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Efficient generation of a photon pair in a bulk periodically poled potassium titanyl phosphate
Optics Communications 278 (2007) 363–367 www.elsevier.com/locate/optcom
Efficient generation of a photon pair in a bulk periodically poled potassium titanyl phosphate Bao-Sen Shi b
a,*
, Chang Zhai a, Guang-Can Guo a, Yun-Kun Jiang b, Akihisa Tomita
b
a Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, PR China Quantum Computation and Information Project, ERATO-SORST, JST, 34 Miyukigaoka, Tsukuba, Ibaraki 305-8501, Japan
Received 29 January 2007; received in revised form 23 April 2007; accepted 12 June 2007
Abstract In this report, we demonstrate the efficient generation of collinearly propagating photon pairs in a bulk periodically poled potassium titanyl phosphate pumped by a cw laser. The detected coincidence counts are more than 7400/s with 3.58 mW pump power in a Hanbury–Brown–Twiss-type experiment. The estimated photon pair production rate is about 0.73 MHz/mW. This is very promising for some applications, such as quantum key distribution, proof of the Bell-inequality, preparation of single photon states in broadband wave packets, Franson-type interference and so on. 2007 Elsevier B.V. All rights reserved. Keywords: PPKTP; Spontaneous parametric downconversion; Photon pair
Sources for creating entangled photon pairs are essential tools for a variety of fundamental quantum mechanical and quantum information experiments, such as in testing Bell-inequalities [1–3], quantum cryptography [4–7], teleportation [8–12], dense coding [13], quantum computation [14] and other areas. By far, the most efficient way of obtaining the entangled photon pairs is spontaneous parametric downconversion (SPDC) [15,16]. Although a lot of important results have been obtained, many experiments like teleportation or entanglement swapping, still suffer from the low production rates leading to low signal-tonoise ratios and long measurement times. SPDC can be used to generate a multiphoton state [17–19], these experiments also suffer from the problems shown above. Therefore, how to efficiently generate a photon pair is still a hot topic in quantum information and quantum optics fields. Usually, there are two ways to increase the photon pair production rate: one is to use the high power laser, but this way is limited by the available laser system; *
Corresponding author. E-mail address: [email protected] (B.-S. Shi).
0030-4018/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2007.06.044
another is to use some new nonlinear optical materials, such as periodically poled nonlinear crystals or waveguides [20–22], or photonic crystal fibers [23,24]. A periodically poled crystal, like a periodically poled lithium niobate (PPLN) or a periodically poled potassium titanyl phosphate (PPKTP), with an appropriate grating period, permits efficient three-wave mixing at user-selectable wavelengths by the technique of quasi-phase matching (QPM) [25]. QPM allows one to utilize larger nonlinear coefficients in some materials, thus leading to substantially higher two-photon production rates. For example, the largest nonlinear coefficient of KTP is approximately twice larger than the one enabling birefringent phase matching. Because of high efficiency of the periodical poled crystal, it can be also used to efficiently generate a multiphoton state directly [26]. Photonic crystal fiber also shows very high nonlinear effect because of its very small mode area. The high intensity of light guided through it results in large nonlinear optical effects. For example, in Ref. [24], about 3.2 · 105 coincidence count are detected per second with a 2-m long photonic crystal fiber at pump power 0.5 mW, this is the highest demonstrated to date with a fiber-based
364
B.-S. Shi et al. / Optics Communications 278 (2007) 363–367
photon pair. The fiber-based photon pair source is inherently compatible with telecom system, and removes the suffering from the lower coupling efficiency from free space to fiber in the cases of a bulk crystal or waveguide. One drawback of this source is its a little lower true coincidence to accidental count ratio. The differences between waveguide and bulk structure are following. First, waveguide structure is more efficient than bulk structure because an optical waveguide confines light to cross-sectional transverse dimensions of the order of the wavelength of the radiation, the efficiency grows with the square of the interaction length. This is in contrast to bulk case, where the efficiency grows only linearly with length because of diffraction. Second, the waveguide provides a way to precisely control the spatial mode of the photon pair. In contrast to bulk case, a spatial filter is used to select spatial mode. One thing we want to point out is that the coupling from laser to waveguide is not easy. In this paper, we consider to use a type-I phase matching PPKTP