Pulsed optically pumped 87Rb vapor cell frequency standard: A multilevel approach

We present a multilevel theoretical approach to describe the behavior of a pulsed optically pumped (POP) Rb-87 frequency standard based on a microwave cavity-vapor cell arrangement. The full Zeeman manifold of the ground-state hyperfine levels is then considered, and the dynamics induced among them by relaxation processes (buffer gas, spin exchange, and cell-walls collisions) is taken into account. The model includes as well the absorption of the pumping laser along the cell and the cavity feedback on the atoms; the effects related to a nonuniform excitation of the atomic sample are also discussed. Theoretical predictions are proven with a laboratory prototype of POP passive maser in which the clock transition is excited by means of the Ramsey technique. The agreement between theory and experiment is very satisfactory from both a quantitative and qualitative point of view, in terms of the shape of the Ramsey fringes, microwave power delivered by the atoms, and short-term frequency stability. In particular, a frequency stability of 1.2x10(-12) at one second has been measured, in very good agreement with the expected value. On this basis, the model has been extended to predict the short-term frequency stability of a POP frequency standard operating with optical detection. A shot-noise limited frequency stability (Allan deviation) of sigma(y)(tau)approximate to 3x10(-14)tau(-1/2) is foreseen. This value can be degraded by microwave phase noise and laser fluctuations so that the overall predicted clock stability is sigma(y)(tau)approximate to 1.5x10(-13)tau(-1/2).