Technical Overview

Introduction

The central issue of the experiments is quantum superposition. Superposition in quantum mechanics means that a particle can be in multiple states at the same time. The superpositions make a complex wave in space and can be described mathematically by Eq.(1),

(1)
\begin{align} \big|\Psi\big>=c_1\big|\Psi_1\big>+c_2\big|\Psi_2\big>+...+c_n\big|\Psi_n\big> \end{align}

where the c’s are the coefficient, or “how much is present”, for the respective state of Ψ. This has some interesting implications, such as the idea that a particle can be in multiple places at the same time or have multiple momentums simultaneously.

Richard Feynman has described superposition as the “only mystery” of quantum mechanics. Superposition implies that the quantum theory is non-local. [1] Locality is the principle that distant objects cannot have a direct influence on one another. If something is non-local it is not only influenced by its immediate surroundings, but also by objects at any distance. Einstein rejected this possibility, but subsequent experiments based on John Bell’s tests for non-locality have confirmed it. [2] These experiments are known as Bell’s inequalities experiments. Einstein famously called this non-locality “spooky action at a distance.” [3] Interference of quanta has been used in order to understand the consequences of superposition. Schrödinger realized that the non-local behavior is a result of non-separable superpositions called “entangled states.” [4] In the past decade there have been significant advances in the experimental production and study of entangled states. There are possibilities to use such non-local quantum states for many interesting applications, such as quantum communication and quantum computing. The new techniques developed in order to delve deeper into the possibilities of quantum mechanics have also made it easier to display some of the basic, but confusing, features of quantum mechanics such as superposition, which until the recent developments were hard to demonstrate. With the invention of new technology it is now relatively easy, and a good time, to develop and set up a series of single photon experiments to support the understanding of difficult and evasive quantum mechanics principles at the undergraduate level.

Most of the traditional experiments used in attempt to demonstrate the existence of the indivisible nature of the photon have possible alternative explanations in terms of classical waves. Even Einstein’s Nobel Prize winning work on the photoelectric effect has a possible wave explanation. [5] By using entangled photon states, it is possible to eliminate the classical explanations and the indivisibility of the photon can be demonstrated. Grangier et. al. was the first to demonstrate the single photon’s existence. [6]

During the fall semester we assembled and performed a few experiments. The first was an experiment used to understand coincidences and accidental coincidences. We then set up an experiment to understand and observe spontaneous down conversion. Finally we set up a reproduction of the Grangier experiment used to prove the existence of single photons. But first, we had to set up what we called the “optics playground” in order to get an understanding of how all the optics equipment worked. In the optics playground we also set up a sort of dumbed down “quantum eraser”.

Optics Playground

In order to understand how to use the optics equipment we first had to complete a few challenges in the “optics playground”. We had to learn how to adjust all the equipment and align the laser beam both level and parallel. We then had to setup an interferometer so that we could see an interference pattern. We were using the simplest type of interferometer, the Mach-Zender interferometer. This is when we introduced a pseudo quantum eraser. Since the beams in each path of the interferometer were “tagged” with a different polarization, we had to use a polarizer after the beams recombined to “erase” the polarization information. I describe this as only a “pseudo” quantum eraser because it can be explained completely classically. These tasks also presented us with the opportunity to understand collimation, and the various optics components such as polarizing beam splitters, half wave plates, and polarizers.

Understanding Coincidences and Accidental Coincidences

In an effort to understand the concept of coincidences and the formula used to describe accidental coincidences we designed a side experiment. Using RadAlert detectors (simple radiation monitors) we were able to use radiation sources to generate pulses and random coincidences. Accidental coincidences are random, causally unrelated events that occur nearly simultaneously. [7] The project was held up for a period of time of about four weeks due to what we thought were equipment compatibility problems. We did not move on for this period of time because we wanted to have a complete understanding of the coincidence formula and ensure that it was an accurate formula. We were finally able to figure out the compatibility problem by building a comparator circuit so that we would have a nice square pulse to work with. Shortly after doing this we discovered that the ugly pulse we were receiving from the RadAlert detectors was due to a faulty cable. This was a frustrating experience, but from it I learned much about electronics applications, where by I was forced to try to solve the problem with alternative circuitry. We were finally able to successfully test and verify the coincidence formula.

Spontaneous Parametric Down Conversion

Spontaneous parametric down conversion is the nonlinear process by which two photons (the signal and idler) are created from a parent photon (the pump). The down converted photons are produced simultaneously in an entangled state. [8] They are correlated in energy and momentum and due to the conservation of energy and momentum they each have one half that of the pump photon. The down converted photons are produced by passing a beam through a barium-borate (BBO) crystal with the optical axis oriented at a chosen angle to the propagation direction of the pump beam in order to produce our laboratory angle of 3 degrees. Our laser is a 405 nm, which puts it in the blue spectrum, diode laser. After down conversion the two down converted photons have wavelength of 810 nm, which is not visible light. Our laser wavelength was chosen as such because the detectors are optimized at a certain wavelength. This laser enabled us to generate down converted photons as close as possible to this optimized wavelength.

