# Double-slit experiment

Quantum Measurement

You may be familiar with an experiment known as the " double-slit experiment," as it is often introduced at the beginning of quantum-mechanics textbooks. The experimental arrangement can be seen in Fig. 1. Electrons are emitted one by one from the source in the electron microscope. They pass through a device called the "electron biprism", which consists of two parallel plates and a fine filament at the center. The filament is thinner than 1 micron (1/1000 mm) in diameter. Electrons having passed through on both sides of the filament are detected one by one as particles at the detector. This detector was specially modified for electrons from the photon detector produced by Hamamatsu Photonics (PIAS). To our surprise, it could detect even a single electron with almost 100 % detection efficiency.

Fig. 1 Double-slit experiment with single electrons

Let's start the experiment and look at the monitor.

At the beginning of the experiment, we can see that bright spots begin to appear here and there at random positions (Fig. 2 (a) and (b)). These are electrons. Electrons are detected one by one as particles. As far as these micrographs show, you can be confident that electrons are particles. These electrons were accelerated to 50,000 V, and therefore the speed is about 40 % of the speed of the light, i. e., it is 120,000 km/second. These electrons can go around the earth three times in a second. So, they pass through a one-meter-long electron microscope in 1/100,000,000 of a second. It is all right to think that each electron is detected in an instant after it is emitted.

Interference fringes are produced only when two electrons pass through both sides of the electron biprism simultaneously. If there were two electrons in the microscope at the same time, such interference might happen. But this cannot occur, because there is no more than one electron in the microscope at one time, since only 10 electrons are emitted per second.

Please keep watching the experiment a little longer. When a large number of electrons is accumulated, something like regular fringes begin to appear in the perpendicular direction as Fig. 2(c) shows. Clear interference fringes can be seen in the last scene of the experiment after 20 minutes (Fig. 2(d)). It should also be noted that the fringes are made up of bright spots, each of which records the detection of an electron.

We have reached a mysterious conclusion. Although electrons were sent one by one, interference fringes could be observed. These interference fringes are formed only when

Fig. 2 Single electron events build up to from an interference pattern in the double-slit experiments.

electron waves pass through on both sides of the electron biprism at the same time but nothing other than this. Whenever electrons are observed, they are always detected as individual particles. When accumulated, however, interference fringes are formed. Please recall that at any one instant there was at most one electron in the microscope. We have reached a conclusion which is far from what our common sense tells us.