LMU
MPQ
Quantum Optics Group (LMU) - Quantum Many Body Systems Division (MPQ)

Aharonov-Bohm Interferometer

In this new Berry-flux Interferometer with ultracold neutral atoms (right), the Berry curvature of a lattice band structure plays the role of the magnetic field in the original Aharonov-Bohm interferometer (left).  Analogous to the original case,  the Berry flux enclosed by the interferometer loop gives rise to a measurable phase shift even if the curvature vanishes everywhere along the chosen path.

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Berry-flux Interferometer

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The Graphene-like Honeycomb lattice structure is created by three intersecting laser beams (arrows). The atoms are loaded into the minima (blue) of this potential landscape and can quantum-mechanically tunnel between them. One possible position is illustrated by the small sphere.

 

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The phase acquired in the Aharonov-Bohm effect is directly analogous to the concept of curvature in geometry. It can be visualized by following a moving vector on a surface. The vector moves such that it remains parallel to the surface and keeps its original angle with the tangent of the path taken (parallel transport).If the surface is flat (left), the vector will remain unchanged while travelling. In contrast, if the surface is curved—such as the surface of a sphere (right) —the vector will rotate while travelling and will not return to its initial direction. Its rotation angle after travelling along a closed loop is a direct measure of the curvature of the surface within the loop. In direct analogy to geometric phases, the rotation angle depends only on the chosen loop and the geometry of the surface, but not on the speed of the movement. Analogously, the state of a quantum system can pick up a geometric phase while completing a closed path in e.g. real space or momentum space, which depends on the enclosed Berry curvature.

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