We present a simple but highly efficient source of polarization-entangled photons based on spontaneous parametric down-conversion (SPDC) in bulk periodically poled potassium titanyl phosphate crystals (PPKTP) pumped by a 405 nm laser diode. Utilizing one of the highest available nonlinear coefficients in a non-degenerate, collinear type-0 phase-matching configuration, we generate polarization entanglement via the crossed-crystal scheme and detect 0.64 million photon pair events/s/mW, while maintaining an overlap fidelity with the ideal Bell state of 0.98 at a pump power of 0.025 mW.
© 2012 Optical Society of America
A number of key experiments [1–3] have shown that entangled photons are not only of paramount importance to questions regarding the nature of physical reality , but can also find real-world applications in quantum communication. Considerable progress has been made in the distribution of entanglement over long-distance free-space links [5,6], with the next generation of envisaged projects likely to advance to experiments involving ground to satellite or inter-satellite links  ultimately enabling efficient quantum communication on a global scale. Many obstacles must be overcome towards the realization of world-wide quantum networks, in particular, the engineering of robust sources of entangled photons with sufficient brightness and entanglement visibility. Several schemes for the generation of photon pairs have been proposed and demonstrated [8–10], but at present by far the most convenient choice remains spontaneous parametric down-conversion (SPDC) in χ(2) nonlinear crystals. In the first generation of type-II SPDC based sources , correlations in energy and momentum were exploited to generate polarization-entangled photons in restricted spatial regions. The pair collection efficiency was improved by overlapping type-I emission cones from separate crystals . The scheme was however limited to relatively short crystals due to the non-collinear configuration. A significant increase in the yield was obtained with a collinear non-degenerate configuration, which allowed the entangled photons to be efficiently coupled into single-mode fibers . Further improvements were achieved in sources that made use of periodically poled materials [14–16]. Current developments in waveguide technology also present an attractive option for future entangled photon sources [17, 18].
The approach presented in this paper is based on collinear, non-degenerate SPDC emission around 810 nm from two crossed type-0 PPKTP crystals pumped by a 405nm laser diode (LD), as previously demonstrated in . With respect to this previous setup, which made use of beta-BaB2O4 crystals (BBO), we make use of two 20 mm periodically poled KTiOPO4 (PP-KTP) crystals. The crossed-crystal geometry allows accessing the largest nonlinear coefficient in PPKTP which is almost an order of magnitude larger than that utilized in other schemes and allows us to achieve unprecedented pair detection rates, under relaxed alignment requirements [14,19,20]. High entanglement visibility was obtained by efficient cancellation of which-crystal information via an appropriately chosen Yttrium Vanadate (YVO4) crystal [15, 21, 22]. The tailored nonlinearity applied here enables the use of well-developed blue laser diodes to generate photon pairs in a spectral region efficiently detectable with silicon avalanche photodiodes . The simple, inherently robust set-up, together with the high yield of photon pairs, make our source of entangled photon pairs a valuable tool for the envisaged future field trials over atmospheric free-space links.
1. Type-0 SPDC in PPKTP
Spontaneous parametric down-conversion in second-order nonlinear crystals is a process in which atoms of the crystal mediate the conversion of a high energy pump photon into two photons with lower frequency, conventionally termed signal and idler photons. Depending on the polarizations of the interacting fields, one distinguishes between type-0, type-I and type-II SPDC, whereby type-I and II processes involve orthogonally polarized fields, whereas in type-0 processes all photons are co-polarized. SPDC is possible for wavelengths that fulfill both energy conservation ωp = ωs + ωi as well a phase-matching conditions (here ωp,s,i denote the angular frequencies of the respective pump, signal and idler photons, while k⃗p,s,i denote the respective wave-vectors). Recent advances in periodic poling technology, achieving increasingly shorter poling periods Λ, allow first-order quasi-phase-matching for almost any wavelengths and polarizations. The spectral properties of the SPDC emission are given byFigure 1 shows the temperature-dependent SPDC response of photon pairs emitted collinearly from a 20 mm flux grown type-0 PPKTP crystal  with a poling period of 3.425 μm, pumped by a single-frequency laser diode with a center wavelength (CWL) of 405.4 nm. From this we determined the SPDC CWL and FWHM of signal and idler photons shown in Fig. 2. An important parameter subject to optimization when designing an efficient entangled photon source, is the focus geometry. It has been shown in several theoretical and experimental studies [14, 25, 26], that efficient coupling of SPDC into single-mode fibers (SMF) is achieved by selecting the confocal beam parameters of pump, signal and idler fields appropriately. We performed an experimental optimization of these parameters for our 20 mm type-0 PPKTP crystals and found the highest coincidence rates for a waist combination of wp ∼ 18μm and ws,i ∼ 24μm for the pump, signal and idler modes, respectively. With the pump waist fixed to its optimal value, we see that the maximal coincidences were obtained by setting . This can be understood as matching the Rayleigh ranges zR = w2π/λ of SPDC and pump fields to optimize coupling. Note that these values are consistent with the optimal values of wp ∼ 22μm and ws ∼ 31μm predicted in .
