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In 1959, Yakir Aharonov and David Bohm stated that a potential was itself a fundamental physical entity, and would affect a charged particle even in a region in which there was no magnetic field, and therefore no force acting on the charged particle. They proposed the following experiment to verify the existence of the effect. If a current is applied to a solenoid of infinite length, the magnetic field would not exist outside the solenoid, but there would be a vector potential. If one beam of electrons passåes on one side of the solenoid and another beam of electrons passes on the other side of the solenoid, the phase difference between the two beams would be proportional to the magnetic flux inside the solenoid, even though neither electron beam would be subjected to a magnetic field. This is referred to as the Aharonov-Bohm (AB) effect, and was the subject of many fierce debates since it related to a fundamental of physics. Those who accepted the AB effect insisted that vector potential physically influences electrons, while those argued against the existence of the AB effect claimed that vector potential was a mere mathematical entity.

Vector potential was used by James Clark Maxwell 150 years ago as a physical quantity to describe electromagnetism. However, vector potentials have soon been regarded only as a mathematical auxiliary which has no physical meaning but which is convenient for calculations. However, in the late 1970s, vector potential underwent a revival as the most fundamental physical quantity in unified theories of fundamental forces in Nature. Theories of gauge fields were regarded as the most likely candidate for unified theories that encompassed electromagnetism, weak and strong nuclear forces, and gravity. The simplest example of a gauge field is the vector potential in electromagnetism. The AB effect indicates that the gauge field is not merely a mathematical auxiliary but a real physical quantity which can produce an observable effect. This increased the significance of the AB effect.

In 1982, using a holography electron microscope Tonomura and his colleagues measured the phase difference in the form of interference fringes produced by two beams of electrons, one passing through the inside and the other passing through the outside of a doughnut-shaped ferromagnet. They clearly showed that there exists a phase difference between the two electrons beams passing through a space where there is no magnetic field, and that the extent of the phase difference precisely matches the predicted value. For this work, Tonomura received the Nishina Memorial Prize in 1982.

Soon after the publication, an objection was raised to this experiment: Since the electron beams contacted the magnet, i.e. there were leakage magnetic fields in space, this created the phase difference, so the experiment did not prove the existence of the AB effect. To settle this controversy, it was necessary to make a leak-free coil or a magnet with no magnetic leakage. To overcome this difficulty Tonomura and his colleagues resorted to a microfabrication technique developed to produce semiconductor devices.

In 1986, Tonomura and his colleagues fabricated a doughnut-shaped (toroidal) ferromagnet six micrometers in diameter (Fig. 1(a) and (b)), and covered it with a niobium superconductor to completely confine the magnetic field within the doughnut, in accordance with the Meissner effect. With the magnet maintained at 5 K, they measured the phase difference from the interference fringes between one electron beam passing though the hole in the doughnut and the other passing on the outside of the doughnut. The results are shown in Fig. 1(a). Interference fringes are displaced with just half a fringe of spacing inside and outside of the doughnut, indicating the existence of the AB effect. Although electrons pass through regions free of any electromagnetic field, an observable effect was produced due to the existence of vector potentials. In this way, the long dispute on the AB effect was brought to a close by this one picture.

Tonomura was awarded the Asahi Prize in 1987, the Japan Academy Prize and Imperial Prize in 1991, the Benjamin Franklin Medal in Physics in 1999 and selected as "Persons of Cultural Merits" in 2002.

Fig 1
Fig. 1

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