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 RoadRochester, NY14627

Abstract: We present an experimental setup to observethe 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 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

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

Figures 2 and 3: Images of Experimental Setup

2.2 Experimental Procedure

Our light source will be anargon 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 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

Alpha=45 / Alpha=135
Beta / Coincidence / Single 1 / Single 2 / Coincidence / Single 1 / Single 2
0 / 263 / 32349 / 29677 / 271 / 27190 / 29150
10 / 347 / 32120 / 29430 / 201 / 27182 / 30393
20 / 427 / 31866 / 29340 / 136 / 26447 / 28606
30 / 473 / 31215 / 29602 / 58 / 27353 / 30221
40 / 497 / 30350 / 29625 / 28 / 26944 / 29510
50 / 537 / 30611 / 29536 / 15 / 26157 / 30489
60 / 505 / 30799 / 29308 / 52 / 26942 / 30245
70 / 431 / 30960 / 29420 / 79 / 27088 / 30371
80 / 366 / 31502 / 29174 / 171 / 27688 / 30339
90 / 299 / 31040 / 29406 / 238 / 27537 / 29811
100 / 189 / 31692 / 29083 / 341 / 28279 / 30550
110 / 120 / 31740 / 29007 / 412 / 28209 / 30293
120 / 52 / 31681 / 28548 / 466 / 28300 / 30055
130 / 39 / 32243 / 28809 / 482 / 28558 / 30597
140 / 18 / 32260 / 28465 / 503 / 28553 / 30285
150 / 50 / 32263 / 29177 / 506 / 29542 / 30506
160 / 104 / 31879 / 28704 / 446 / 27629 / 29131
170 / 172 / 31922 / 28856 / 386 / 28479 / 31010
180 / 255 / 31489 / 28798 / 284 / 28166 / 30501
190 / 338 / 28500 / 27300 / 211 / 28406 / 30917
200 / 345 / 27600 / 25200 / 134 / 27999 / 31018
210 / 475 / 28800 / 26200 / 66 / 27260 / 30117
220 / 470 / 28400 / 27000 / 75 / 26646 / 30196
230 / 470 / 26800 / 26700 / 22 / 27023 / 30399
240 / 440 / 25200 / 25700 / 45 / 27028 / 30027
250 / 370 / 28100 / 26200 / 92 / 27489 / 30405
260 / 307 / 28400 / 25700 / 160 / 27388 / 30183
270 / 275 / 29600 / 26500 / 247 / 28125 / 30390
280 / 215 / 29500 / 25400 / 309 / 28177 / 30368
290 / 120 / 30600 / 27000 / 444 / 28251 / 30502
300 / 65 / 30000 / 26600 / 476 / 29014 / 30101
310 / 30 / 27000 / 26200 / 529 / 28872 / 30143
320 / 19 / 28000 / 26400 / 531 / 28849 / 30310
330 / 40 / 28600 / 25000 / 494 / 29082 / 30294
340 / 90 / 29000 / 24200 / 439 / 28894 / 30131
350 / 160 / 28900 / 25300 / 379 / 28544 / 30627
360 / 200 / 27700 / 26200 / 330 / 28687 / 30215

Table 1: Experimental Data of Single and Coincident Photon Counts with alpha at 45 and 135 degrees

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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