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 Results Conclusions

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 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

Laser

AP

D

AP

D

Beam Stop

BBO crystals

Mirror

Quartz Plate

Blue Filter

Experimental Setup

Laser

Quartz Plate

Mirror

BBO Crystals

Experimental Setup

APD

APD

Beam Stop

Interference Filters

Polarizers

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

Downconverted Light Cone from 2mm thick BBO Type I crystal

Video (Click to Play)

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

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

Experimental Setup

Polarizers Select a particular

polarization state Block other

photon polarizations Used to measure photon

polarization with APDs

Laser

AP

D

AP

D

Experimental Setup

APDs Single-photon

counting avalanche

photodiodes Dual APDs record

coincidence photon

count (26 ns) PerkinElmer SPCM-AQR

Laser

AP

D

AP

D

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

Observations/Data

Observations/Data

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/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

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

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

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.

Acknowledgements

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

Questions?

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.