2. Entangled photon source
We generate co-polarized photon pairs at non-degenerate wavelength around 810 nm via the large nonlinearity of KTP . This operating wavelength was selected with respect to possible free-space communication applications, as an optimized tradeoff between atmospheric transmission, beam divergence over long-distance links, detector efficiency and the availability of compact LD pump sources. The periodic poling of the crystal allows tailoring the interaction to a collinear non-critical phase-matching condition. This eliminates spatial walk-off and allows efficient coupling into a single-mode fiber, where the signal and idler photons are spectrally isolated using a fiber-based wavelength division multiplexer (WDM). The single-mode WDM output provides a versatile plug-and-play interface and ensures minimum diffraction over long distance links. Polarization-entanglement is generated in a crossed-crystal configuration . In this scheme two mutually orthogonally oriented PPKTP crystals are placed directly one after the other. This double-crystal configuration is pumped with UV-light polarized diagonally with respect to the two crystallographic z-axis, which leads to equal probabilities for photon pair emission from the first crystal (in state |HsHi〉) or from the second one (state |VsVi〉). Thus a polarization-entangled state
However, as a consequence of the crossed-crystal geometry, the |HsHi〉 pairs generated in the first crystal acquire an additional phase shift relative to the |VsVi〉 pairs emitted from the second. As this can yield which-crystal information that leads to de-phasing of the entangled state, compensation of this phase is required. To briefly discuss the compensation scheme, we compare photon pairs generated at the input facet of the first and second crystal. In this case the accumulated phase difference, resulting from individually acquired phases of horizontally and vertically polarized signal and idler photons at the output of the second crystal, readsFig. 3. In order to counteract this de-phasing effect, a 30.01 mm YVO4 crystal exhibiting opposite birefringent characteristics ϕC(λs,λi) is inserted after the down-conversion crystals. According to 13, 22], still allowing the use of free-running or pulsed pump sources. A more detailed calculation in the time domain can be found in [21, 22].
3. Experimental setup
In the experimental setup (Fig. 4), the astigmatic output beam of a volume holographic stabilized laser diode (Ondax Inc.) with a center wavelength of 405.04 nm is corrected by a 2:1 astigmatism telescope consisting of two cylindrical lenses. The circular pump beam is then focused to the optimized waist size of approximately 18 μm [25, 26] at the center interface of two 20 mm crossed PPKTP crystals. The crystals have a poling period of 3.425 μm for type-0 collinear phase-matching from 405 nm to the non-degenerate wavelengths 783nm (signal) and 837 nm (idler). The two crystals are mounted on a double-oven consisting of two individual Peltier elements to account for differences in the crystals and maintain them at phase-matching temperatures for equal center wavelengths. For our crystals this amounted to a temperature difference of 0.22°C (most likely due to imperfections in the crystal growing process resulting in inhomogeneities of the refractive index). The SPDC photons inherit a mode with a waist size of ∼ 24 μm and propagate collinearly with the pump laser. A dichroic mirror (DM) transmits 99% of the pump photons and reflects the SPDC photons through a 30.01 mm YVO4 crystal, which reverses dispersive de-phasing effects. An additional 100 μm thick YVO4 plate was angle tuned to set the relative phase of the polarization-entangled state. A color-glass long pass filter isolates the remaining pump photons and rejects stray light. Using a f =11 mm aspheric lens, the SPDC photons are coupled into a single-mode fiber, guiding the photons to a WDM which splits signal and idler photons with non-degenerate wavelengths into two output fibers. To assess the performance of the source, the output ports of the WDM were each collimated and sent to a free-space single-port polarization analyzer, consisting of a quarter-wave plate (QWP) and a thin-film polarizer. The photons are then further filtered via an interference filter with a FWHM of 3.5 nm and a peak transmission of ∼90%, placed in signal path. This surpessed broadband background emission from the PPKTP crystals and increased the spectral overlap of SPDC from the two crystals (see Fig. 5). After traversing the analyzer modules, the signal and idler photons are coupled into multi-mode fibers and guided to two single-photon avalance diodes (SPAD) with an approximate detection efficiency of ∼ 40% (∼500 cps dark counts), where coincident measurement events were recorded via a fast time-to-digital converter (quTAU) with the coincidence window set to 2.4 ns.
