Download Lab Report 3 - The Institute of Optics

OPT 223 Laboratory: Entanglement
Jonathan Brand, Cheonha Jeon, Ezra Milby, Dan Easterly, Jaime Gruttadauria, Brandon
Zimmerman
Group 4, Spring 2009
University of Rochester, Institute of Optics
275 Hutchinson Road Rochester, NY 14627
Abstract: We present an experimental setup to observe the phenomenon of quantum
entanglement. In our experiment we will entangle photons by way of spontaneous
parametric down conversion. We will measure the detection of these entangled pairs as a
function of polarization angles from two oriented polarizers placed strategically in front
of two Avalanche Photon Detectors. As seen in the experimental data and analysis
section of the report, we will use our measurements to show that our polarized states
agree with the predictions of quantum mechanics by reproducing the data graphically to
observe and verify the functional behavior of entangled states.
1. Introduction
Entanglement of quantum systems has become a critical research area of quantum
mechanics, and the press for quantum information and communication. Quantum
entanglement is a phenomenon that says if two particles interact with each and either
particle remains unmeasured, that these two particles can become correlated in a sense
that their fates are intertwined forever. Mathematically, once entangled these particles
can be described by sharing one wavefunction. This wavefunction contains the combined
and shared information in regards to both of their quantum states, and thus any reaction
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from one state unavoidably alters the fate the second. Particles will remain entangled
regardless of the distance between them.
In order to exploit entangled systems for applications in quantum information we
must first efficiently create, detect, and sustain this phenomena. Two methods for
efficiently obtaining and validating entangled states will be performed in this lab
experiment. The first will be through the process of parametric down conversion.
Parametric down conversion is the process of entangling states with respect to their
polarization. In this experiment we will use BBO crystals to perform this process. The
second part of this lab will validate entanglement through the violation of Bell’s
Inequalities. Bell’s Inequalities is an approach to testing the quantum limits of entangled
states. By calculating Bell’s value of S we can determine whether our parametrically
down converted photons are indeed entangled.
To produce polarized-entangled photons we will use the process of spontaneous
down conversion. Spontaneous down conversion is the non-linear process that allows a
horizontal (vertical) photon of wavelength lambda that is incident on a Beta Barium
Borate (BBO) crystal to emerge from that crystal as vertical (horizontal) polarized
photons of wavelength twice the original lambda value as seen in figure 1. The polarized
entangled states will emerge as a cone of light. In our experiment we will detect these
low intense entangled pairs with two Avalanche Photon Detectors (APDs).
2. Procedure
2.1 Experimental Setup
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As seen in Figure 1, the primary components of this experiment consist of:

argon source

optical filters

Quartz Plate

Mirrors

Beta Barium Borate (BBO) Crystals

Polarizers

Beam Stop

Avalanche Photon Detectors (APD) aligned with fiber laser

Lab View computer software
Figure 1: Schematics of Experimental Setup
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Figures 2 and 3: Images of Experimental Setup
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2.2 Experimental Procedure
Our light source will be an argon laser. Immediately our beam will pass through a
blue filter to filter out all other shorter wavelengths of light. After passing through
the blue filter the beam propagates through a quartz plate. Through rotation, the
quartz plate will be used to adjust the phase difference between the horizontal and
vertically polarized components of signal and idler beam. The beam is then directed
from the quartz plate through a pair of BBO crystals. It is at the BBO crystals where
photons will be entangled with respect to their polarization through parametric down
conversion. At the end of the setup two Avalanche Photon Detectors are placed
strategically to detect the down converted photons. By rotating the polarizers placed
in front of each APD we can detect the polarization state of the coincident photons.
Special filters will be placed in front of the APD detectors so to guarantee that only
down converted photons can be detected. The data will be recorded from the APDs to
a Lab View interface program in which we can determine entanglement through the
functional representation of the data being that of a cosine squared pattern.
3. Experimental Data and Analysis
3.1 Observance of Entanglement
In the first part of the lab procedure we will measure the coincident photon counts
on APD detectors A and B by keeping one polarizer fixed at the angles 45, and 135
degrees. The second polarizer will be rotated in ten degree increments from 0 to 360
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degrees. The coincident photon counts on each detector will be recorded at each position.
Using Excel the coincident counts will be plotted as a function of polarization angle. We
will look for a cosine squared function, as entanglement is represented by this periodic
function, as well as determining the visibility for each setup.
4. Experimental Results
Beta
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
250
260
270
280
290
300
310
320
330
340
Alpha=45
Single
Coincidence 1
263
32349
347
32120
427
31866
473
31215
497
30350
537
30611
505
30799
431
30960
366
31502
299
31040
189
31692
120
31740
52
31681
39
32243
18
32260
50
32263
104
31879
172
31922
255
31489
338
28500
345
27600
475
28800
470
28400
470
26800
440
25200
370
28100
307
28400
275
29600
215
29500
120
30600
65
30000
30
27000
19
28000
40
28600
90
29000
Single
2
29677
29430
29340
29602
29625
29536
29308
29420
29174
29406
29083
29007
28548
28809
28465
29177
28704
28856
28798
27300
25200
26200
27000
26700
25700
26200
25700
26500
25400
27000
26600
26200
26400
25000
24200
Alpha=135
Single
Coincidence 1
271
27190
201
27182
136
26447
58
27353
28
26944
15
26157
52
26942
79
27088
171
27688
238
27537
341
28279
412
28209
466
28300
482
28558
503
28553
506
29542
446
27629
386
28479
284
28166
211
28406
134
27999
66
27260
75
26646
22
27023
45
27028
92
27489
160
27388
247
28125
309
28177
444
28251
476
29014
529
28872
531
28849
494
29082
439
28894
Single
2
29150
30393
28606
30221
29510
30489
30245
30371
30339
29811
30550
30293
30055
30597
30285
30506
29131
31010
30501
30917
31018
30117
30196
30399
30027
30405
30183
30390
30368
30502
30101
30143
30310
30294
30131
6
350
360
160
200
28900
27700
25300
26200
379
330
28544
28687
30627
30215
Table 1: Experimental Data of Single and Coincident Photon Counts with alpha at 45
and 135 degrees
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Figures 4-6: Experimental functional results of photon counts and verification of
entanglement
Fringe Visibilities were calculated at the values:
V= .935 for alpha @ 45 degrees
V=.941 for alpha @ 135 degrees
Conclusion
In this experiment we looked to observe the quantum mechanical phenomena of
entanglement through parametric down conversion. In the first part of the lab we used
our experimental setup to collect data from parametrically down converted entangled
photons. This data consisted of the number of photon counts detected at particular
polarization angles. Once this data was collected we plotted the coincident photon counts
as a function of polarization angles. Derivations show that entangled states produce a
function with the characteristics of a cosine squared function. In all cases of positioning
polarizer B at 45 and 135 degrees, while polarizer A was rotated incrementally 360
degrees the cosine squared function was generated and thus entangled quantum states
were present and the their corresponding fringe visibilities calculated as well.
References
1.
OPT 253K Entanglement and Bell’s Inequalities Laboratory Manual
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