bulk crystal to generate a photon pair. In type I case, the high d33 nonlinearity of KTP is used and the same-polarization photon pairs are yielded, in contrast with the case of type II, the relatively small d24 nonlinearity is used and the photon pairs yielded have the orthogonal polarization. The bandwidth of the photon created in degenerated type-I case is much larger than that in type-II case. There are some reported experiments using the PPKTP crystal. In Ref. [27], a type-II phase matching bulk PPKTP is used to generate a polarization entangled photon pair by post-selection, and followingly, the postselection is removed by using bi-directional pumped technique in Ref. [28]. The highest detected photon pairs in a bulk PPKTP crystal is about 22 kHz/s/mW [29], where, a 10 mm long type-II bulk PPKTP is used. The highest measured flux of 8.5 · 105 photon pairs per second per mW of pump power in a PPKTP waveguide to our knowledge is reported in Ref. [30], where, a type-II PPKTP waveguide is used. In Ref. [31], a PPKTP waveguide pumped by an ultrashort pulse is used to generate a pulsed photon pair. Two perpendicular type-I PPKTP crystals are used to generate a nondegenerate polarization photon pair with the production rate 1.2 · 107 Hz for a power of 62 mW in Ref. [32]. In Ref. [33], a bulk type-I PPKTP crystal pumped by a femtosecond laser is used to efficiently generate a pulsed photon pair, and the time uncertainty of the photon pair creation is checked in Ref. [34]. The results show that the pulsed photon pair source generated with the PPKTP is not very useful for some applications, such as quantum teleportation, swapping etc., because usually one needs to know precisely the time when the photon pair generates in such application. The experimental results show that the time uncertainty of the photon creation is quite large even the short pulse pump laser is used. All results shown above clearly demonstrate the high efficiency of PP crystal. Although the high detected photon pairs can also be obtained even by using a common crystal, such as BBO crystal, (like demonstrated in Ref. [35], the brightest source to date is created, about 2 MHz per second photon pairs
are detected, but 310 mW pump power is used.) the high pump power is needed. In this paper, we study the generation of a collinearly propagating photon pair by pumping a 2.12 mm long type-I phase matching bulk PPKTP crystal with a cw laser. Using a single mode fiber as a spatial filter, we detect about 7400/s net coincidence counts with 3.58 mW pump power in a Hanbury–Brown–Twiss-type experiment. The estimated photon pair production rate is about 0.73 MHz/ mW per second. This is very promising for many applications in quantum information and quantum optical fields, such as efficient preparation of single photon states in broadband wave packets [29], testing Bell-inequalities [1– 3], quantum key distribution based on Bell-inequality [4– 7], Franson-type interference [36]. Very recently, entanglement swapping using cw laser is reported, which shows the important step towards real word quantum network with truly independent and distant nodes [37]. The key point in this experiment, we think is the high efficient photon pair source with PP crystal pumped by cw laser. Our source may be used in such application. The PPKTP crystal we use in experiment is bought from Raicol Crystal Company. The crystal is cut at type-I phase matching, with 1.05 mm (z) · 2.1 mm (y) · 2.12 mm (x) size, where, z, y, x means height, width and length respectively. The PPKTP is antireflection coated on both facets at 800 nm and 400 nm. It is placed at a temperature-stabilized laser diode (LD) holder with built-in Peltier device with a stability of ±0.01 C , and this Peltier device can work below 200 C. The grating period of the PPKTP is about 3.25 mm. The experimental set-up is shown in Fig. 1. The laser beam from a violet laser diode (NICHIA, model NDHV310ACA) is used to pump the PPKTP crystal. Before the crystal, a lens with 20-cm focal length is used to focus the laser beam, which gives about 70 lm beam waist inside crystal. After crystal, a bandpass filter (color glass filter RG 715) is used to cut the remaining violet pump laser. The power measured before the crystal is about 3.58 mW. After crystal about 25 cm, there is an objective lens (numerical aperture of 0.15), by which the SPDC photons are coupled into a single mode fiber. The fiber is connected to a fiber beamsplitter (OFR). Each output of the fiber beamsplitter is connected to a single photon detector (PerkinElmer SPCM-AQR-14-FC). The outputs of the detectors are sent to a coincidence circuit for coincidence counting, which mainly consists in a logic level adapter module (KN200), a discriminator (KN1300), a variable delay (KN330), a coincidence gate (KN470), (all above
Fig. 1. Experimental set-up. OB: objective lens; BS: fiber splitter; D: single photon detector; C.C: coincidence circuit.
