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We investigate the dispersive Casimir-Polder interaction between a Rubidiumatom and a suspended graphene sheet subjected to an external magnetic field B.We demonstrate that this concrete physical system allows for an unprecedentedcontrol of dispersive interactions at micro and nanoscales. Indeed, we showthat the application of an external magnetic field can induce a 80% reductionof the Casimir-Polder energy relative to its value without the field. We alsoshow that sharp discontinuities emerge in the Casimir-Polder interaction energyfor certain values of the applied magnetic field at low temperatures. Moreover,for sufficiently large distances these discontinuities show up as aplateau-like pattern with a quantized Casimir-Polder interaction energy, in aphenomenon that can be explained in terms of the quantum Hall effect. Inaddition, we point out the importance of thermal effects in the Casimir-Polderinteraction, which we show that must be taken into account even forconsiderably short distances. In this case, the discontinuities in theatom-graphene dispersive interaction do not occur, which by no means preventsthe tuning of the interaction in ~50% by the application of the externalmagnetic field.

Tuning quantum fluctuations with an external magnetic field: Casimir-Polder interaction between an atom and a graphene sheet