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
Filter
Filterr
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
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
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
Camera
Filter 2
Lens
Filter 1
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 downconverted 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_do
wn-conversion
http://www.optics.rochester.edu/workgroups/lukishova/Q
uantumOpticsLab/homepage/opt253_08_lab1_entangl_m
anual.pdf