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Flux Lattices Reformulated



Ian B. Spielman, Gediminas Juzeliunas


We theoretically explore the optical flux lattices produced for ultra-cold atoms subject to laser fields where both the atom-light coupling and the effective detuning are spatially periodic. We analyze the geometric vector potential and the magnetic flux it generates, as well as the accompanying geometric scalar potential. We show how to understand the gauge-dependent Aharonov-Bohm singularities in the vector potential, and calculate the continuous magnetic flux through the elementary cell in terms of these singularities. The analysis is illustrated with a square optical flux lattice. We conclude with an explicit laser configuration yielding such a lattice using a set of five properly chosen beams with two counterpropagating pairs (one along the x axes and the other y axes), together with a single beam along the z axis. We show that this lattice is not phase-stable, and identify the one phase-difference that affects the magnetic flux. Thus armed with realistic laser setup, we directly compute the Chern number of the lowest Bloch band to identify the region where the non-zero magnetic flux produces a topologically non-trivial band structure.
New Journal of Physics


artificial gauge fields, spin orbit coupling, topological insulators, ultracold atoms


Spielman, I. and Juzeliunas, G. (2012), Flux Lattices Reformulated, New Journal of Physics, [online], (Accessed May 29, 2024)


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Created December 12, 2012, Updated February 19, 2017