Download Lab Report 4 - University of Rochester

Optics 223: Entanglement and Bell’s Inequalities
Stephen Eggers and Daniel Balonek
Group 3: Friday, April 10, 2009
Abstract
By creating two different photons whose polarization states were entangled through the use of
BBO crystals through a process called Spontaneous Parametric Down-Conversion, we were able
to measure the coincidence counts between two single-photon detectors to calculate Bell’s
Inequalities and verify that they are indeed violated, thus proving that there is no classical
explanation for this phenomenon.
Theory
Entanglement is one of the fascinating results of Quantum Mechanics where the property of one
particle depends on the property of the other. Two particles that are entangled have wave
functions that cannot be separated. Any measurement performed on one particle would change
the state of the other. The quantum mechanical state describing the particle’s momentum, spin,
or polarization may be entangled. We entangled the polarization in this lab through Beta Barium
Borate crystals. For each horizontally polarized photon of wavelength λ incident on the crystal,
two photons of wavelength 2λ exit with vertical polarization. We used two BBP crystals to create
two exiting cones overlapped with one another composed of vertical and horizontally polarized
and entangled photons.
Set-Up and Procedure
As shown in figure 1 a ~100mW pump argon ion laser of wavelength λ=363.3 nm and a vertical
polarization passes through a blue filter to remember parasite fluorescence inherent in the argon
laser, then through a birefringent quartz material to create a phase difference. It is then redirected
through two BPO Type-1 crystals mounted back-to-back and perpendicular to one another. The
down-converted photons from the BPO are emitted in two overlapping cones (one horizontallypolarized and the other vertically-polarized) with a wavelength of 2λ=727.6nm. One side of the
cone is passed through Polarizer B, and the other side of the cone is passed through Polarizer A,
and then each is detected using avalanche photodiodes (APD) detectors. The polarizers are
adjusted, and the APDs (which are equidistant from the center of the crystal) then can count the
photons arriving at each detector. This data is fed to a computer which calculates a coincidence
count which consists of how similar the counts are in relation to APD B and APD A. We made
two sets of measurements in our lab. In the first set, we set Polarizer A to 45 degrees, and then
rotated Polarizer B from 0 to 360 degrees while taking measurements every 10 degree interval.
In the second set, we set Polarizer A to 135 degrees, and rotated B again from 0 to 360 degrees.
We would expect for entangled photons that the coincidence count would be highest when
Polarizer A and Polarizer B were at the same angle. Our measured data is presented in the table
on the next page.
Figure 11
Schematic of Experimental Setup
Measured Data
Set 1: Polarizer A at 45 Degrees
Polarizer B
Coincidence
Single
Single B
(degrees)
Count
A Count
Count
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
1.
1
210
242
380
414
448
439
442
385
310
271
180
107
60
32
22
37
85
145
230
254
361
382
29738
28306
28786
27631
27645
27472
27587
27607
27967
28484
28410
28791
29019
29378
29156
29441
28991
28599
27824
27517
26960
26229
27458
26536
27054
26682
26774
26875
26903
26951
26861
26456
26780
26379
26607
26485
26301
26494
26301
26204
26325
26099
25920
26036
Set 2: Polarizer A at 135 Degrees
Polarizer B
Coincidenc
Single
Single B
(degrees)
e Count
A Count
Count
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
324
210
140
80
35
20
58
111
190
280
400
490
540
590
586
563
508
419
317
227
158
87
Lukishova, S. G. (2008). Lab. 1. Entanglement and Bell’s Inequalities [Laboratory Manual]. University of Rochester
31082
30761
30582
30406
29897
30042
29043
30824
30600
31000
31000
32143
32000
32700
32300
32500
32300
32000
31000
30800
30400
30300
33497
33189
33879
34203
34309
34437
34488
34284
34200
34000
34000
33060
34000
33900
33400
33500
33300
33600
33700
33400
33900
33900
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
420
448
445
381
353
251
185
111
59
27
18
44
79
138
210
26345
25949
26451
26672
26589
27723
28296
28309
28882
29189
29181
28781
28496
28056
27271
25962
25779
25743
25774
25601
26069
25800
25749
25879
25871
25926
25895
25458
25558
25207
220
230
240
250
260
270
280
290
300
310
320
330
340
350
360
38
28
55
112
200
387
404
500
556
630
602
589
522
436
357
Table 1
Raw Data collected
Figure 2
Coincidences at 45 and 135 degrees with theoretical fit
29700
29800
30300
30500
31300
31200
31900
32700
33000
33100
33100
32600
32800
31900
31600
33800
34200
34100
34000
34200
33800
33900
34300
33600
34100
33700
33600
33800
33500
34000
Figure 3
Singles counts for 45 and 135 degrees
Results:
Data was taken with respect to coincidence count vs. polarizer B angle and single counts
vs. polarizer B angle. The data was plotted in figures 2 and 3. As can be seen from figure 2 the
measured data correlated very well with a theoretical fit. The theoretical fit function was cos(ab)^2, where ‘a’ represents the angle at which polarizer A was orientated and ‘b’ represents the
orientation of polarizer B. The single photon counts were plotted on figure 3. As can be seen
from the graph our single photon count for each detector, A and B, were fairly consistent. The
visibility of the coincidence count was also calculated with equation 1. At 45 degrees the
visibility was calculated to be .923 and at 135 degrees it was calculated to be .938. The
discrepancy in the height of each of the curves in figure 2 is due to the fact that the power level
of the input laser was changed in between each trial, from 80mW to 98mW for 45 degrees and
135 degrees respectively.
References
Lukishova, S. G. (2008). Lab. 1. Entanglement and Bell’s Inequalities [Laboratory Manual]. University of
Rochester