Design and realization of a low phase gradient microwave cavity for a continuous atomic fountain clock

Recently, microwave phase gradients were identified as the main source of uncertainty in the continuous fountain clock. Indeed, because of its particular geometry with two interaction zones, a dedicated research effort was necessary to reduce this effect. With the help of 3D finite element simulations and ultra-precise machining, we report here on the design and realization of a new kind of low phase gradient microwave cavity. The proposed geometry based on a ring waveguide of rectangular cross-section has a theoretical spatial phase variation of 30 μrad over the interaction zones, which corresponds to a predicted relative frequency shift below 10^-15.