16 January 2015 No More Fields

Scheme representation of the Aharonov-Bohm effect (Wikipedia)

Self accelerating particles self-induce Aharonov-Bohm phase: Review in Nature’s News and Views. Imagine a magnetic field that creates a solenoid and is surrounded by a region completely free of electromagnetic field. In classical physics if the electron moves in this free region, it does not experiment any type of magnetic force. In quantum physics, if the electron orbits around the solenoid, its wave function experiences a phase shift proportional to the flux of the magnetic field even though the field is zero in the region where the particle passes through. This effect, famously known as the Aharonov-Bohm effect – is a result of the fact that the wave function is a gauge dependent quantity (i.e. it depends on the electromagnetic vector potential, which is a non-unique, non-physical quantity). It is important to clarify, however, that the physics regarding this famous effect, i.e. the accumulated phase depends entirely on the magnetic field inside the solenoid. In fact, the Aharonov-Bohm effect is not restricted to Schrodinger equation describing non-relativistic electrons. The effect occurs essentially for other types of wave equations.

In the recent News & Views article entitled ‘Quantum mechanics: No more fields’ in Nature Physics, ICREA Professor at ICFO Maciej Lewenstein discusses a recent fascinating discovery from Moti Segev group at Technion, who find novel solutions of the Dirac wave equation, for which Aharonov-Bohm effect occurs in zero electromagnetic field. These solutions have shown to be shape-invariant solutions and describe self-accelerating electrons, or more generally spin-½ fermions. The self-acceleration of the particles lead to the accumulation of a phase, analogous to the Aharonov–Bohm effect, but in free space. So, just by preparing the initial wave packet in the appropriate form, one can obtain the corresponding phase that coincides with the free propagation state of the packet.

Prof Lewenstein speculates on the possible realization of this idea with ultracold atoms, as well as with the generalization of this concept to non-Abelian magnetic fields, commonly considered in gauge theories describing elementary particles, such as those depicted by the Standard Model.

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