quantum entanglement and bell’s inequalities kristin m. beck and jacob e. mainzer demonstrating...
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![Page 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](https://reader037.vdocuments.net/reader037/viewer/2022110207/56649d435503460f94a1e889/html5/thumbnails/1.jpg)
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
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Outline
Relevant Physics Concepts Experimental Setup and Procedure Relationship between Setup and Physical
Concepts Results Conclusions
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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
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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)
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Experimental Setup
Laser
AP
D
AP
D
Beam Stop
BBO crystals
Mirror
Quartz Plate
Blue Filter
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Experimental Setup
Laser
Quartz Plate
Mirror
BBO Crystals
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Experimental Setup
APD
APD
Beam Stop
Interference Filters
Polarizers
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Experimental Setup
BBO (Beta Barium Borate) Crystal Negative uniaxial nonlinear crystal Spontaneous parametric
down-conversion
Laser
AP
D
AP
D
λ|H
2λ
2λ
|VV
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Downconverted Light Cone from 2mm thick BBO Type I crystal
Video (Click to Play)
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Experimental Setup
|H + |V
|H Cone
|V Cone
Dual BBO crystal Setup
|V |H
BBO crystals
Phase difference between down-converted photons
|Vs Vi + |HsHi
Entangled State
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Experimental Setup
Quartz Plate Birefringent material Introduces a phase difference
between two polarization
components Eliminates phase
difference introduced by
BBO crystals
Laser
AP
D
AP
D
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Experimental Setup
Polarizers Select a particular
polarization state Block other
photon polarizations Used to measure photon
polarization with APDs
Laser
AP
D
AP
D
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Experimental Setup
APDs Single-photon
counting avalanche
photodiodes Dual APDs record
coincidence photon
count (26 ns) PerkinElmer SPCM-AQR
Laser
AP
D
AP
D
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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 cos2(α – β) because of entanglement
Measurement at one polarizer affects measurement at the other polarizer
A 0o-90o polarizer setup should yield a minimum coincidence count
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Observations/Data
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Observations/Data
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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
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Observations/Data
Calculations resulted in 18 statistically significant values of S above 2.0
2.518 +/- 0.0572.516 +/- 0.0642.506 +/- 0.0582.501 +/- 0.0632.485 +/- 0.0592.482 +/- 0.063
2.473 +/- 0.0622.472 +/- 0.0602.386 +/- 0.0602.374 +/- 0.0612.366 +/- 0.0662.352 +/- 0.065
2.333 +/- 0.0652.324 +/- 0.0642.316 +/- 0.0632.314 +/- 0.1372.303 +/- 0.0632.096 +/- 0.061
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Error
Our calculation for σS is:
Sources of experimental error :
(1) Errors in aligning polarizers, each 1 degree of error
(2) accidental coincidences (Nacc = tNaNb/Tmeasure)
10/9/08 :: 14.47813 Tmeasure = 1s
10/14/08 :: 76.66656 Tmeasure = 5s
10/16/08 :: 91.93551 Tmeasure = 5s
(3) human error in selecting the proper counts to record
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Conclusion
Quantum entanglement was demonstrated by a cos2(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
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References
D. Dehlinger and M.W. Mitchell, “ Entangled photons, nonlocality, and Bellinequalities 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.
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Acknowledgements
Dr. Lukishova Anand Jha 243W Staff: Prof Howell, Steve Bloch
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Questions?
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Bell’s Inequalities & HVT Presently
Loopholes in setup: Detector Static polarizers
QUEST = QUantumEntanglement in Space ExperimenTs (ESA)
A. Zeilinger. Oct. 20, 2008. “Photonic Entanglement and Quantum Information” Plenary Talk at OSA FiO/DLS XXIV 2008, Rochester, NY.