[2] A.C. Melissinos, J. Napolitano, Experiments in Modern Physics 2nd Ed., Academic Press (2003).

The concept of wave particle duality is perhaps best expressed by the following quote: 

“But what is light really? Is it a wave or a shower of photons? There seems no likelihood for forming a consistent description of the phenomena of light by a choice of only one of the two languages. It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do.”

– A.Einstein and I. Leopold. The evolution of physics: the growth of ideas from early concepts to relativity and quanta. CUP Archive, 1961.

Experimentally, light can be shown to have the properties of both waves and particles. Furthermore, whether light behaves as a wave or a particle depends on the nature of the measurement being made and the information available to the observer. For purposes of this discussion, we will define something as being a particle or a wave based on the following criteria:

1. Localization: Particles have well defined discrete locations in space at any particular time, whereas waves extend continuously throughout space.   - Interference: Waves can superimpose at a given location and exhibit interference effects, whereas particles do not.  

In this experiment you will perform two sets of measurements to determine whether – and under what conditions – photons are observed to behave as particles and/or as waves.

In the first experiment we will look at light through a beamsplitter. Consider the case of a simple 50/50 beamsplitter with photodetectors (PDs) positioned to detect the transmitted and reflected light as shown in Fig. 1. Considering light as an electromagnetic wave, we would say that half of the intensity of the incident beam is transmitted and detected by PD #1, and half is reflected and detected by PD #4. Regardless of the intensity of the electromagnetic wave (i.e. the brightness of the light source) there would always be some light being detected at each PD. Quantum mechanics, however, considers light as being made up of particles called photons, each photon carrying a quantum of energy E = hc/λ, where h is Planck's constant, c is the speed of light in a vacuum, and λ is the wavelength. How do photons behave when they interact with the beamsplitter? Do they behave as you would expect for a wave (as described above) or do they behave as particles? If the intensity of the light source is low enough, we can observe what happens as photons enter the beamsplitter one photon at a time.

{ ${/download/attachments/211388203/Beamsplitter.png?version=1&modificationDate=1556896210000&api=v2}$ Figure 1: Schematic showing how a 50/50 beamsplitter works.

In the second experiment, we will look at light through an interferometer. Consider the geometry of the Mach-Zehnder interferometer (see, e.g. Fig. 5) with a single input and two outputs. Light entering the interferometer encounters a beamsplitter, travels along one (or both) of two different paths with (potentially) different lengths, and encounters a second beamsplitter leading to a photodetector at either output. Considering light as an electromagnetic wave, we would say that half the intensity travels each path, and that these paths are superimposed at the outputs of the interferometer. If the two paths through the interferometer are of different lengths, there will be some phase difference between the two waves when they recombine, resulting in interference. Considering light as being made up of photons, however, the picture is not as clear. What happens when a single photon at a time is sent into the interferometer?

Figure 2 gives an overview of the optical table. Note that positioning and alignment of the various components must be done with great precision. (The overlap of paths must be within a few wavelengths of light, a precision on the order of microns!) Due to time constraints, the optical components have been aligned on the table for you. You will perform only a limited number of manipulations during the experiment.

IMPORTANT: Accidentally knocking a single optical component out of alignment by the slightest amount could result in a full day's delay. Think about where you are putting your hands. Take care not to bump into things. Don't adjust the optics yourself except where explicitly instructed.

{ ${/download/attachments/211388203/WPD_layout_full.png?version=1&modificationDate=1556896210000&api=v2}$ Figure 2: Layout of components on the optical table.

For simplicity we can break the whole setup down in to three parts based on function – a photon source, and two separate experiments. Let us look at each part and describe the components within each section.

The left side of the optical table contains our photon source. (See Fig. 3.) Light from a 20 mW 405 nm laser diode (called the pump beam) is reflected off of two mirrors so that it passes through a beta barium borate (BBO) crystal which is mounted on a rotation stage. Most of the photons in the pump beam pass through the BBO crystal unaffected. However, about 1 out of 106 pump photons will excite the BBO crystal in such a way that when the crystal deexcites, a pair of entangled photons are emitted. This process is referred to as spontaneous parametric down-conversion; the photons emitted have correlated polarizations and together have a total momentum and energy equal to that of the incident photon (as required by conservation laws).

Some of these down-converted photon pairs will be of equal energy (meaning each photon has half the energy of the pump photon) and will therefore emerge with identical angles relative to the pump beam (as required by momentum conservation). We will refer to one of these down-converted photons as the idler photon and the other as the signal photon. (Because the photons are always produced in pairs, we can, for example, use the detection of an idler photon as an indication that a signal photon was simultaneously created… or vice versa.)

In our experimental configuration, the pump beam and BBO crystal have been oriented to create down-converted photons that are vertically-polarized with wavelengths of 810 nm (i.e., half the energy of the 405 nm pump photons).

{ ${/download/attachments/211388203/WPD_layout_p1.png?version=1&modificationDate=1556896210000&api=v2}$ Figure 3: The photon source