B.-S. Shi et al. / Optics Communications 278 (2007) 363–367
from Kaizu Works) and a counter (SR400, Standford Research Systems). The coincidence window is about 5 ns. This crystal is made for the phase matching at wavelength 400 nm, but unfortunately, the wavelength of our used cw laser is not 400 nm, is about 402.8 nm measured by an optical spectrum analyzer (ANDO AQ-6315A with a resolution of 0.05 nm), therefore we have to increase the temperature of the crystal to make the phase-matched. We calculate the optimal temperature for phase matching at wavelength 402.8 nm, taking the measured temperature 29 C for second harmonic generation at wavelength 400.194 nm as a reference [33] (This wavelength is the measured value by ANDO AQ-6315A with a resolution of 0.05 nm), the calculated results are shown in Fig. 2. From this figure, we see that the phase-matched temperature is about 160 C. Besides, we change the grating period by tilting the crystal about 20 with respect to the pump beam to lower the temperature in our experiment. The experimental single counts and coincidence counts versus the temperature are shown in Fig. 3. From Fig. 3, we see that we really realize the phase matching at high temperature, the optimal temperature is about 172.9 C, and more than 7600/s high coincidence counts with the accidental coincidence counts less than 200/s are obtained at this optimal temperature. Here, the accidental coincidence count is calculated by the formula: S1 · S2 · t, where, S1(2) is the net single count of the detector 1(2), and t is the coincidence window. The net single count is estimated by the single count at optimal temperature substracting the single count at temperature below 100 C , which corresponds to no phase matching case. The estimated photon pair production rate can be calculated by the formula N ¼ R1 S 1 S 2 , R is the net coincidence count [20]. We get N = 2.63 · 106 Hz corresponding to our measured data: S1 = 145 kHz, S2 = 271 kHz, and R = 7457. The experimental results prove that we can change the phase-matched wavelength by adjusting the temperature of crystal. There is the difference between calculated results and the experimental results. The optimal temperatures are different. We think the main reasons are
Fig. 2. Calculated fundamental wavelength versus temperature phase matching.
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Fig. 3. (a) Single counts (with accident counts) plotted versus the temperature of the PPKTP and (b) coincidence count (with accident counts) plotted versus the temperature of the PPKTP.
from the followings: it may be from the index of refraction calculated, because all Sellmerier equations are approximate, not exact equations. Another is from our temperature controller. At high temperature operation, the value shown by indicator of the sensor of the temperature controller is not correspond to the value set by controller. For example, the temperature for the maximal coincidence counts in our experiment is shown by sensor is 172.9 C , but the set temperature is only 166 C. We also calculate the spectrum of the downconverted photons, which is shown in Fig. 4. The calculated bandwidth at half-maximum (FWHM) is more than 50 nm. Actually, we try to measure it by using an optical spectrum analyzer, but fail. The spectrum of SPDC photon is /1/L, where, L is the length of the crystal. The efficiency of the SPDC is /L2 assuming the negligible pump focusing [38], therefore, the total efficiency is /L. When the pump focusing is not negligible, two things should be considered: (i) a focused pump is composed of many differently directed plane waves, there is phase mismatching effect in each direction which is
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downconversion efficiency (a.u.)
1.0 o
T=160 C 0.8
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0.0 0.70
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Fig. 4. The calculated spectrum of the downconverted photon pairs.
different from the phase matching direction. This will lower pffiffiffi the production rate with a factor 1= L. (ii) The focusing can increases the intensity density of the pump, which increases the production rate with a factor /1/A, where, A is the waist area of the pump beam pffiffiffi in crystal. The total effect is that the production is / L at optimal focusing [39]. The optimal focusing is considered in Ref. [39], which is found by the geometrical relation L/zR to be 1 to 2, where, L is the crystal length, and zR is the Rayleigh-range of the mode-profile. We calculate the divergence of the SPDC radiation, which is shown in Fig. 5. The calculated divergence is about 0.04/nm assuming negligible pump focusing. We also calculate the divergence of the degenerated SPDC radiation based on the temperature of the crystal, which is shown in Fig. 6. There is one thing we want to address: although the production rate is quite high in our experiment, the detected single counts are not high. We
Fig. 5. The divergence of the SPDC radiation assumes negligible pump focusing. (a) k = 805.6 nm, (b) k = 804.6 nm, (c) k = 802.6 nm and (d) k = 800.6 nm.
