Wave-particle duality of light for the classroom

A. Weis1 and T. L. Dimitrova1,2
1 Physics Department, University of Fribourg, Fribourg, Switzerland
2 University of Plovdiv "Paissi Hilendarski", Plovdiv, Bulgaria


Two-beam interference

The double slit – one of the simplest optical components – has played, and continues to play a role of outmost importance in the discussion of the borderline between classical and quantum physics. There is probably no single person with a Master’s degree in physics who has not heard (or read) about Feynman’s beautiful discussion of the double slit experiment performed with individual particles. It is well accepted that the interference pattern from a double slit, used by Thomas Young and others in the 19th century to "demonstrate" the wave nature of light, is the result of the superposition of many individual events, in each of which the "photon interferes with itself", in the phrasing of P. A. M. Dirac. Very few, however, are the people who have actually seen (or, even less, heard) this experiment as a real presentation.

Single electron interference

Experimental pictures illustrating how a smooth (classical) interference pattern arises from single particle events when single electrons are made to interfere have been recorded by several scientists, of which the recording by Tonomura et al. [1] is the most well known. We recall that Feynman also used electron interference in his textbook discussion. In 2002 the double slit experiment with single electrons was chosen in a reader poll of Physics World as the "most beautiful experiment in physics" [2]. However, beautiful as such experiments may be, the apparatus used is a "black box", that hardly gives any didactical insights in a public or lecture demonstration. It thus leaves (or confirms) the impression that quantum mechanics happens at a small, i.e., invisible scale, and that it has no macroscopic implementation.

Figure 1. Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, and 500’000 frames.

Single photon interference with a CCD camera

In 2003, A. Weis and R. Wynands at the University of Bonn (Germany) designed a lecture demonstration experiment of single photon interference from a double slit [3]. Light from a laser pointer was so strongly attenuated that at each instant there was only a single photon between the double slit and the detector. The diffracted light was recorded by a single photon imaging camera consisting of an image intensifier (multichannel plate, MCP) followed by phosphor screen and a CCD camera. When adding consecutive camera frames one sees the gradual appearance of the smooth classical interference pattern (Fig. 1). This demonstration thus nicely illustrates the continuous transition from the quantum picture of light to its wave interpretation. In 2005 one of us (A.W.) improved this experiment by using a camera with a higher pixel resolution [4]. The pictures of Fig. 1 were recorded with that improved system.

Single photon interference with a Mach-Zehnder interferometer

This beautiful experiment has the drawback that the camera used costs more than 20’000 EUR. It also has the danger that a younger student may not be so astonished about it, since he may believe that a single photon may easily "slip" through both slits whose separation can barely be seen by the unaided eye. In 2007 T. Dimitrova and A. Weis have developed an alternative two-path interference experiment [4], by replacing the double slit with a Mach-Zehnder interferometer (MZI), and the CCD camera with a photomultiplier (PM). Fig. 2 illustrates the general layout of that experiment.

Figure 2. Mach-Zehnder interferometer operated with strong light (left) and with individual photons (right). BF: attenuating filters. A 5 mW green laser is used as primary light source.

The use of a MZI "opens" the black box and allows the visualization of the interfering paths. The macroscopic spatial separation of the beams is well visible and allows easy manipulations of the light in the two paths, such as the selective blocking of one path, the selective change of one path length, or the insertion of which-path labeling polarizers. Conventionally the wave nature of light is presented by projecting the interference pattern on a screen (projection mode). Alternatively, one may displace one of the MZI mirrors by a piezo-transducer (Figure 2, left) driven by a periodic voltage ramp (scanning mode). In this way the path length difference of the two MZI arms undergoes a periodic change whose effect can be recorded by a photodiode with a small aperture (bottom trace of Fig 3). The interference pattern thus appears as a sinusoidal variation of the photocurrent displayed on an oscilloscope.

For experiments with individual photons (Figure 2, right) we insert strongly attenuating filters at the entrance of the MZI. The exiting light is registered by a single photon detecting photomultiplier (PM) equipped with a collimator and filters that suppress stray light sufficiently to perform the demonstration in daylight environment. The PM pulses are sent to an oscilloscope and to a loudspeaker so that single photon events can both be seen and heard. In the scanning mode the oscilloscope display of single photon events looks random. However, when many oscilloscope traces are averaged (top traces of Fig. 3), individual pulses pile up to yield the smooth sinusoidal modulation that is typical for waves. The transition from the observation of individual particles (photons) to the typical intensity distribution of interfering waves corresponds to the observation in the CCD camera experiment (Fig. 1).

The demonstration thus shows, in a single experiment that the wave-particle duality is an inherent property of light. Both the particle and the wave nature are seen simultaneously and independently from the experimental conditions. It also illustrates that the wave aspect is related to the propagation of light, while the particle aspect is connected to its detection.

Figure 3. Digital oscilloscope traces of PM pulses produced by single photons (blue) from the MZI in scanning mode. The top trace is a single trace, and below are averages of 4, 16, 64, and 128 traces, respectively. As more and more traces are accumulated, the particle aspect reduces to shot noise on a classical interference pattern. Bottom trace (red): classical interference fringes from strong light recorded by a photodiode.

Figure 4. Demonstration that each photon interferes with itself. Left: a small background photon rate is observed when the photons have a choice of two paths. The photon pulses are seen as wall projection of an oscilloscope trace. Right: the photon count rate increases when one path is blocked, thereby forcing the photons to follow a specific path.

The photon interferes with itself

The most astonishing fact that each photon "interferes with itself" can be shown in the following way. The PM is positioned (in projection mode) at an interference minimum, thus detecting only a few (background) photons (Fig. 4, left). When one of the two arms is blocked, the rate of detected photons is seen (and even more dramatically, heard) to increase (Fig. 4, right). This shows that when each photon is forced to follow a specific path (right), its probability to be detected is higher than when it is left with a choice of two possible paths (left). The photon thus seemingly knows, whether or not both paths are open, a demonstration of macroscopic delocalization.

Copies of the device presented here are currently operated as lecture demonstration experiments at the universities of Fribourg and Plovdiv, and at ETH-Zurich and EPF-Lausanne, while student laboratory versions are used at the University of Bonn and at EPF-Lausanne.

The authors thank the mechanical and electronics workshops of the Physics Department at the University of Fribourg for skillful help. A. W. acknowledges the assistance of G. Monney for setting up the interferometer and H. Vuillème for preparing the photographs of Fig. 4.



[1] Tonomura A., Endo J., Matsuda T., Kawasaki T., and Ezawa H., Demonstration of single-electron build-up of an interference pattern, Am. J. Phys. 57 (1989) 117.
[2] Crease R. P., The most beautiful experiment, Physics World, September 2002, p. 19 (http://physicsworld.com/cws/article/print/9746).
[3] Weis A. and Wynands R., Three demonstration experiments on the wave and particle nature of light, Physik und Didaktik, 1/2 (2003) 67.
[4] Dimitrova T. L. and Weis A., The wave–particle duality of light: a demonstration experiment, Am. J. Phys., 76 (2008) 137-142


The movie shows the diffraction of individual photon from a double slit recorded by a single photon imaging camera (image intensifier + CCD camera). The single particle events pile up to yield the familiar smooth diffraction pattern of light waves as more and more frames are superposed (Recording by A. Weis, University of Fribourg).



[Released: May 2009]