Single Photon Quantum Interference Project

Wenbo Ge and Duoduo Xu

Abstract

We have examined the quantum nature of light by measuring the anti-correlation parameter α, for which Quantum Theory predicts α≥0, but Semiclassical Theory gives α≥1. Our best result gives α=0.0278±0.0003, which violates the Semiclassical prediction by 3241 standard deviations. Then we show Quantum Mechanics violates local realism by measuring Bell-Clauser-Horne inequality. Our result gives H=0.21±0.02, which violates the inequality set by local realism by 10.5 standard deviations.

Introduction

The nature of light was not clear in the early 20th century. The discovery of photoelectric effect made people thought about the nature of light again. Einstein first pointed out that light is made by photons. Einstein's theory explained the photoelectric effect successfully. It seemed that light is indeed made by photons. However, an alternative Semiclassical theory at that time could also interpret the photoelectric effect correctly. In the Semiclassical theory light is still treated as electromagnetic wave, the quantum effect in the photoelectric experiment is owe to the quantization of atoms in the device. What on earth is light? Photons or electromagnetic wave?Scientists in the 20th century made a lot of experiments to find out this problem and finally succeeded. The first half of this project is to follow their exploration process and prove the existence of photon.

The second part of this project is to perform Hardy's test and prove that quantum mechanics disobey local realism. Before quantum mechanics, local realism was used as the principle for physics theory. “Locality here means that the results of measurements in one location should not affect the results of measurement in another location if there is no causal relationship between the measurement. Reality refers to the idea that we should be able to assign definite value to physically measurable quantities prior to their actual measurement. By saying quantum mechanics violates local realism, we mean that we are forced to give up either locality or reality to explain quantum mechanical predictions ”.[3] Before Hardy's test of local realism, physicist thought all physics theory should obey local realism. Einstein tried to prove quantum mechanics is not a complete theory by illustrating that it disobey local realism.

Theory

Quantum theory, which agrees the existence of photon, predicts α≥0; While Semiclassical theory gives a different prediction that α≥1. α is called anti-correlationparameter which is an experimental parameter defined by

In the equation, the subscripts A, B, and AB refer to incidents and P refers to the probability of the corresponding incident happenning.

The picture above roughly explains what happenns in the experiment. In general, some detectors are used to measure laser beams. The picture above shows two detectors,detector A and detector B, measuring two laser beams. During the measurement, when a detector receive the laser, it will send out electric pulse signals to a counter, which is not shown in the picture. The counter will record the number of signals received in a given time and sends it to the computer. Then the anticorrelation parameter can be calculated by computer. Specifically, incident A refers to a photon is registered at detector A; incident B refers to a photon is registered at detector B;Incident AB refers to two detectors each detect a photon at the same time.

In the experiment, the directly measured values are rate R, which is the number of incident per second. Rewrited the equation of anticorrelation parameter gives

τ is a constant in the experiment. If any experiment gives a result, which indicate α is not always no less than one, the Semiclassical theory will be proved to be wrong; and the existence of photon is proved.

For Hardy's test of local realism, there is a inequality that can be tested by experiment. The inequality is called Bell-Clauser-Horne inequality. It is written by

If quantum mechanics obeys local realism, the experiment results will be consisent with this inequality. P in the inequality refers to probability and those angles in the brackets are the angles of half wave plate used in the experiment. A detailed discussion of this inequality can be found in ref [3].

For our convenience, two angles, α and β, are selected in the experiment. Rewirte the inequality gives

A experiment parameter, H, is defined by

The Bell-Clauser-Horne inequality then becomes H≤0.

Experiment Setup

The first three sub-experiments that exam the quantum nature of light involve less components than the last one. The following is a graph of the apparatus setup in the final Hardy’s test experiment and some of them were not in use in the first four experiment.

The experiments that determine the nature of light involve Pump laser, mirrors, irises, Half Wave Plate(HWP), BBO, filter in B arm, HWP and PBS in B arm only, detector A,B,B’(C), and !HeNe laser setup for calibration.