Fig. 6. The divergence of the degenerated SPDC radiation based on the temperature of the crystal. (a) T = 160 C, (b) T = 161 C, (c) T = 162.5 C and (d) T = 165 C.
think the main reason is that our coupling is not optimal. Some papers already discuss about optimal coupling the downconverted photons into single mode fiber [39,40]. We check our coupling along the way shown in Ref. [39], find that the geometric relation L/zR is far from two to three for the fiber modes. Another thing we want to point out is the relatively lower coincidence count to single count ratio. This is mainly limited by (i) the optical losses in our experimental set-up, including the coupling loss of the photon pairs from the space to fiber, the non-unit detector efficiency; (ii) the presence of the uncorrelated photons. An important source of uncorrelated photons in KTP crystal is fluorescence related to gray-tracking [41] and originating from color-center formation which may be of the same order of magnitude in intensity as SPDC. This has been observed in SPDC from bulk PPKTP [27] and waveguide PPKTP [29]. It is difficult to differentiate the fluorescence from the SDPC photons, because fluorescence spectrally almost overlaps SPDC. One possible way to reduce partly fluorescence is using their different bandwidth [29]. There is another thing we want to address is that although the SPDC photons in each pair have the same polarization, they are entangled in time/energy bases, this could be verified by using a Franson-type two photon interferometer. In Ref. [33], the same PPKTP pumped by a femtosecond laser is used to generate a pulse photon pair. The estimated production rate is about 1.06 MHz/mW. Compared with the rate of this work 0.73 MHz/mW, is only slightly higher, but not as high as we hope. We think the main reason is following: although the femtosecond laser is used in Ref. [33], the effective bandwidth of the pump laser is not the bandwidth of the laser used, it is more narrower than that. This is proven in Ref. [33] indirectly by checking the bandwidth
B.-S. Shi et al. / Optics Communications 278 (2007) 363–367
of the second harmonic wave from 800 nm to 400 nm. In Ref. [33], although the measured bandwidth of the pump laser is about 11 nm, the bandwidth of second harmonic wave is only 0.18 nm. Further direct proof is made by estimating the time uncertainty of the photon creation time in a 5 mm PPKTP crystal via a phase-sensitive interference experiment in Ref. [34]. We experimentally find that the time uncertainty of the photon pair creation is much larger than the coherence time of the femtosecond pump laser used. This is mainly caused by the very narrow intrinsic bandwidth of the PPKTP crystal, so the PPKTP serves as a narrow band filter. Therefore, although the power of the femtosecond pump laser in Ref. [33] is 1 mW, the actual useful power is much less than it. In Ref. [33], the bandwidth of pump laser measured is about 3.2 nm, but the useful bandwidth is only 0.18 nm, so the useful power is only about 0.056 mW assuming the pump pulse is the rectangular simply. That is the reason why the photon pair production rate in Ref. [33] is only a little higher than that of this work. Another thing we want to point out is that the SPDC pumped by cw laser is sensitive to the temperature of the crystal, in contrast with the results in Ref. [33]. In Ref. [33], the SPDC is not very sensitive because of very wide bandwidth of the pumped laser used. In conclusion, we experimentally demonstrate the efficient generation of photon pairs with a type-I phase matching PPKTP bulk crystal pumped by cw laser. The detected net coincidence counts is more than 7400/s with pump power of 3.58 mW in a Hanbury–Brown–Twiss-type experiment. The estimated photon pair production rate is about 0.73 MHz/mW. This is very promising for applications in quantum information, such as efficient preparation of single photon states in broadband wave packets [29], testing Bell-inequalities [1–3], quantum key distribution based on Bell-inequality [4–7], Franson-type interference [36] and so on. Acknowledgements B.S. Shi, C. Zhai and G.C. Guo supported by National Natural Foundation of Science, (Grant No. 10674126), National Fundamental Research Program (Grant No. 2006CB921900). B.S. Shi thanks Prof. Imai for his support for his visiting QCI project. This experiment was done in NEC Tsukuba Laboratory. References [1] J.S. Bell, Physics (Long Island City, NY) 1 (1964) 195.
