” source of polarization-entangled photon pairs by using SPDC in a two-crystal configuration. The researchers “obtained a $242 - \sigma$ violation of Bell’s inequalities in less than three minutes, and observed near-perfect photon correlations when the collection efficiency was reduced.”

 Figure 11: Experimental setup. Source: (Kwiat, Waks, White, Appelbaum, & Eberhard, 1999).

Entangled photons were generated when the SPDC process was induced in two type-I Beta Barium Borate (BBO) crystals pumped with 351.1 nm laser light from an $Ar^+$ laser source. The two type-I BBO crystals were aligned such that their optic axes were orthogonal to each other. The laser beam, polarized at 45º to the BBOs optical axes, was made to impinge on the BBOs resulting in the emergence of two entangled photons, one of which was polarized vertically and the other horizontally and whose energies and momenta were strictly conserved.

Coincidence detections of the signal and idler photons were performed on the two avalanche photo diode detectors by rotating the linear polarizers to select 16 different incident polarizations for the purpose of evaluating the CHSH inequality (S). The team obtained a value for S=2.7007±0.0029, confirming that no local hidden variable theory accounts for the correlation between the photon polarizations. In other words, the researchers successfully demonstrated the phenomenon of photon polarization-entanglement.

Following the initial BBO experiment, many improvements were made in entangled-pair generation efficiency, while maintaining a high degree of entanglement. Incidentally, SPDC is not the only mechanism for generating photon pairs, although perhaps the most widely used. Many new sources are under development that may yield big increase in the generation efficiency (Wong , Shapiro, & Kim, 2006).