Zeeman optical pumping of $^{87}$Rb atoms in a hollow core photonic crystal fibre

Preparation of an atomic ensemble in a particular Zeeman state is a critical step of many protocols for implementing quantum sensors and quantum memories. These devices can also benefit from optical fibre integration. In this work we describe experimental results supported by a theoretical model of single-beam optical pumping of $^{87}$Rb atoms within a hollow-core photonic crystal fibre. The observed 50% population increase in the pumped F=2, m$_F$=2 Zeeman substate along with the depopulation of remaining Zeeman substates enabled us to achieve a 3 times improvement in the relative population of the m$_F$=2 substate within the F=2 manifold, with 60% of the F=2 population residing in the m$_F$=2 dark sublevel. Based on our theoretical model, we also propose methods to further improve the pumping efficiency in alkali-filled hollow-core fibres.