With the polarizers removed from the polarization analyzer, but the spectral filters in place, we detect a total coincidence rate of Rc = 16000 cps and a signal singles rate Rs =89000 cps at a pump power of merely 0.025 mW. Together with a measured FWHM of 2.3 nm, these values amount to a detected pair rate of 640 kcps/mW and a detected spectral brightness of 278 kcps/mW/nm at a conditional coincidence ratio to our knowledge the highest reported normalized detected pair rate for this type of system.
The polarization-entanglement was characterized by measuring the polarization correlation functions in two mutually unbiased bases (Fig. 6). To more completely assess the degree of entanglement a quantum state tomography was performed, whereby a Bell state fidelity F = 〈Φ+|ρ|Φ+〉 of 0.983 ± 0.005 was achieved at a pump power of 0.025 mW. As discussed in the following, accidental coincidences were negligible at such low pump powers. We attribute the bounded visibility to remaining which-crystal information due to non-identical SPDC spectra of the two crystals (overlap integral ∼99%, see Fig. 5) and imperfect timing compensation, as well as a weak polarization dependence of the WDM splitting ratio (∼ 10% variation with input polarization). Scaling from our detected brightness at low pump powers we estimate a detected coincidence rate larger than 20 Mcps locally detectable at 40 mW pump power. With the typical saturation rate of 10 Mcps for commercial silicon SPADs, the total singles count rates of 2 × Rc/ηc ∼ 200 Mcps would already require an array of about 60 detectors for registration of the pair coincidences at ∼30% of the detector saturation level. In addition to this immense logistic requirement there is a fundamental limitation, due to multi-pair emission in SPDC.
5. Multi-pair limited entanglement visibility at high pump power
By careful design of the focusing and spectral characteristics of the pump beam and the SPDC photons originating from two crossed PPKTP crystals, we achieve a detected pair rate of 640 kcp/mW, a detected spectral brightness of 278 kcp/mW/nm and a Bell state fidelity of 0.98. Combined with the compact footprint and with the simplicity and ruggedness of the configuration, these results make the source an ideal device for future field experiments on quantum communications and quantum entanglement tests, and well-suited for mobile and space applications. The benefit of using one of the highest nonlinear coefficients via noncritical quasi phase-matching in KTP, as well as the collinear emission geometry providing the optimal configuration for high collection efficiencies from long crystals, enable us to reach for the maximal brightness expected in schemes based on bulk SPDC. Furthermore, we showed that the potential pair creation rate of our source leads to a photon flux which extends beyond the capabilities of current single-photon detectors and commercially available timing electronics.
We thank Josep M. Perdigues and Eric Wille of the European Space Agency for valuable discussions. Project funding EQUO ESTEC Contract N.: AO/1-5942/08/NL/EM and contracts TEC 2010-14832 and FIS2011-23520 funded by the Spanish Ministry of Science and Innovation. HW, RU and JR acknowledge funding by the EU-project Q-ESSENCE. JPT acknowledges support from the Government of Spain ( FIS2010-14831) and the project PHORBITECH (FET-Open grant number 255914).
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