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?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...

Schematics

 

FilterFilterr

 

 

The Experimental Set up

 

 

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

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

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

BBO Crystal Set

 

In the BBO crystals two photons are created from the incident photon, both

with longer than the original wavelength

726.7 nm

726.7 nm

363.8 nm

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

The beam stop absorbs the high power laser light.

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).

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

 

 

Filter 1

Filter 2

Camera

Lens

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.

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

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

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

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:

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:

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

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

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

David

Will

Kara

Sandi

Special Thanks to Dr.Svetlana G. Lukishova

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