Tuning the Casimir-Polder interaction via magneto-optical effects in graphene

We investigate the dispersive Casimir–Polder interaction between a rubidium atom and a suspended graphene sheet subjected to an external magnetic field $\mathbf{B}$. We demonstrate that this concrete physical system allows for an unprecedented control of dispersive interactions at micro- and nanoscales. Indeed, we show that the application of an external magnetic field can induce an $80\%$ reduction in the Casimir–Polder energy relative to its value without the field. We also show that sharp discontinuities emerge in the Casimir–Polder interaction energy for certain values of the applied magnetic field at low temperatures. Moreover, for sufficiently large distances, these discontinuities show up as a plateau-like pattern with a quantized Casimir–Polder interaction energy, in a phenomenon that can be explained in terms of the quantum Hall effect. In addition, we point out the importance of thermal effects in the Casimir–Polder interaction, which we show must be taken into account even for considerably short distances. In this case, the discontinuities in the atom-graphene dispersive interaction do not occur, which by no means prevents the tuning of the interaction in $\sim 50\%$ by the application of the external magnetic field.

Figure 1

System of suspended graphene and an isotropic particle at a distance $z$, in presence of a static perpendicular magnetic field.

Figure 2

(a) The Casimir–Polder energy of a rubidium atom in front of a graphene sheet subjected to a magnetic field $B$ as a function of $B$ and distance $z$. (b), (c) The Casimir–Polder energy as a function of $B$ for two fixed distances: (b) $z=100$ nm, and (c) $z=1\mu \mathrm{m}$. In all plots ${\mu }_c=0.115$ eV, $T=4$ K, and we have normalized $U_4(z,B)$ by the energy in the absence of magnetic field, $U_4(z,0)$.

Figure 3

The left side shows the energy-momentum dispersion diagram of graphene in a magnetic field. The blue lines show the usual linear dispersion relation of graphene while the Landau levels brought forth by the introduction of $B$ are represented by the black dots. The long (short) vertical arrow shows the lowest energy interband (intraband) transition crossing the chemical potential (dot-dashed green line). The right side shows the Fermi–Dirac distribution at temperature $T$.

Figure 4

(a) The Casimir–Polder interaction energy $U_{300}(z,B)$ [normalized by $U_{300}(z,0)]$ between a rubidium atom and a graphene sheet as a function of both distance and external magnetic-field strength for $T=300$ K. (b) The Casimir–Polder energy [normalized by $U_0(z,0)]$ as a function of the mutual distance between atom and graphene sheet for $T=0$ K (solid line), $T=4$ K (dashed line), and $T=300$ K (dot-dashed line). In both panels (a) and (b) the graphene chemical potential is ${\mu }_c=0.115$ eV.