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Single and Entangled Photon Sources Renald Dore1 Jaime Cristian Vela2 1 Institute of Optics, 2Department of Physics and Astronomy, University of Rochester December 11th, 2013 Abstract In this experiment we demonstrate the violation of Bell’s inequalities by producing two polarization entangled photons through spontaneous parametric down conversion. Using two avalanche photodiodes, we measure how the orientation of two polarization angles affects the coincidence counts of entangled photon pairs incident on the avalanche photodiodes. Bell’s inequalities state that observable S shall be no larger than 2, yet we observe a value of 2.54, meaning we have violated Bell’s inequality and proved that we have entangled photons. Introduction Today’s research in quantum entanglement offers new and exciting possibilities in future technology. These include quantum cryptography, quantum computing, and even quantum state teleportation where entangled particles give information about each other no matter how far apart they are located, due to them sharing the same wave function. In quantum mechanics, a particles state doesn’t exist until it is measured, but in entangled species, by making a measurement on one entangled particle we can reliably know information about the other without actually making any measurement on it [1]. In this experiment we test the nonlocality hypothesis of nature by studying entangled photons through spontaneous parametric down conversion and calculating bell’s inequalities for these photons whose polarization states are measured. By violating Bell’s inequality, a classical relationship, we prove that the relationship between the particles is indeed quantum and cannot be explained by classical interpretation. Theory Two entangled particles (A and B) reliably give information about one another due to them sharing the same wave function, or that is, that their wave functions cannot be separated [2]. Any measurement performed on particle A would simultaneously give information of B without and consideration of the separation between them. This phenomenon is completely quantum mechanical and has now classical explanation. In the laboratory we can produce entangled photons through a nonlinear process called spontaneous parametric down conversion (SPDC) [3]. In SPDC, a photon is down converted to two lower energy photons, where the conservation of momentum and energy is conserved. Using type 1 beta barium borate crystals (BBO), which are especially cut with regard to their optical axis, a horizontally polarized photon is incident on the crystal with wavelength λ and consequentially, two photons of wavelength 2λ emerge with vertical polarization with respect to the incident photon. Figure 1 depicts this process. Figure 1. Down conversion of photon with horizontal polarization. For this process, if we rotate the basis, we achieve the same results but with opposite polarizations. Figure 2. Down conversion of photon with vertical polarization. By using a pair of BBO crystals, as shown in figure 3, we can produce the down converted quantum state shown in equation 1. Figure 3. A pair of type one BBO crystals aligned perpendicular with respect to their axis of polarization. (eqs.1) The down converted pair has the probability of detection described by (eqs. 2) which, after some calculations, can be written as (eqs. 3) Where the angle corresponds to the angle of a half wave plate. In the special case where , then we have (eqs. 4) So finally, the coincidence counts is written as (eqs. 5) Where C is an offset to account for the imperfections in the polarizers and alignment of the crystals [2]. We will use the Clauser-Horne-Shimony-Holt (CHSH) inequality to measure entanglement of photons in this experiment [2]. The inequality is shown in equation 6 and 7 below, where (eqs. 6) and (eqs. 7) and N(a,b) is the coincidence count when polarizer A is at a and polarizer B is at b. Experimental Setup The laboratory setup was composed by several components including: 100 mW 363.8nm argon-ion laser, filter, mirror, Beta Barium Borate (BBO) crystals, polarizers and APD’s. It utilizes spontaneous down conversion in conjunction with CHSH inequality to demonstrate the entanglement of polarization states of the photons. Figure 4. Schematic of the experimental setup. The above setup uses a high power 100mw Argon-Ion laser (363.8nm wavelength) as a light source. The laser beam first passes through