When linear polarized light first hit on HWP, the polarization plane is rotated by a certain degree depends on the need of rotation angle of our experiment. In our experiment, we rotate the HWP when collecting data and we find the angle which gives us the highest counts at detectors. The HWP in the front of the beam splitter in the B arm readjusts the polarization direction of the beam to secure that when the photon arrives at the beam splitter, it have equal probability to go through either transmitted path or 90 degrees reflected path.

BBO non-linearly down converts the light into pairs of entangled photons. Specifically,the entangled photons rsquo; polarizations is different from the pump photon by 90 degrees angle.

The Polarizing Beam Splitter (PBS) splits the down converted photon into either transmitted or reflected beams. The signals generated by photon arrivals are collected at the detector at the end.

!HeNe laser helps to find the correct location of detector B, D’ and the beam splitter. We use detector E (refer to the figure above) to collect the laser beam and transmit it to detector B using a wire. Because the real entangled photon beam are invisible (wavelength is 810 nm), it is very hard to find the proper location for beam splitter and D’. The visible !HeNe laser beam is shot from detector B back into BBO to mimic the path so that we can place the beam splitter along the path to make sure the beam fully goes through the splitter. D’(C in the figure above) can be located once beam splitter has the proper location.

Hardy's test involves more components and the full diagram is exactly shown in the figure in this section. A second BBO crystal is added and it produces two pairs of entangled photon beams. Quarter Wave Plate (QWP) is added between the HWP and the BBO. It compensate the phase lost due to the small distance between the two BBO crystals. Without the QWP, the two pairs of entangled photon beams can not be produced at the same time.

Setups in A arm should then be made to be identical as B arm applying the same rules. Again, !HeNe laser is used for locating the beam splitter and detector D.

Results and conclusion

The diagram above shows the anticorrelation parameter between detector A and detector B for two entangled beams. As expected by quantum theory, entangled photons are highly correlated to each other and the anti-correlation parameter α is much bigger than 1. The results displays the property of entangled photons. Since Semiclassical theory allows this result, the existence of photons is not proved yet.

After the first experiment, we built a simple model trying to estimate the efficiency of down-conversion process. It is achieved by exploring the relation between laser intensity and the magnitude of α. Assume the percentage of down-converted photons in the incoming laser is λ. Noise is represented by R_N. To make our model simple, we assume

With these basic assumption our model gives

Using χ² fit method we find the minimum χ²=257.63 when λ=0.0667.The result indicates that roughly 6.67% of the pump photons were down-converted to entangled pairs. The measured results and predicted results by theory are shown in the diagram below.

The diagram above shows the results of anti-correlation parameter between detector B and detector B' for transmitted beam and reflected beam without conditioned on a detecton at detector A. This results indicate that if light is maded by photons, it must be made of photon bunches instead of single photons. Although this result can't deny the Semiclassical theory, it helps to build quantum optics, which gives a more accurate description for light.

The diagram above shows the results of anti-correlation parameter between detector B and detector B' for transmitted beam and reflected beam conditioned on a detecton at detector A. When the measurement is conditioned on a detection at detector A it can make sure that the photon measured by other detectors is not in bunches. If so, the quantum theory gives α=0. The results agree with the prediction by quantum theory and is contradict to Semiclassical theory. Therefore, the existence of photon has been proved.

The diagram above shows the results for Hardy's test. Finally H=0.21±0.02, which violates the inequality set by local realism H≤0 by 10.5 standard deviations. Quantum mechanics is indeed inconsistent with local realism.

Reference

[1] B. J. Pearson, P. Jackson. “A hands-on introduction to single photons and quantum mechanics for undergraduates.” Am. J. Phys. 78(5), 471-484 (2010)

[2] M. Beck. “Quantum mechanics —theory and experiment ” Oxford University Press.

[3] J. A. Carlson, M. D. Olmstead, and M. Beck. “An experiment implementing Hardy Rsquo;s test of local realism.” Am. J. Phys. 74(3), 180-186 (2006)

[4] https://wiki.umn.edu/MXP/QuantumInterferenceLab

-- Main.gexxx153- 14 May 2015