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Efficient generation of a photon pair in a bulk periodically poled potassium titanyl phosphate Bao-Sen Shi b
a,*
, Chang Zhai a, Guang-Can Guo a, Yun-Kun Jiang b, Akihisa Tomita
b
a Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, PR China Quantum Computation and Information Project, ERATO-SORST, JST, 34 Miyukigaoka, Tsukuba, Ibaraki 305-8501, Japan
Received 29 January 2007; received in revised form 23 April 2007; accepted 12 June 2007
Abstract In this report, we demonstrate the efficient generation of collinearly propagating photon pairs in a bulk periodically poled potassium titanyl phosphate pumped by a cw laser. The detected coincidence counts are more than 7400/s with 3.58 mW pump power in a Hanbury–Brown–Twiss-type experiment. The estimated photon pair production rate is about 0.73 MHz/mW. This is very promising for some applications, such as quantum key distribution, proof of the Bell-inequality, preparation of single photon states in broadband wave packets, Franson-type interference and so on. 2007 Elsevier B.V. All rights reserved. Keywords: PPKTP; Spontaneous parametric downconversion; Photon pair
Sources for creating entangled photon pairs are essential tools for a variety of fundamental quantum mechanical and quantum information experiments, such as in testing Bell-inequalities [1–3], quantum cryptography [4–7], teleportation [8–12], dense coding [13], quantum computation [14] and other areas. By far, the most efficient way of obtaining the entangled photon pairs is spontaneous parametric downconversion (SPDC) [15,16]. Although a lot of important results have been obtained, many experiments like teleportation or entanglement swapping, still suffer from the low production rates leading to low signal-tonoise ratios and long measurement times. SPDC can be used to generate a multiphoton state [17–19], these experiments also suffer from the problems shown above. Therefore, how to efficiently generate a photon pair is still a hot topic in quantum information and quantum optics fields. Usually, there are two ways to increase the photon pair production rate: one is to use the high power laser, but this way is limited by the available laser system; *
Corresponding author. E-mail address: [email protected] (B.-S. Shi).
0030-4018/$ - see front matter 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2007.06.044
another is to use some new nonlinear optical materials, such as periodically poled nonlinear crystals or waveguides [20–22], or photonic crystal fibers [23,24]. A periodically poled crystal, like a periodically poled lithium niobate (PPLN) or a periodically poled potassium titanyl phosphate (PPKTP), with an appropriate grating period, permits efficient three-wave mixing at user-selectable wavelengths by the technique of quasi-phase matching (QPM) [25]. QPM allows one to utilize larger nonlinear coefficients in some materials, thus leading to substantially higher two-photon production rates. For example, the largest nonlinear coefficient of KTP is approximately twice larger than the one enabling birefringent phase matching. Because of high efficiency of the periodical poled crystal, it can be also used to efficiently generate a multiphoton state directly [26]. Photonic crystal fiber also shows very high nonlinear effect because of its very small mode area. The high intensity of light guided through it results in large nonlinear optical effects. For example, in Ref. [24], about 3.2 · 105 coincidence count are detected per second with a 2-m long photonic crystal fiber at pump power 0.5 mW, this is the highest demonstrated to date with a fiber-based
364
B.-S. Shi et al. / Optics Communications 278 (2007) 363–367
photon pair. The fiber-based photon pair source is inherently compatible with telecom system, and removes the suffering from the lower coupling efficiency from free space to fiber in the cases of a bulk crystal or waveguide. One drawback of this source is its a little lower true coincidence to accidental count ratio. The differences between waveguide and bulk structure are following. First, waveguide structure is more efficient than bulk structure because an optical waveguide confines light to cross-sectional transverse dimensions of the order of the wavelength of the radiation, the efficiency grows with the square of the interaction length. This is in contrast to bulk case, where the efficiency grows only linearly with length because of diffraction. Second, the waveguide provides a way to precisely control the spatial mode of the photon pair. In contrast to bulk case, a spatial filter is used to select spatial mode. One thing we want to point out is that the coupling from laser to waveguide is not easy. In this paper, we consider to use a type-I phase matching PPKTP bulk crystal to generate a photon pair. In type I case, the high d33 