Casimir-Polder interaction of fullerene molecules with surfaces

We calculate the thermal Casimir-Polder potential of ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ fullerene molecules near gold and silicon nitride surfaces, motivated by their relevance for molecular matter-wave interference experiments. We obtain the coefficients governing the asymptotic power laws of the interaction in the thermal, retarded, and nonretarded distance regimes and evaluate the full potential numerically. The interaction is found to be dominated by electronic transitions and hence independent of the internal temperature of the molecules. The contributions from phonon transitions, which are affected by the molecular temperature, give rise to only a small correction. Moreover, we find that the sizable molecular line widths of thermal fullerenes may modify the nonretarded interaction, depending on the model used. Detailed measurements of the nonretarded potential of fullerene thus allow one to distinguish between different theories of incorporating damping.

Figure 1

Nine-oscillator fit (solid line) to the spectroscopic data (dashed line) of the permittivity of a thin ${\mathrm{C}}_{60}$ film.

Figure 2

Seven-oscillator fit (solid line) to the spectroscopic data (dashed line) of the permittivity of a thin ${\mathrm{C}}_{70}$ film.

Figure 3

Four-parameter semiquantum model fit (solid line) to the spectroscopic data (dashed line) of the permittivity ${\mathrm{Si}}_3{\mathrm{N}}_4$.

Figure 4

Dependence of the retarded CP coefficient $C_4$ of ${\mathrm{C}}_{60}$ on the static permittivity.

Figure 5

CP potential of ${\mathrm{C}}_{60}$ in front of an Au surface at room temperature and its asymptotes.

Figure 6

CP potential of ${\mathrm{C}}_{60}$ in front of an Au surface at different temperatures.

Figure 7

Comparison of the CP potentials of ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ in front of gold and silicon nitride surfaces at room temperature.

Figure 8

Comparison of the CP potentials of fullerene in front of ${\mathrm{Si}}_3{\mathrm{N}}_4$ and ${\mathrm{SiN}}_x$ surfaces at room temperature, normalized with respect to the corresponding Au potentials.