the narrowband blue filter to remove all the unwanted wavelengths and to transmit photons with double the wavelength of the Argon-ion laser at 727.6nm. The light then passes through the quartz plate which compensates the phase of the laser beam and then the light hits the high reflective mirror to be directed towards the BBO Crystals. Beta Barium Borate (BBO) Crystals are the main component of the parametric down conversion where an incident photon is converted into two photons of longer (twice) wavelength called signal and idler photons. In this process the momentum and energy are conserved. The BBO crystals were type I meaning the polarization of the signal and idler photons was orthogonal to the polarization of the incident photon. There will be two cone of light with equal number of photons produced by the BBO crystals, a horizontal cone and a vertical cone. The overlapping of this this two cones is performed thanks to the use of the quartz plate which adds phase to the lagging cone. Using this nonlinear scheme, which produces the signal and idler photons, can create polarized entangled states. Light after passing through the BBO crystal gets directed towards two different polarizers, where the Bell’s Inequalities can be calculated at different polarizer orientations. The final parts of this experiment are the pair of single-photon counting avalanche photodiodes (APD) modules. Coincidence counts can be measured using the two polarizers in front of the APDs. When the two polarizers are at parallel angles relative to each other both the signal and idle photons hit the APDs, while when the two polarizers are at perpendicular angles relative to each other only one of the photons hits the APDs. In the latter case only the entangled photon pair passes and this results in the minimum photon coincidence count. As discussed in the theory part, there should be a cos2 dependence of the coincidence counts on the difference between each of the polarization angles. Procedure 1- Align the system with the help of the TA and use the EM-CCD camera to overlap the horizontally polarized cone of light with the vertically polarized cone of light. 2- Observe the fringe visibility (Visibility= ) of the photon coincidence count and see if it exceeds the value of 0.71. If the value of the fringe visibility is greater than 0.71 then the Bell’s Inequality is violated. 3- Check to see if the single counts of each APD are dependent or independent of its accompanying polarizer angle. If there is dependence on the polarizer angle, then there is phase misalignment and the quartz plate must be adjusted accordingly. 4- Take measurements of the coincidence count while changing the angle of the polarizers in order to calculate Bell’s Inequalities. The specific angles to be measured are α={00,450,900,1350} and β={22.50,67.50,112.50,157.50}. 5- After the system is aligned and the visibility is >0.71, repeat step for one more time. 16 measurements will be used to calculate inequality. 6- Violate and confirm the violation of Bell’s Inequalities. 7- Possibility to try and obtain results from the usage of random angles. Results and Analysis After making the proper adjustments and aligning the system, the results were recorded in excel files and plotted accordingly. The measurements were recorded using a laser power of 25mW, an acquisition time of 500ms and 20 measurements per each angle. Average Coincidence Count 70 60 0,0 50 45,45 40 30 90,90 20 135,13 5 10 0 -30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 Rotation Angle (Horizontal Axis) Figure 5. Coincidence Count vs. Angle of Rotation of the Quartz plate in the horizontal axis. The optimal angle for the Quartz in the 0 horizontal axis would be at the 3 angle on the graph. Average Coincidence Count 90 80 70 60 0,0 50 45,45 90,90 40 135,135 30 20 10 0 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 18 20 Rotation Axis (Vertical Axis) Figure 6. Coincidence Count vs. Angle of Rotation of the Quartz plate in the vertical axis. The optimal angle for the Quartz in the 0 vertical axis would be at the -2 angle on the graph. 100 90 Coincedence Count 80 70 60 50 40 30 20 10 0 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 Polarizer Angle Polarizer A: 90 Polarizer A: 0 Figure 7: Coincidence Count vs. Angle of Rotation of Polarizer. Fringe Visibility of 0.958435. 160 Coincedence Count 140 120 100 80 60 40 20 0 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 Polarizer Angle Polarizer A: 135 Polarizer A:45 Figure 8: Coincidence Count vs. Angle of Rotation of Polarizer. Fringe Visibility of 0.9588565. 