We present a prospective experimental study on double-resonance Ramsey spectroscopy in a micro fabricated Rb vapor cell, in view of future miniature atomic clocks with improved stability performance. Ramsey signals with a narrow central fringe width of 1.5 kHz combined with a competitive contrast of > 5 % are observed, resulting in a clock short-term stability of ≈ 1×10-11τ−1/2. The employed pulsed optical pumping (POP) scheme bears promise for reduced light-shift effects and thus for improved clock stability on medium- to long-term timescales.
We present a prospective experimental study on double-resonance Ramsey spectroscopy in a micro fabricated Rb vapor cell, in view of future miniature atomic clocks with improved stability performance. Ramsey signals with a narrow central fringe width of 1.5 kHz combined with a competitive contrast of > 5 % are observed, resulting in a clock short-term stability of ≈ 1×10-11τ−1/2. The employed pulsed optical pumping (POP) scheme bears promise for reduced light-shift effects and thus for improved clock stability on medium- to long-term timescales.
We demonstrate and study a microcell microwave atomic clock based on optical-microwave double resonance (DR) interrogation operated in a pulsed Ramsey scheme, called the \ensuremath{\mu}POP clock, based on a microfabricated Rb vapor cell and a micro-loop-gap microwave resonator. For the mm-scale dimensions of this cell, the population and coherence relaxation rates of the Rb clock transition are on the order of 4--5 kHz, which puts constraints on the useful Ramsey times and overall pulse sequence in view of optimized clock performance. Our proof-of-principle demonstration of the \ensuremath{\mu}POP clock shows that the pulsed DR approach is nevertheless feasible and results in a short-term clock stability of 1 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11}$ \ensuremath{\tau}${}^{\ensuremath{-}1/2}$ and reaching the \ensuremath{\le}2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}12}$ level at timescales of 1000 s to one day. The short-term instability budget established for the \ensuremath{\mu}POP clock shows that the main limitation to the short-term stability arises from the detection noise. Thanks to the pulsed Ramsey scheme, light-shift effects are strongly reduced in the \ensuremath{\mu}POP clock, which opens perspectives for further improvements of long-term clock stability, in view of future generations of miniature vapor-cell clocks with enhanced performances based on the DR scheme.
This thesis presents results on two microwave, double-resonance, Rubidium 87 atomic clocks. These studies are motivated by the need for compact and miniature clocks with improved performances or improved Size,Weight and Power (SWaP). A first clock study, covered in chapter 3, focuses on the μPOP clock, the first demonstration of Double Resonance (DR) Ramsey operation in a micro-manufactured hot-vapor cell clock.With a short-termstability of σy(τ ) ≤ 2 × 10−11τ−1/2 and long-termstability of 1.5 × 10−12 at one day, the μPOP clock features state-of-the-art stability for microwave miniature cell clocks. As demonstrated in [1], the μPOP clock short-term stability has been optimized to mitigate the Dick effect and laser Relative Intensity Noise (RIN) contributions, with the latter being the biggest contributor to the short-termstability. The long-terminstability budget shows that the intensity and frequency light shifts contributions are one and two order of magnitudes lower than the measured stability with a contribution of the order of 10−13 and 10−14 at one day, respectively. This confirms the interest of the Pulsed Optically Pumped (POP) approach compared to the ContinuousWave (CW) scheme and sets the potential performances of the μPOP clock. Other long-termcontributors to the instabilities have been evaluated. In the upper limit, the contribution of the cell-temperature shift to the instability is estimated to be two orders of magnitude below the measured stability, confirming the benefit of the N2 and Ar buffer gas-mixture approach for a close to zero cell-temperature sensitivity coefficient. The last two effects, the microwave-power and the position shifts are the greatest contributor to the mid and long-termstability with the latter being the limiting long-term phenomenon whose contribution must be carefully evaluated using the Groslambert covariance. The μPOP studies conclude with the description of a fast and reliable method for measuring the relaxation rates in Ramsey DR vapor-cell clocks. At the nominal cell temperature, namely ≈ 100◦C, the population and coherence relaxations rates are measured to be at the