Feasibility of hollow core fiber based optical lattice clock

The possibility of building the optical lattice clock based on the narrow $^1S_0$-$^3P_0$ transition in Hg and other alkaline-earth like atoms optically trapped inside the hollow core fiber has been studied. The general form of the long range atom-surface interaction potential at non-zero temperatures has been calculated for the hollow capillary geometry. The resulting $^1S_0$-$^3P_0$ transition frequency shift has been calculated for Sr and Hg atoms as a function of their position inside the capillary. Its dependence on the geometric parameters and optical properties of the capillary material has been analyzed. The resonant enhancement of the atom-surface interaction potential and radiative decay rate of the $^3P_0$ state at certain parameters of the waveguide has been studied. For the silica capillary with inner radius $R_{in}>15$ $\mu m$ and thickness $d\sim 1$ $\mu m$ the atom surface interaction induced $^1S_0$-$^3P_0$ transition frequency shift on the capillary axis can be suppressed down to the level $\delta \nu/\nu<10^{-18}$. The additional frequency shifts and atom loss from the optical trap due to the residual birefringence of the waveguide and collisions with the buffer gas molecules have been evaluated.