# Wave and Particle: Light is Both!

Modern quantum physics emphasizes the wave-particle duality of light. This denotes the fact that light behaves as a wave or a particle depending on the circumstances. The question arises as to whether there is an experiment which illustrates both the wave and particle properties of light. This experiment does exist: the double-slit experiment using single particles of light. This will be described below.

The double-slit experiment is one of the simplest and most famous experiments in physics.

We obtain a basic understanding of the double-slit experiment by first looking at the example for water waves. Figure 1 shows how water waves spread out in circles from two points and how they overlap. Whenever a wave crest meets another wave crest this creates higher waves, whereas a wave crest which meets a wave trough results in the waves ceasing to exist.

Figure 1: Interference of water waves
Source: http://www.nonlinearstudies.at/images/gg_wasser_06.jpg

In Figure 1 the water waves may be produced, for example, by two rods which are periodically immersed into the water. Similarly, sea waves from the left could meet a barrier with gaps at the two positions from which the circular waves originate. This already creates a double-slit setup. Now we look at the right edge of the wave field in Figure 1 and imagine a wall there on which the waves dissipate their energy. We would see that depending on the wave height the water sprays up at different heights onto the wall. How high the spray reaches follows a quadratic rule: If one wave is double the height of another, the first wave sprays water up the wall four times as high as the second wave. The wave intensity therefore increases with the square of the wave height. We know of a similar rule from driving: If we double the speed, the braking distance becomes four times as long.

Figure 2 shows the double-slit experiment with light, whereby the light source is monochromatic. Both slits create circular light waves which overlap, as we already saw in the example with water. On the right side of Figure 2 there is a yellow curve which represents the intensity of the light when it hits a screen. Three typical characteristics of wave interference occur:

1. The highest light intensity on the screen is behind the middle section of the double slit which hides the view of the source.
2. There are areas on the screen which have a direct view of the source but no light hits this area.
3. There are more intensity maxima than there are slits.

Figure 2: Double-slit experiment with monochromatic light
Source: http://www.cobocards.com/pool/de/card/7puji0113/online-karteikarten-beugung-und-interferenz-am-doppelspalt/

### The double-slit experiment with single photons: In which the wave-particle duality becomes apparent

Every light source transmits a great number of light particles per unit of time. We see these as a constant flux of light. If we diminish the light source considerably, however, (which is not easy in practice) the light source will eventually stop giving light constantly and will start to flicker irregularly. We cannot see this with the naked eye but can use light amplifiers similar to night-vision equipment to observe it. If the light source is diminished still further it will only flare up briefly now and again and between these intervals it will remain dark for increasingly long periods. If the design of the light source is correct, each flash of light is a single photon – a light particle.

These single photons can be directed at a double slit as shown in Figure 2. Instead of a screen we will use a highly sensitive detector, similar to those used in modern digital cameras but considerably more sensitive. This detector will be applied with long exposure times, typically minutes or more. Before it was possible to carry out this experiment, most phyicists believed that single photons would not show any interference and that interference was a cumulative effect of many photons which all influence each other. Figure 3 shows the result of this experiment. It is important to remember that in this experiment there is only one single light particle at a time propagating through the test setup. No other light particles can influence this light particle on its way through the setup.

Figure 3: Double-slit experiment with single photons
Source: http://www.sps.ch/fr/articles/progresses/wave_particle_duality_of_light_for_the_classroom_13/

The top left image in Figure 3 is the result after a short exposure time, after around 100 photons have landed on the detector. Each dot of light represents one photon, which behaves as a particle here: it hits exactly one position – one detector pixel. If the wave property would dominate, each photon would be distributed over the whole detector surface, just as a sea wave does not hit the beach at one point only but over the whole length of the beach. The top left image shows that the photons are randomly distributed on the detector, whereby this is only valid with restrictions at longer exposure times, as we will see.

With increasing exposure time – in Figure 3 top middle and top right, and again from below left to below right – it becomes clear that the photons are landing at random positions but with a wave-like distribution of probability. A long exposure time with a high number of detected photons leads to the interference image which we know from a normal monochromatic light source at the double slit. Nature therefore behaves consistently. However, the question arises how this wave-like distributed probability of the positioning of the photons can be explained when there is only one particle at a time in the test setup.

The simplified explanation is that the photon behaves like a wave at the double slit, this wave passes through both slits and interferes with itself behind the double slit. If we describe the situation according to the Copenhagen interpretation of quantum mechanics, then it is not the photon which interferes – because there is no information about the existence and behavior of the photon between the source and detector. What interferes is the wave function of the photon, an abstract mathematical entity whose square of the absolute value determines the probability of landing on the different elements of the detector. At any rate, at the double slit there is wave-like behavior whereas the photon behaves like a particle at the detector. This means that the wave-particle duality of light can be clearly seen in this setup.

### The wave-particle duality at Anton Paar products

The wave-particle duality of light plays a major role at two Anton Paar products: Litesizer, which measures the particle size using the principle of dynamic light scattering, and SAXSpace, a small-angle X-ray scattering system. In both measuring instruments the incidental photons of the primary beam excite the loosely bonded electrons in the sample so that they resonate. As the excited electrons in the sample resonate coherently and transmit waves, these waves interfere with the incidental waves and create an interference pattern. The wave property of the photons comes to the fore. The detector detects the interference signal as single photons, so their particle property dominates again. The detector signal is used to determine the particle size and the structure of the samples in the nanometer range.

To conclude I refer to the video at the end of the given website in which you can follow the development of the results shown in Figure 3. If you click on the figure, the video starts: Wave particle duality of light for the classroom.