Direction-dependent coupling between a nanofiber-guided light field and a two-level atom with an electric quadrupole transition

We study the directional dependence of the coupling between a nanofiber-guided light field and a two-level atom with an electric quadrupole transition. We examine the situation where the atom lies on the fiber transverse axis $x$, the quantization axis for the atomic internal states is the other orthogonal transverse axis $y$, the atomic upper and lower levels are the magnetic sublevels $M'$ and $M$ of hyperfine-structure levels of an alkali-metal atom, and the field is in a quasilinearly polarized fundamental guided mode HE$_{11}$ with the polarization $\xi=x$ or $y$. We find that the absolute value of the quadrupole Rabi frequency depends on the propagation direction of the light field in the cases of ($M'-M=\pm1$, $\xi=y$) and ($M'-M=\pm2$, $\xi=x$). We show that the directional dependence of the coupling leads to the directional dependence of spontaneous emission into guided modes. We find that the directional dependence of the atom-field coupling in the case of quadrupole transitions is not entirely due to spin-orbit coupling of light: there are some other contributions resulting from the gradient of the spatial phase factor of the field.