nonlinearity of KTP is used and the same-polarization photon pairs are yielded, in contrast with the case of type II, the relatively small d24 nonlinearity is used and the photon pairs yielded have the orthogonal polarization. The bandwidth of the photon created in degenerated type-I case is much larger than that in type-II case. There are some reported experiments using the PPKTP crystal. In Ref. [27], a type-II phase matching bulk PPKTP is used to generate a polarization entangled photon pair by post-selection, and followingly, the postselection is removed by using bi-directional pumped technique in Ref. [28]. The highest detected photon pairs in a bulk PPKTP crystal is about 22 kHz/s/mW [29], where, a 10 mm long type-II bulk PPKTP is used. The highest measured flux of 8.5 · 105 photon pairs per second per mW of pump power in a PPKTP waveguide to our knowledge is reported in Ref. [30], where, a type-II PPKTP waveguide is used. In Ref. [31], a PPKTP waveguide pumped by an ultrashort pulse is used to generate a pulsed photon pair. Two perpendicular type-I PPKTP crystals are used to generate a nondegenerate polarization photon pair with the production rate 1.2 · 107 Hz for a power of 62 mW in Ref. [32]. In Ref. [33], a bulk type-I PPKTP crystal pumped by a femtosecond laser is used to efficiently generate a pulsed photon pair, and the time uncertainty of the photon pair creation is checked in Ref. [34]. The results show that the pulsed photon pair source generated with the PPKTP is not very useful for some applications, such as quantum teleportation, swapping etc., because usually one needs to know precisely the time when the photon pair generates in such application. The experimental results show that the time uncertainty of the photon creation is quite large even the short pulse pump laser is used. All results shown above clearly demonstrate the high efficiency of PP crystal. Although the high detected photon pairs can also be obtained even by using a common crystal, such as BBO crystal, (like demonstrated in Ref. [35], the brightest source to date is created, about 2 MHz per second photon pairs
are detected, but 310 mW pump power is used.) the high pump power is needed. In this paper, we study the generation of a collinearly propagating photon pair by pumping a 2.12 mm long type-I phase matching bulk PPKTP crystal with a cw laser. Using a single mode fiber as a spatial filter, we detect about 7400/s net coincidence counts with 3.58 mW pump power in a Hanbury–Brown–Twiss-type experiment. The estimated photon pair production rate is about 0.73 MHz/ mW per second. This is very promising for many applications in quantum information and quantum optical fields, such as efficient preparation of single photon states in broadband wave packets [29], testing Bell-inequalities [1– 3], quantum key distribution based on Bell-inequality [4– 7], Franson-type interference [36]. Very recently, entanglement swapping using cw laser is reported, which shows the important step towards real word quantum network with truly independent and distant nodes [37]. The key point in this experiment, we think is the high efficient photon pair source with PP crystal pumped by cw laser. Our source may be used in such application. The PPKTP crystal we use in experiment is bought from Raicol Crystal Company. The crystal is cut at type-I phase matching, with 1.05 mm (z) · 2.1 mm (y) · 2.12 mm (x) size, where, z, y, x means height, width and length respectively. The PPKTP is antireflection coated on both facets at 800 nm and 400 nm. It is placed at a temperature-stabilized laser diode (LD) holder with built-in Peltier device with a stability of ±0.01 C , and this Peltier device can work below 200 C. The grating period of the PPKTP is about 3.25 mm. The experimental set-up is shown in Fig. 1. The laser beam from a violet laser diode (NICHIA, model NDHV310ACA) is used to pump the PPKTP crystal. Before the crystal, a lens with 20-cm focal length is used to focus the laser beam, which gives about 70 lm beam waist inside crystal. After crystal, a bandpass filter (color glass filter RG 715) is used to cut the remaining violet pump laser. The power measured before the crystal is about 3.58 mW. After crystal about 25 cm, there is an objective lens (numerical aperture of 0.15), by which the SPDC photons are coupled into a single mode fiber. The fiber is connected to a fiber beamsplitter (OFR). Each output of the fiber beamsplitter is connected to a single photon detector (PerkinElmer SPCM-AQR-14-FC). The outputs of the detectors are sent to a coincidence circuit for coincidence counting, which mainly consists in a logic level adapter module (KN200), a discriminator (KN1300), a variable delay (KN330), a coincidence gate (KN470), (all above
Fig. 1. Experimental set-up. OB: objective lens; BS: fiber splitter; D: single photon detector; C.C: coincidence circuit.