320 340 The graphs above represent the effect that the orientation of the polarizers has on the Fringe Visibility. The Fringe Visibility was calculated to be 0.958435 when the polarizers positions were 1350 and 450. The Fringe Visibility was calculated to be 0.9588565 when the polarizers positions were 900 and 00. Both these values are above 0.71 suggesting that the Bell’s Inequality was violated. The measurements were recorded using a laser power of 25mW, an acquisition time window of 500ms, total acquisition time of 10s, coincidence time window of 2.6*108 s and 20 measurements per each angle. The below measurements were recorded using a laser power of 25mW, acquisition time window of 500mW, total acquisition time of 15s, coincidence time window of 2.6*10-8s and 30 measurements taken for each angle. Polarizer B Polarizer A -45 -22.5 -45 22.5 -45 67.5 -45 112.5 0 -22.5 0 22.5 0 67.5 0 112.5 45 -22.5 45 22.5 45 67.5 45 112.5 90 -22.5 90 22.5 90 67.5 90 112.5 Net coincidence Std. Dev. Net Coincidence 118.0197 9.77147 29.71924 5.98667 9.149151 3.19644 92.47203 8.79237 85.00017 8.94074 71.19628 8.50213 8.52593 3.07306 23.55562 4.52883 4.814389 2.59287 42.98622 5.83184 50.05641 8.3308 13.69465 2.88496 40.65945 5.73846 3.950726 2.52709 48.09043 5.42493 82.69109 9.53734 E Std. Dev. of E 0.846588 0.043130257 0.696722 0.053005732 0.46032 0.060650716 -0.51458 0.063136022 S 2.518212 Std. Dev. of S 0.111060764 Violated Bell's Inequality 4.666019 Table 1: The angles above are chosen specifically to maximize the difference between quantum and classical results. The coincidence counts correspond to the combinations of these angles and are used to calculate Bell’s Inequality. The data show that Bell’s Inequality is violated and that also CHSH inequality is violated, because S=2.51821 >2.0. Polarizer A Polarizer B 0 22.5 0 67.5 0 112.5 0 157.5 45 22.5 45 67.5 45 112.5 45 157.5 90 22.5 90 67.5 90 112.5 90 157.5 135 22.5 135 67.5 135 112.5 135 157.5 Net coincidence Std. Dev. Net Coincidence 69.01223 7.58219 8.711241 2.61209 21.30755 5.3687 86.73302 8.20149 43.135 5.78782 49.9647 6.01808 14.19915 4.44235 5.375227 2.79758 4.029181 2.96822 49.12256 7.41263 83.52402 9.54746 39.37713 6.31218 26.82713 5.00172 9.88968 3.30864 88.87463 8.21829 112.9117 11.9397 S Std. Dev. of S 2.546682 0.119412 Violated Bell's Inequality by # of Standard Deviations 4.578123 Table 2: The angles above are chosen specifically to maximize the difference between quantum and classical results. The coincidence counts correspond to the combinations of these angles and are used to calculate Bell’s Inequality. The data show that Bell’s Inequality is violated and that also CHSH inequality is violated, because S=2.546682 >2.0. Polarizer A Polarizer B -10 20 -10 40 -10 60 -10 80 35 20 35 40 35 60 35 80 80 20 80 40 80 60 80 80 125 20 125 40 125 60 125 80 Net coincidence Std. Dev. Net Coincidence S 0.708909 Std. Dev. of S 66.27565 8.03326 0.15709 33.80179 6.14162 8.010204 2.93297 Violated Bell's Inequality by # of Standard Deviations 2.113004 2.05918 -8.21879 54.80029 7.2715 56.85992 5.82346 45.29528 8.54441 27.52615 5.12869 7.044696 2.60878 23.99263 4.79331 45.12073 6.41487 62.77326 6.94279 19.1446 5.89964 1.423591 1.21343 7.988232 3.45147 38.54907 5.94428 Table 3: The angles above are chosen arbitrarily. The coincidence counts correspond to the combinations of these angles and are used to calculate Bell’s Inequality. The data show that Bell’s Inequality is not violated and that also CHSH inequality is not violated, because S=0.708909 < 2.0. Conclusion In this experiment we were able to produce entangled photons with and Argon Ion laser and BBO crystals. We showed the cos2 dependence of the coincidence counts on the difference between each of the polarization angles. We also violated the Bell’s and CHSH Inequalities. This experiment verified the phenomenon of quantum entanglement in the polarization state of photon pairs. Contributions Jaime Cristian Vela worked on: Abstract, Introduction, and Theory. Renald Dore worked on: Experimental Setup, Procedure, Results and Analysis, Conclusion. References [1] J. Gribbin. In Search of Schrodinger’s Cat” Bantam Books. New York. 1984. [2] S. Lukishova. Lab 1 Entanglement and Bell’s Inequalites. University of Rochester, Institute of Optics. 2008. [3] J. Eberly. Bell’s Inequalities and Quantum Mechanics. Amer. J. Phys. 70 (3), 286, March, 2002.