For the "Hopf bundle" $S^1{ ightarrow}S^{2n,1}{ ightarrow}mathbb{C}H^n$, horizontal lifts of simple closed curves are studied. Let ${gamma}$ be a piecewise smooth, simple closed curve on a complete totally geodesic surface $S$ in the base space. Then the holonomy displacement along ${gamma}$ is given by $$V({gamma})=e^{{lambda}A({gamma})i}$$ where $A({gamma})$ is the area of the region on the surface $S$ surrounded by ${gamma}$; ${lambda}=1/2$ or 0 depending on whether $S$ is a complex submanifold or not. We also carry out a similar investigation for the complex Heisenberg group $mathbb{R}{ ightarrow}mathcal{H}^{2n+1}{ ightarrow}mathbb{C}^n$.