Espectros Raman del Carbono amorfo

Since the first demonstration of a source producing polarization-entangled photon pairs based on an atomic decay, a wealth of theoretical proposals and experimental prototypes have been reported. Nowadays, the generation of entangled photon pairs is a routine lab work and the development of sources focuses largely on their simplifi- cation and/or optimization of their performance. The most widely spread way how to generate entangled photon pairs relies on the emission from the SPDC. Nevertheless, novel techniques of photon-pair generation based on the four-wave mixing process in nonlinear optical fibres or on the decay processes in semiconductor structures have been suggested, offering a great potential to outperform the traditional approaches eventually, and thus to be once widely integrated in practical applications. In the fol- lowing the most common methods are briefly described, pointing out their strengths and/or weaknesses and possible future prospects.

3.2.1 SPDC sources

Presently, the two most established methods to generate polarization-entangled pho- ton pairs utilize spontaneous parametric down conversion. The first makes use of type-II phase-matching in a single crystal [56], whereas the second relies on the coherent spatial overlap of the emissions from two adjacent type-I phase-matched nonlinear crystals [57]; (for further details see section 2.5.2). Usually, due to the

non-collinear geometry of the methods, the nonlinear crystal must be relatively short (typically in the range from 0.5 mm to 3 mm), thereby limiting strongly the potential brightness of the methods to the order of only hundreds of coincidence counts per second. Many variations of the two original proposals including confinement of the nonlinear crystal in a cavity [72] or phase-compensated collection of a wider solid angle of the emitted light [73] were reported over the past few years enhancing the yield of down-conversion photons by roughly an order of magnitude.

Birefringent phase matching in materials with a relatively high nonlinearity, such as beta-barium borate or lithium iodate (LiIO3), is regularly applied for the SPDC process. However, this method fails, when the material does not exhibit sufficient birefringence at the interacting wavelengths. As an alternative, quasi-phase matching in periodically poled structures can be used, opening the possibility to noncritically phase match almost any combination of wavelengths within the transparency range of the nonlinear materials. This enables to access the highest nonlinear coefficients of many materials, such as lithium niobate (LiNBO3), lithium tantalate (LiTaO3) or potassium titanyl phosphate (KTiOPO4), thereby enhancing the overall conversion efficiency of the SPDC process.

Different configurations of sources using bulk periodically poled crystals were in- vestigated over the recent few years. The best results were reported in collinear geometry using bi-directional pumping of a single periodically poled crystal [74, 75] or coherent overlap of the emissions from two crystals [76, 77, 78]. This way, the brightness increased by at least one order of magnitude in comparison to sources using BBO crystals, reaching values above 104 _{detected pairs/s/mW, while at the} same time keeping the high purity of polarization entanglement. A further boost of photon-pair yield might be expected, when exchanging bulk crystals for nonlinear periodically poled waveguides. Due to the field confinement, waveguides provide an improved mode overlap of the interacting waves, leading to an enhancement of the conversion efficiency. Conversion efficiencies of up to 10−6_{, roughly 4 orders of magni-} tude more than that obtained with BBO crystal, were already demonstrated, though without the possibility for direct generation of polarization entanglement [79, 80].

3.2.2 Fiber sources

Four-wave mixing (FWM) via the third-order (χ(3)_{) nonlinearity of optical fibers can} be utilized to generate correlated photon pairs at unequal wavelengths [81]. The gen- erated pairs are predominantly co-polarized with the pump, which can be exploited for obtaining polarization entanglement by bi-directional pumping of a fiber Sagnac loop [82]. This geometry has the advantage that the counter-propagating pairs re- main in a coherent superposition without the need for any phase or path adjustments. Substantial interaction lengths together with the strong mode confinement lead to unprecedented brightness [83]. However, the occurrence of significant spontaneous Raman background makes the actual production of high-purity polarization entan- glement complicated. Usually, pumping at very low powers, a careful filtering of

true correlated photon pairs and an operation at liquid nitrogen temperatures is re- quired, to reach near-to-unity quantum-interference visibility [84]. This problem can be somewhat avoided by pumping the fiber in normal dispersion regime generating photons at widely spaced wavelengths (typically by hundreds of nanometers) outside the Raman scattering region. In either case, the need of mode-locked picosecond lasers for pumping the FWM process together with the difficulties in extracting high- purity polarization entanglement make today’s fiber sources less suitable for practical applications. Nevertheless, the achieved high production rates suggest their possible future applicability in multi-photon quantum information experiments [85].

3.2.3 Semiconductor sources

Semiconductor quantum dots became widely utilized as optically and electrically driven sources of single photons on demand. Few years ago, the biexciton decay in a single quantum dot via an intermediate exciton level was proposed to provide a source of triggered, entangled photon pairs [86]. In contrast to afore-mentioned methods based on SPDC and FWM processes, which generate probabilistic numbers of photons pairs, the biexciton decay produces no more than two photons per excitation cycle. This makes such a compact and integrated device a favorable alternative to other sources, with the additional benefit of being easily implemented using simple, LED- like technologies.

Practically, structure asymmetries lead to polarization dependent splitting of the intermediate exciton level, resulting in only polarization correlated photons. How- ever, two schemes to eliminate the polarization splitting by control of growth or application of magnetic field, have enabled the recent observation of polarization- entangled photons, although at very poor quality [87]. Many tremendous engineering challenges still remain in order to realize a practical quantum dot source of entangled photons. Improvements must be made to the efficiency of the device, to the frequency of operation, and, most importantly, to the degree of entanglement.