1. Quantum Entanglement and Bell’s Inequalities Kristin M. Beck and Jacob E. Mainzer Demonstrating quantum entanglement of photons via the violation of Bell’s Inequality

2. Outline Relevant Physics Concepts Experimental Setup and Procedure Relationship between Setup and Physical Concepts Results Conclusions

3. Physical Concepts Quantum Entanglement between two particles Particles’ wave functions cannot be separated Measurement of one particle affects the state of the other No classical model of this behavior In this lab, polarization states of two photons were entangled

4. Physical Concepts Bell’s Inequality Classical relationship Used to discern quantum effects from classical effects In this lab, violation of a Bell’s Inequality is used to show no hidden variables (EPR paradox)

5. Experimental Setup Laser APD Beam Stop BBO crystals Mirror Quartz Plate Blue Filter

6. Experimental Setup Laser Quartz Plate Mirror BBO Crystals

7. Experimental Setup APD Beam Stop Interference Filters Polarizers

8. Experimental Setup BBO (Beta Barium Borate) Crystal Negative uniaxial nonlinear crystal Spontaneous parametric down-conversion Laser APD λ |H 2λ2λ 2λ2λ |VV

9. Downconverted Light Cone from 2mm thick BBO Type I crystal Video (Click to Play)

10. Experimental Setup |H + |V |H Cone |V Cone Dual BBO crystal Setup |V|H BBO crystals Phase difference between down-converted photons |V s V i + |H s H i Entangled State

11. Experimental Setup Quartz Plate Birefringent material Introduces a phase difference between two polarization components Eliminates phase difference introduced by BBO crystals Laser APD

12. Experimental Setup Polarizers Select a particular polarization state Block other photon polarizations Used to measure photon polarization with APDs Laser APD

13. Experimental Setup APDs Single-photon counting avalanche photodiodes Dual APDs record coincidence photon count (26 ns) PerkinElmer SPCM-AQR Laser APD

14. How does our setup relate to the key physical concepts? What we expect to observe by moving the polarizers Coincidence count related to polarizer angles α and β by cos 2 (α – β) because of entanglement Measurement at one polarizer affects measurement at the other polarizer A 0 o -90 o polarizer setup should yield a minimum coincidence count

15. Observations/Data

17. How does our setup relate to the key physical concepts? Application of Bell’s Inequality Calculating S, average polarization correlation between pairs of particles Classically, by Bell’s Inequality, |S| ≤ 2 |S| > 2 evidence for quantum entanglement Calculated by measuring coincidence counts (N) for various polarizer angles

18. Observations/Data Calculations resulted in 18 statistically significant values of S above 2.0 2.518 +/- 0.057 2.516 +/- 0.064 2.506 +/- 0.058 2.501 +/- 0.063 2.485 +/- 0.059 2.482 +/- 0.063 2.473 +/- 0.062 2.472 +/- 0.060 2.386 +/- 0.060 2.374 +/- 0.061 2.366 +/- 0.066 2.352 +/- 0.065 2.333 +/- 0.065 2.324 +/- 0.064 2.316 +/- 0.063 2.314 +/- 0.137 2.303 +/- 0.063 2.096 +/- 0.061

19. Error Our calculation for σS is: Sources of experimental error : (1) Errors in aligning polarizers, each 1 degree of error (2) accidental coincidences (N acc = tN a N b /T measure ) 10/9/08 :: 14.47813 T measure = 1s 10/14/08 :: 76.66656 T measure = 5s 10/16/08 :: 91.93551 T measure = 5s (3) human error in selecting the proper counts to record

20. Conclusion Quantum entanglement was demonstrated by a cos 2 (α – β) coincidence count dependence Additionally, we verified quantum behavior by calculating Bell’s Inequality and showing that it violated the classical limit |S| ≤ 2

21. References D. Dehlinger and M.W. Mitchell, “ Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory”, Am. J. Phys, 70, 903 (2002). J. Eberly, “Bell inequalities and quantum mechanics”, Amer. J. Phys., 70 (3), 286, March (2002). S. Lukishova. 2008. Entanglement and Bell’s Inequalities. OPT253. University of Rochester, Rochester, NY.

22. Acknowledgements Dr. Lukishova Anand Jha 243W Staff: Prof Howell, Steve Bloch

23. Questions?

24. Bell’s Inequalities & HVT Presently Loopholes in setup: Detector Static polarizers QUEST = QUantum Entanglement in Space ExperimenTs (ESA) A. Zeilinger. Oct. 20, 2008. “Photonic Entanglement and Quantum Information” Plenary Talk at OSA FiO/DLS XXIV 2008, Rochester, NY.