Quantum walk under artificial magnetic field

What is it about?

The article investigates the spreading and entanglement dynamics of a two dimensional discrete-time quantum walk if the walker gains phases analogue of the Peierls phases gained by a charged particle under a constant magnetic field moving in a discrete lattice.

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Why is it important?

The dynamics of the walk is significantly affected by the choice of the magnetic flux through the unit cell depending on whether it is a rational or irrational number, i.e., while a rational flux ratio results in the well-known ballistic spreading of the walk, an irrational one causes diffusive spreading. Moreover, the so-called "the most irrational number", the golden ratio, makes the walker dynamically localized around the origin. On the other hand, the asymptotic behavior of the coin-position entanglement vanishes for both rational and irrational flux ratios. Instead, one can obtain nearly maximally entangled states even for large step numbers.