1. Entanglement and Bell’s Inequalities Aaron Michalko Kyle Coapman Alberto Sepulveda James MacNeil Madhu Ashok Brian Sheffler

2. Correlation Drawer of Socks – 2 colors, Red and Blue, – Four combinations: RR, RB, BR, BB – (pR 1 + qB 1 ) (pR 2 + qB 2 ) – 50% Same, 50% Different – NO CORRELATION

3. Correlation What if socks are paired: RR, BB If you know one, you know the other 100% Same, 0% Different Perfectly Correlated Entanglement ~ Correlation

4. What is Entanglement? Correlation in all bases What is a basis? – Like a set of axes – Our basis is polarization: V and H – Photons either VV or HH – Perfectly correlated

5. How do we Entangle Photons? Parametric down conversion – Non-linear, birefringent crystal – 2 emitted photons, signal and idler

6. How do we Entangle Photons? 2 crystals create overlapping cones of photons Photons are entangled: – We don’t know if any photon is VV or HH…or maybe both…

7. Logic Exercise Three Assumptions: – When a photon leaves the source it is either H or V – No communication between photons after emission – Nothing that we don’t know, V/H is a complete description

8. Logic Exercise Polarizers set at 45 50% transmit at each polarizer Logical Conclusion: – 25% Coincident – 50% One at a time – 25% No Detection >>> NO CORRELATION

9. Logic Exercise Entangled Source 50% coincidence reading 50% no reading >>>100% Correlation

10. Lab setup

12. Lab Activity 1 We measured the coincidence counts of entangled photons Each passed through a polarizer set at the same angle

13. Lab Activity 2 We only changed one polarizer angle this time What do you think will happen?

14. Logic Exercise Which assumption is incorrect: – Reality – Locality – Hidden Variables

15. Bell’s Inequalities Let A,B and C be three binary characteristics. Assumptions: Logic is valid. The parameters exist whether they are measured or not. No statistical assumptions necessary! Let’s try it!

16. CHSH Bell’s Inequality Let’s define a measure of correlation E: If E=1, perfect correlation. If E=-1, perfect anticorrelation.

17. Hidden Variable Theory Deterministic – Assumes Polarization always has a definite value that is controlled by a variable – We’ll call the variable λ

18. HVT v. QM Comparing P VV for HVT and QM looks like: The look pretty close…but HVT is linear

19. CHSH Bell’s Inequality cont. Let’s introduce a second measure of correlation: According to HVT S≤2 for any angle.

20. CHSH Bell’s Inequality cont. QM predicts S≥2 in some cases. a=-45°, a’=0°, b=22.5°, b’=-22.5° S(QM)=2.828 S(HVT)=2 This means that either locality or reality are false assumptions!

21. Our Lab Activity We recorded coincidence counts with combinations of | polarization angles S = 2.25 We violated Bell’s inequality! That means our system is inherently quantum, and cannot be explained using classical physics

22. This is a little scary… HVT is not a valid explanation for the behavior of entangled photons So…that means we either violate: 1.Reality 2.Locality

24. Thank You George!!!