Quantum Entanglement and Bells Inequalities Kristin M Beck

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Quantum Entanglement and Bell’s Inequalities Kristin M. Beck and Jacob E. Mainzer Demonstrating quantum

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

Outline n Relevant Physics Concepts n Experimental Setup and Procedure n Relationship between Setup

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

Physical Concepts Quantum Entanglement between two particles n Particles’ wave functions cannot be separated

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

Physical Concepts Bell’s Inequality n Classical relationship n Used to discern quantum effects from

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

D AP Beam Stop AP D Experimental Setup BBO crystals Quartz Plate Laser Mirror

D AP Beam Stop AP D Experimental Setup BBO crystals Quartz Plate Laser Mirror Blue Filter

Experimental Setup Laser Quartz Plate Mirror BBO Crystals

Experimental Setup Laser Quartz Plate Mirror BBO Crystals

Experimental Setup Interference Filters Beam Stop APD Polarizers

Experimental Setup Interference Filters Beam Stop APD Polarizers

Experimental Setup D AP AP D BBO (Beta Barium Borate) Crystal n Negative uniaxial

Experimental Setup D AP AP D BBO (Beta Barium Borate) Crystal n Negative uniaxial nonlinear crystal n Spontaneous parametric down-conversion 2λ λ |H |VV 2λ Laser

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

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

Experimental Setup Dual BBO crystal Setup Entangled State |Vs Vi + |Hs. Hi BBO

Experimental Setup Dual BBO crystal Setup Entangled State |Vs Vi + |Hs. Hi BBO crystals |H |H Cone |V |H + |V |V Cone Phase difference between down-converted photons

AP D AP Quartz Plate n Birefringent material n Introduces a phase difference between

AP D AP Quartz Plate n Birefringent material n Introduces a phase difference between two polarization components n Eliminates phase difference introduced by BBO crystals D Experimental Setup Laser

D AP Polarizers n Select a particular polarization state n Block other photon polarizations

D AP Polarizers n Select a particular polarization state n Block other photon polarizations n Used to measure photon polarization with APDs AP D Experimental Setup Laser

AP D AP APDs n Single-photon counting avalanche photodiodes n Dual APDs record coincidence

AP D AP APDs n Single-photon counting avalanche photodiodes n Dual APDs record coincidence photon count (26 ns) n Perkin. Elmer SPCM-AQR D Experimental Setup Laser

How does our setup relate to the key physical concepts? What we expect to

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

Observations/Data

Observations/Data

Observations/Data

Observations/Data

How does our setup relate to the key physical concepts? Application of Bell’s Inequality

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

Observations/Data Calculations resulted in 18 statistically significant values of S above 2. 0 2.

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

Error n Our calculation for σS is: n Sources of experimental error : (1)

Error n Our calculation for σS is: n Sources of experimental error : (1) Errors in aligning polarizers, each 1 degree of error (2) accidental coincidences (Nacc = t. Na. Nb/Tmeasure) 10/9/08 : : 14. 47813 Tmeasure = 1 s 10/14/08 : : 76. 66656 Tmeasure = 5 s 10/16/08 : : 91. 93551 Tmeasure = 5 s (3) human error in selecting the proper counts to record

Conclusion n Quantum entanglement was demonstrated by a cos 2(α – β) coincidence count

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

References D. Dehlinger and M. W. Mitchell, “ Entangled photons, nonlocality, and Bell inequalities

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. OPT 253. University of Rochester, NY.

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

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

Questions?

Questions?

Bell’s Inequalities & HVT Presently n Loopholes in setup: n Detector n Static polarizers

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