Feasibility of the optical fiber clock

We explore the feasibility of a compact high-precision Hg atomic clock based on a hollow core optical fiber. We evaluate the sensitivity of the ${}^1{S}_0$-${}^3{P}_0$ clock transition in Hg and other divalent atoms to the fiber inner core surface at non-zero temperatures. The Casimir-Polder interaction induced ${}^1{S}_0$-${}^3{P}_0$ transition frequency shift is calculated for the atom inside the hollow capillary as a function of atomic position, capillary material, and geometric parameters. For ${}^{199}\mathrm{H}\mathrm{g}$ atoms on the axis of a silica capillary with inner radius $\ge 15\mu \mathrm{m}$ and optimally chosen thickness $d\sim 1\mu \mathrm{m}$, the atom-surface interaction induced ${}^1{S}_0$-${}^3{P}_0$ clock transition frequency shift can be kept on the level $\delta \nu \mathrm{/}{\nu }_{\mathrm{H}\mathrm{g}}\sim {10}^{-19}$. We also estimate the atom loss and heating due to the collisions with the buffer gas, lattice intensity noise induced heating, spontaneous photon scattering, and residual birefringence induced frequency shifts.