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from Kaizu Works) and a counter (SR400, Standford Research Systems). The coincidence window is about 5 ns. This crystal is made for the phase matching at wavelength 400 nm, but unfortunately, the wavelength of our used cw laser is not 400 nm, is about 402.8 nm measured by an optical spectrum analyzer (ANDO AQ-6315A with a resolution of 0.05 nm), therefore we have to increase the temperature of the crystal to make the phase-matched. We calculate the optimal temperature for phase matching at wavelength 402.8 nm, taking the measured temperature 29 C for second harmonic generation at wavelength 400.194 nm as a reference [33] (This wavelength is the measured value by ANDO AQ-6315A with a resolution of 0.05 nm), the calculated results are shown in Fig. 2. From this figure, we see that the phase-matched temperature is about 160 C. Besides, we change the grating period by tilting the crystal about 20 with respect to the pump beam to lower the temperature in our experiment. The experimental single counts and coincidence counts versus the temperature are shown in Fig. 3. From Fig. 3, we see that we really realize the phase matching at high temperature, the optimal temperature is about 172.9 C, and more than 7600/s high coincidence counts with the accidental coincidence counts less than 200/s are obtained at this optimal temperature. Here, the accidental coincidence count is calculated by the formula: S1 · S2 · t, where, S1(2) is the net single count of the detector 1(2), and t is the coincidence window. The net single count is estimated by the single count at optimal temperature substracting the single count at temperature below 100 C , which corresponds to no phase matching case. The estimated photon pair production rate can be calculated by the formula N ¼ R1 S 1 S 2 , R is the net coincidence count [20]. We get N = 2.63 · 106 Hz corresponding to our measured data: S1 = 145 kHz, S2 = 271 kHz, and R = 7457. The experimental results prove that we can change the phase-matched wavelength by adjusting the temperature of crystal. There is the difference between calculated results and the experimental results. The optimal temperatures are different. We think the main reasons are
Fig. 2. Calculated fundamental wavelength versus temperature phase matching.
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Fig. 3. (a) Single counts (with accident counts) plotted versus the temperature of the PPKTP and (b) coincidence count (with accident counts) plotted versus the temperature of the PPKTP.
from the followings: it may be from the index of refraction calculated, because all Sellmerier equations are approximate, not exact equations. Another is from our temperature controller. At high temperature operation, the value shown by indicator of the sensor of the temperature controller is not correspond to the value set by controller. For example, the temperature for the maximal coincidence counts in our experiment is shown by sensor is 172.9 C , but the set temperature is only 166 C. We also calculate the spectrum of the downconverted photons, which is shown in Fig. 4. The calculated bandwidth at half-maximum (FWHM) is more than 50 nm. Actually, we try to measure it by using an optical spectrum analyzer, but fail. The spectrum of SPDC photon is /1/L, where, L is the length of the crystal. The efficiency of the SPDC is /L2 assuming the negligible pump focusing [38], therefore, the total efficiency is /L. When the pump focusing is not negligible, two things should be considered: (i) a focused pump is composed of many differently directed plane waves, there is phase mismatching effect in each direction which is
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downconversion efficiency (a.u.)
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Fig. 4. The calculated spectrum of the downconverted photon pairs.
different from the phase matching direction. This will lower pffiffiffi the production rate with a factor 1= L. (ii) The focusing can increases the intensity density of the pump, which increases the production rate with a factor /1/A, where, A is the waist area of the pump beam pffiffiffi in crystal. The total effect is that the production is / L at optimal focusing [39]. The optimal focusing is considered in Ref. [39], which is found by the geometrical relation L/zR to be 1 to 2, where, L is the crystal length, and zR is the Rayleigh-range of the mode-profile. We calculate the divergence of the SPDC radiation, which is shown in Fig. 5. The calculated divergence is about 0.04/nm assuming negligible pump focusing. We also calculate the divergence of the degenerated SPDC radiation based on the temperature of the crystal, which is shown in Fig. 6. There is one thing we want to address: although the production rate is quite high in our experiment, the detected single counts are not high. We
Fig. 5. The divergence of the SPDC radiation assumes negligible pump focusing. (a) k = 805.6 nm, (b) k = 804.6 nm, (c) k = 802.6 nm and (d) k = 800.6 nm.
