We demonstrate a high-performance pulsed optically pumped (POP) Rb vapor-cell clock based on a magnetron-type microwave cavity of only 44 cm 3 external volume. Using optical detection, an unprecedented 35% contrast of the Ramsey signal has been obtained. Both the signal-to-noise ratio (of 30 000) and the estimated shot-noise limit of 1.7 Â 10 À14 s À1/2 are at the same level as those found with a bigger cylindrical TE 011 cavity (100 cm 3 inner volume) and are sufficient for achieving excellent clock stability. Rabi oscillations are measured and indicate a sufficiently uniform microwave magnetic field distribution inside the cavity. The instability sources for the POP clock's performance are analyzed. A short-term stability of 2.1 Â 10 À13 s À1/2 is demonstrated which is consistent with the noise budget.

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Long-term frequency instabilities in vapor-cell clocks mainly arise from fluctuations of the experimental and environmental parameters that are converted to clock frequency fluctuations via various physical processes. Here, we discuss the frequency sensitivities and the resulting stability limitations at one-day timescale for a rubidium vapor-cell clock based on a compact magnetron-type cavity operated in air (no vacuum environment). Under ambient laboratory conditions, the external atmospheric pressure fluctuations may dominantly limit the clock stability via the barometric effect. We establish a complete long-term instability budget for our clock operated under stable pressure conditions. Where possible, the fluctuations of experimental parameters are measured via the atomic response. The measured clock instability of <2 × 10 −14 at one day is limited by the intensity light-shift effect, which could further be reduced by active stabilization of the laser intensity or stronger optical pumping. The analyses reported here show the way toward simple, compact, and low-power vapor-cell atomic clocks with excellent long-term stabilities ≤10 −14 at one day when operated in ambient laboratory conditions.

We numerically and experimentally evaluate the impact of the inhomogeneity of the microwave field in the cavity used to perform double-resonance (DR) Ramsey spectroscopy in a buffer gas alkali vapour cell. The Ramsey spectrum is numerically simulated using a simple theoretical model and taking into account the field distribution in a magnetron-type microwave resonator. An experimental evaluation is performed using a DR pulsed optically pumped (POP) atomic clock. It is shown that the sensitivity to the microwave power of the DR POP clock can be reproduced from the combination of two inhomogeneities across the vapour cell: microwave field inhomogeneity and atomic ground-state resonance frequency inhomogeneity. Finally, we present the existence of an optimum operation point for which the microwave power sensitivity of our DR POP clock is reduced by two orders of magnitude. It leads into a long-term frequency stability of 1 ´ 10 -14 .

We report on the development of a compact laserpumped Rb clock based on the pulsed optical pumping (POP) technique, in view of future industrial applications. The clock Physics Package (PP) is based on a compact magnetron-type microwave cavity of 45 cm 3 volume, and our current clock PP has a volume of only 0.8 liters, including temperature control and magnetic shields. This clock PP is completed by a newlydeveloped frequency-stabilized laser head of 2.5 liters overall volume, with an acoustic optical modulator (AOM) integrated within the laser head for switching the laser output power. Due to the highly uniform magnetic field inside the microwave cavity, Ramsey signals with high contrast of up to 35% and with a linewidth of 160 Hz have been demonstrated. A typical shortterm clock stability of 2.4×10 -13 τ -1/2 is measured. Thanks to the pulsed operation, the light-shift effect has been considerably suppressed as compared to previously demonstrated continuouswave (CW) clock operation using the same clock PP, which is expected to enable improved long-term clock stabilities down to the 10 -14 level or better.

are relevant. Our ODSE method is inspired by classical nuclear magnetic resonance spin-echo method, combined with optical detection. In contrast to other existing methods, like continuous-wave double-resonance (CW-DR) and Ramsey-DR, principles of the ODSE method allow suppression of decoherence arising from the inhomogeneity of the static magnetic field across the vapor cell, thus enabling measurements of intrinsic relaxation rates, as properties of the cell alone. Our experimental result for the coherence relaxation time, specific for the clock transition, measured with the ODSE method is in good agreement with the theoretical prediction, and the ODSE results are validated by comparison to those obtained with Franzen, CW-DR and Ramsey-DR methods. The method is of interest for a wide variety of quantum optics experiments with optical signal readout.

In today's state of the art compact vapour-cell atomic clocks relying on the pulsed Ramsey-type interrogation, optical detection noise is a major limitation to the achievable short-term stability. In this communication the influence of the optical detection time on the clock's short-term stability is investigated and a new analytical expression is developed to precisely predict the stability performance, taking into account the details of the optical detection phase of a Ramsey-type atomic clock. The theory is in good agreement with the experimental results. It is applied for evaluating the clock's shot-noise limit.

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