  In this paper, we report on numerical calculations of the spontaneous
emission rates and Lamb shifts of a $^{87}\text{Rb}$ atom in a Rydberg-excited
state $\left(n\leq30\right)$ located close to a silica optical nanofiber. We
investigate how these quantities depend on the fiber's radius, the distance of
the atom to the fiber, the direction of the atomic angular momentum
polarization as well as the different atomic quantum numbers. We also study the
contribution of quadrupolar transitions, which may be substantial for highly
polarizable Rydberg states. Our calculations are performed in the macroscopic
quantum electrodynamics formalism, based on the dyadic Green's function method.
This allows us to take dispersive and absorptive characteristics of silica into
account; this is of major importance since Rydberg atoms emit along many
different transitions whose frequencies cover a wide range of the
electromagnetic spectrum. Our work is an important initial step towards
building a Rydberg atom-nanofiber interface for quantum optics and quantum
information purposes.