We were able to understand the angle generated by this process. We chose a laboratory angle of 3 degrees. Using this angle enabled us to calculate the necessary phase matching angle, which is the angle between the crystals optical axis and the pump beam.

This process is how we generated single photons for the rest of the experiments. We generated the entangled pair of photons and then measured the state of the beam in the idler arm. By measuring this beam in the single photon state we were able to collapse the beam in the signal arm into the single photon state as well.

Simple Coincidence Counting Experiment

In order to test our coincidence counting formula and our set up, we ran some simple coincidence counting runs between the detectors that were receiving the down converted photons. With this we were able to once again test the coincidence formula. We were also able to calculate the efficiency of the coincidence detecting system. We calculated an efficiency value of 4.45%.

Proof of the Existence of Photons (the Grangier Experiment)

We set up an experiment that duplicates the experiment of Grangier, Roger and Aspect, in which they were able to generate a single photon source[6]. The experiment has been simplified from what Grangier et. al. did by using a parametric down conversion source instead of an atomic beam source. The parametric down conversion source provides much higher counts than the source used in the original experiment. With this source we were able to demonstrate that if a single photon is incident on a beamsplitter, it can only be detected at one of the outputs. This shows the indivisible “particle-like” nature of a photon. We detected a second-order coherence, also called the anti-correlation parameter, or value slightly higher than 0, but within one standard deviation, which can be accounted for through accidental coincidences.

We plan to set up many more experiments in the spring semester. Entangled states make it possible to produce experimentally certain consequences of two-particle superposition states such as: two-photon interference effects and the violation of Bell’s inequalities. These experiments include bell inequalities experiments, the quantum eraser, and tests of local realism.

Single Photon Interference

In performing the work, we added an interferometer to the signal arm to demonstrate that when an individual photon traverses the interferometer it interferes with itself. We simultaneously measured both the interference and the second-order coherence g(2). We expected to find g(2)<1, this simultaneously demonstrates both particle and wavelike behavior of light. If light were a particle it would have a g(2) value of 0 and if it were a wave we would obtain a g(2) value of 1. We expected to obtain a value that is greater than 0 but less than 1, which can only be explained quantum mechanically.

Quantum Eraser

We plan to construct an experiment where the visibility of an observed fringe pattern is affected by the measurements and path lengths of two spatially separated beams. It is possible to change “how much” of the interference can be observed. If one has any way to determine which path the photon takes through the interferometer then the interference pattern disappears. It is possible to get rid of all information about which path the photon takes, the “which-path” information is said to be erased. In our experiment we will use the different polarizations of the two paths to “tag” the paths and then use a polarizer to erase the path information.

Bell Inequalities

One goal of our project is to replicate experiments used to test Bell inequalities. Bell’s theorem is concerned with the EPR argument. The EPR argument was an attack on quantum theory proposed by Einstein, Podolsky, and Rosen in a paper published in 1935.[3] The EPR paradox, as it has come to be known, stated that measurements that quantum theory posits as impossible, such as the simultaneous measurement of momentum and position, are in fact possible and gave a description on how to carry out the measurements. The conclusion by Einstein, Podolsky, and Rosen from this was that it was possible to have a better description of reality than quantum mechanics allowed. [3] Experimental results show that quantum mechanics is indeed correct, so that means that one of the assumptions that the EPR argument is based on must be wrong. The experiment we plan to set up will test the assumption of locality.

References
1. Feynman, R. P.; Leighton, R. B.; Sands, M., The Feynman Lectures on Physics, Vol. 3; Addison-Wesley: Reading, (1965).
2. D. Dehlinger and M. W. Mitchell, "Entangled photons, nonlocality, and Bell inequalities in the undergraduate laboratory", Am. J. Phys. 70: 903-910 (2002).
3. A. Einstein, N. Rosen and B. Podolsky, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Phys. Rev. 47; 777 (1935)
4. Schrödinger, Erwin. "An Undulatory Theory of the Mechanics of Atoms and Molecules", Phys. Rev. 28 (6): 1049–1070 (December 1926).
5. Einstein, Albert (1905), "On a Heuristic Viewpoint Concerning the Production and Transformation of Light", Annalen der Physik 17: 132–148. (March 1905).
6. P. Grangier, G. Roger, and A. Aspect, "Experimental evidence for a photon anticorrelation effect on a beam splitter: A new light on single-photon interferences", Europhys. Lett. 1: 173-179 (1986).
7. Eckart C. and F.R. Shonka, “Accidental Coincidences in Counter Circuits”, Physical Review 43: 752-756 (May 1938).
8. Galvez E.J., C. H. Holbrow, M. J. Pysher, J. W. Martin, N. Courtemanche, L. Heilig, and J. Spencer, “Interference with correlated photons: Five quantum mechanics experiments for undergraduates”, Am. J. Phys. 73 (2): 127-140 (February 2005)
page revision: 25, last edited: 29 Apr 2009 21:05