1. Entanglement and Bell’s Inequalities
Will Skorski, David Manly, 
Sandi Westover, Isaac Trumper, 
Kara Lambson
William

2. Purpose To show that entanglement exists To obtain entanglement
To violate Bell's inequalities 
William

3. What is Entanglement?
Entanglement is defined by two or more quantum particles (photons) with wave functions that cannot be described separately. Symbolically this looks like: 
In layman's terms the state of one particle can not be changed without directly affecting the state of the second particle . This phenomena can occur no matter the location of the photons or how far apart they may be.
We will be speaking about entanglement in polarization but entanglement can be obtained by  many different physical properties such as energy, momentum...
William

4. William

5. Schematics
Sandi
Filter
Filterr

6. The Experimental Set up
Sandi

7. Sandi
A filter is placed in the laser output in order to remove parasite fluorescence from the argon plasma tube in the laser beam 

8. The mirrors are used to direct the beam into the Quartz Plate
Sandi

9. Sandi
The Quartz Plate is used to correct the phase difference between two polarization components

10. BBO Crystal Set
Sandi

11. 726.7 nm
363.8 nm
726.7 nm
Sandi
In the BBO crystals two photons are created from the incident photon, both with longer than the original wavelength

12. Sandi
The polarizers were used to show that we had entangled photons. One polarizer was kept at a constant angle while the other one was rotated at 10 degree increments

13. The beam stop absorbs the high power laser light.
Sandi
The beam stop absorbs the high power laser light.

14. Sandi
There are two detectors that detect the number of photons (single counts). Using a computer card  we can count the simultaneous counts between detector A and B (coincidence count).

15. How to Obtain Entanglement: Spontaneous Parametric Down-conversion
Photons are passed through two BBO crystals
Conservation of momentum and energy for produced photons
The production of these down-converted photons is very rare, only 1 out of every 1010 photons will be down-converted
David 5-10

16. Camera
Lens
Filter 2
Filter 1

17. Description of the camera set up
Filters 1 and 2 are used to get rid of wavelengths that are unwanted
The lens is used to image cones of photons onto camera sensor
Camera is a CCD (Charge Couple Device) camera used to visually show the conical path and the overlap of two cones with perpendicular polarizations of the parametrically down-converted photons.

18. Camera distance 1 from crystal, 2 second exposure, with polarizer
Camera distance 1 from crystal, 2 second exposure, with polarizer. 255 amplification of photon count

19. 10cm closer distance in positioning of camera
10cm closer distance in positioning of camera. 1 second exposure time, with polarizer. 255 amplification of photon count

20. distance 2, 1 second exposure time, with no polarizer
distance 2,  1 second exposure time, with no polarizer. 255 amplification of photon count

21. How to Prove Entanglement Exists
After passing through the BBO crystals, there are four possible outcomes for the photons. The probability of these outcomes can be expressed by:
We can find the probability of each, which is given by this equation:
Isaac's

22. How to Prove Entanglement Exists
We then introduce a new equation that consists of the different probabilities:
 We also introduce another equation:
This equation is known as Bell's Inequality in the CSCH form, and is derived using the classical relation:
We can calculate E(a,b) by using the previous equations. We find that:
Isaac's:
The proof of Bell's Inequalities relies on the measurement of both E and S. Where for the violation of Bell's Inequalities we must have S greater than 2.

23. How to Prove Entanglement Exists
Measuring both E and S allows us to determine whether or not Bell's Inequalities have been violated. Certain values of S and properties of E show violation. 
We find that S has a maximum value of             where V is the fringe visibility in our experiment. We can calculate fringe visibility by:
We see that in order to violate Bell's Inequalities, V must be greater than 0.71
Isaac's

26. Kara

27. Kara

28. Results – What they mean
cos2 dependence of relative polarizer angles
Fringe Visibility > 0.71
Absolute Value of S >2 illustrates the violation of Bell's inequalities
Conclusion
Our data has proved entanglement through the violation of Bell's inequality at certain angles
Kara

29. Isaac (at the computer where data was sent to and recorded)

30. David

31. Will

32. Kara

33. Sandi

34. Special Thanks to
Dr.Svetlana G. Lukishova

35. References