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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. Relevant Physics Concepts Experimental Setup and Procedure Relationship between Setup and Physical Concepts

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Presentation Transcript
slide1

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
Outline

Relevant Physics Concepts

Experimental Setup and Procedure

Relationship between Setup and Physical Concepts

Results

Conclusions

physical concepts
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

physical concepts4
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)

experimental setup
Experimental Setup

Beam Stop

APD

APD

BBO crystals

Quartz Plate

Laser

Mirror

Blue Filter

slide6

Laser

Quartz Plate

Mirror

BBO Crystals

Experimental Setup

slide7

Interference Filters

APD

Beam Stop

APD

Polarizers

Experimental Setup

experimental setup8
Experimental Setup

BBO (Beta Barium Borate) Crystal

Negative uniaxial nonlinear crystal

Spontaneous parametric

down-conversion

λ

|VV

APD

APD

|H

Laser

slide9

Video (Click to Play)

Downconverted Light Cone from 2mm thick BBO Type I crystal

experimental setup10
Experimental Setup

Entangled State

|Vs Vi + |HsHi

Dual BBO crystal Setup

|H

|V

BBO crystals

|H Cone

|V Cone

|H + |V

Phase difference between down-converted photons

experimental setup11
Experimental Setup

Quartz Plate

Birefringent material

Introduces a phase difference

between two polarization

components

Eliminates phase

difference introduced by

BBO crystals

APD

APD

Laser

experimental setup12
Experimental Setup

Polarizers

Select a particular

polarization state

Block other

photon polarizations

Used to measure photon

polarization with APDs

APD

APD

Laser

experimental setup13
Experimental Setup

APDs

Single-photon

counting avalanche

photodiodes

Dual APDs record

coincidence photon

count (26 ns)

PerkinElmer SPCM-AQR

APD

APD

Laser

how does our setup relate to the key physical concepts
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

how does our setup relate to the key physical concepts17
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

observations data18
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
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

conclusion
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

references
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.

acknowledgements
Acknowledgements

Dr. Lukishova

Anand Jha

243W Staff: Prof Howell, Steve Bloch

bell s inequalities hvt presently
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.