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Entanglement and Bell’s Inequalities

Entanglement and Bell’s Inequalities. Will Skorski, David Manly,  Sandi Westover, Isaac Trumper,  Kara Lambson. Purpose. To show that entanglement exists To obtain entanglement  To violate Bell's inequalities . What is Entanglement?.

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Entanglement and Bell’s Inequalities

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

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

  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...

  4. Schematics Filter Filterr

  5. The Experimental Set up

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

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

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

  9. BBO Crystal Set

  10. 726.7 nm 363.8 nm 726.7 nm In the BBO crystals two photons are created from the incident photon, both with longer than the original wavelength

  11. 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

  12. The beam stop absorbs the high power laser light.

  13. 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).

  14. 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

  15. Camera Lens Filter 2 Filter 1

  16. 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.

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

  18. 10cm closer distance in positioning of camera. 1 second exposure time, with polarizer. 255 amplification of photon count

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

  20. 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:

  21. 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:

  22. 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

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

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

  25. David

  26. Will

  27. Kara

  28. Sandi

  29. Special Thanks to Dr.Svetlana G. Lukishova

  30. References http://en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion http://www.optics.rochester.edu/workgroups/lukishova/QuantumOpticsLab/homepage/opt253_08_lab1_entangl_manual.pdf

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