Fig. 6. The divergence of the degenerated SPDC radiation based on the temperature of the crystal. (a) T = 160 C, (b) T = 161 C, (c) T = 162.5 C and (d) T = 165 C.
think the main reason is that our coupling is not optimal. Some papers already discuss about optimal coupling the downconverted photons into single mode fiber [39,40]. We check our coupling along the way shown in Ref. [39], find that the geometric relation L/zR is far from two to three for the fiber modes. Another thing we want to point out is the relatively lower coincidence count to single count ratio. This is mainly limited by (i) the optical losses in our experimental set-up, including the coupling loss of the photon pairs from the space to fiber, the non-unit detector efficiency; (ii) the presence of the uncorrelated photons. An important source of uncorrelated photons in KTP crystal is fluorescence related to gray-tracking [41] and originating from color-center formation which may be of the same order of magnitude in intensity as SPDC. This has been observed in SPDC from bulk PPKTP [27] and waveguide PPKTP [29]. It is difficult to differentiate the fluorescence from the SDPC photons, because fluorescence spectrally almost overlaps SPDC. One possible way to reduce partly fluorescence is using their different bandwidth [29]. There is another thing we want to address is that although the SPDC photons in each pair have the same polarization, they are entangled in time/energy bases, this could be verified by using a Franson-type two photon interferometer. In Ref. [33], the same PPKTP pumped by a femtosecond laser is used to generate a pulse photon pair. The estimated production rate is about 1.06 MHz/mW. Compared with the rate of this work 0.73 MHz/mW, is only slightly higher, but not as high as we hope. We think the main reason is following: although the femtosecond laser is used in Ref. [33], the effective bandwidth of the pump laser is not the bandwidth of the laser used, it is more narrower than that. This is proven in Ref. [33] indirectly by checking the bandwidth
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of the second harmonic wave from 800 nm to 400 nm. In Ref. [33], although the measured bandwidth of the pump laser is about 11 nm, the bandwidth of second harmonic wave is only 0.18 nm. Further direct proof is made by estimating the time uncertainty of the photon creation time in a 5 mm PPKTP crystal via a phase-sensitive interference experiment in Ref. [34]. We experimentally find that the time uncertainty of the photon pair creation is much larger than the coherence time of the femtosecond pump laser used. This is mainly caused by the very narrow intrinsic bandwidth of the PPKTP crystal, so the PPKTP serves as a narrow band filter. Therefore, although the power of the femtosecond pump laser in Ref. [33] is 1 mW, the actual useful power is much less than it. In Ref. [33], the bandwidth of pump laser measured is about 3.2 nm, but the useful bandwidth is only 0.18 nm, so the useful power is only about 0.056 mW assuming the pump pulse is the rectangular simply. That is the reason why the photon pair production rate in Ref. [33] is only a little higher than that of this work. Another thing we want to point out is that the SPDC pumped by cw laser is sensitive to the temperature of the crystal, in contrast with the results in Ref. [33]. In Ref. [33], the SPDC is not very sensitive because of very wide bandwidth of the pumped laser used. In conclusion, we experimentally demonstrate the efficient generation of photon pairs with a type-I phase matching PPKTP bulk crystal pumped by cw laser. The detected net coincidence counts is more than 7400/s with pump power of 3.58 mW in a Hanbury–Brown–Twiss-type experiment. The estimated photon pair production rate is about 0.73 MHz/mW. This is very promising for applications in quantum information, such as efficient preparation of single photon states in broadband wave packets [29], testing Bell-inequalities [1–3], quantum key distribution based on Bell-inequality [4–7], Franson-type interference [36] and so on. Acknowledgements B.S. Shi, C. Zhai and G.C. Guo supported by National Natural Foundation of Science, (Grant No. 10674126), National Fundamental Research Program (Grant No. 2006CB921900). B.S. Shi thanks Prof. Imai for his support for his visiting QCI project. This experiment was done in NEC Tsukuba Laboratory. References [1] J.S. Bell, Physics (Long Island City, NY) 1 (1964) 195.
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