order of 5 kHz and 4 kHz, respectively. Their values have been measured down to 60◦C with both at the order of 1 kHz. Finally, a theoretical model using only parameters taken from the literature has been derived to describe the measured relaxation rates values with agreement within 20%. Chapter 4 focuses on the simulation and realization of a microwave cavity for a DR cold-atom clock using a GratingMagneto-Optical Trap (GMOT). The final cavity shows a low quality factor of Q ≈ 360 which is in the interest of reducing the cavity-pulling shift. The TE011-like cavity mode is separated by at least 500 MHz from the neighbouring modes as predicted by the simulations. The same simulations allowed to effectively predict the cavity’s resonance frequency with a small error of 60 MHz which can easily be compensated by the cavity frequency tuning mechanism. The expected simulated excellent properties of the resonance mode in termof microwave field uniformity and homogeneity are confirmed by measurement of the field field orientation factor of 97% and low Rabi oscillation damping, respectively. Chapter 5 focuses on the integration of the microwave cavity in a clock setup designed by Erling Riis group from the university of Strathclyde. The clock described in this chapter is the first realization of a DR Ramsey Rb cold-atom clock using a GMOT for cooling and trapping which reduces the clock footprint. In practise, ≈ 106 atoms at ≈ 10 μK are loaded thanks to the grating. Ramsey fringes were successfully obtained with Ramsey times up to 20 ms, limited by the clock geometric design. The clock implements state-selection that allows for increased Signal-to-Noise Ratio (SNR) and better short-term stability of ≈ 1.5 × 10−11τ−1/2. This stability is well-explained by SNR of the fringes. Long-term stability is dominated by the 2nd-order Zeeman shift contribution as the clock is not magnetically shielded. The two studies presented in this thesis, namely the μPOP and cold-atom clocks, pave the way towards more miniature and compact frequency standards, respectively. Further improvements of the former would yield a intensity light shift limited clock with ≈ 10−13 stability at one day. Further version of the latter clock using the cavity as standalone vacuum system would allow for reduced SWaP cold-atom frequency standards.
We demonstrate a high-performance coherent-population-trapping (CPT) Cs vapor cell atomic clock using the push-pull optical pumping technique in the pulsed regime, allowing the detection of high-contrast and narrow Ramsey-CPT fringes. The impact of several experimental parameters onto the clock resonance and short-term fractional frequency stability, including the laser power, the cell temperature, and the Ramsey sequence parameters, has been investigated. We observe and explain the existence of a slight dependence on laser power of the central Ramsey-CPT fringe line-width in the pulsed regime. We report also that the central fringe line-width is commonly narrower than the expected Ramsey line-width given by 1/(2TR), with TR the free-evolution time, for short values of TR. The clock demonstrates a short-term fractional frequency stability at the level of 2.3×10−13 τ−1/2 up to 100 s averaging time, mainly limited by the laser amplitude modulation noise. Comparable performances are obtained in the conventional continuous wave regime, with the use of an additional laser power stabilization setup. The pulsed interaction allows to reduce significantly the clock frequency sensitivity to laser power variations, especially for high values of TR. This pulsed CPT clock, ranking among the best microwave vapor cell atomic frequency standards, could find applications in telecommunication, instrumentation, defense or satellite-based navigation systems.
We present our microwave spectroscopic studies on laser-microwave double-resonance (DR) signals obtained from a micro-fabricated Rb vapor cell.This study focuses on the characteristics and systematic shifts of the ground-state 'clock transition' in 87 Rb (|F g = 1, m F = 0 →| F g = 2, m F = 0 ) used in Rb atomic clocks, and represents a first step toward a miniature atomic clock based on the DR scheme.A short-term clock instability below 2 × 10 11 τ -1/2 is demonstrated, staying below 10 -11 up to τ = 10 4 s.
We report our investigations on a compact high-performance rubidium (Rb) vapourcell clock based on microwave-optical double-resonance (DR).These studies are done in both DR continuous-wave (CW) and Ramsey schemes using the same Physics Package (PP), with the same Rb vapour cell and a magnetron-type cavity with only 45 cm 3 external volume.In the CW-DR scheme, we demonstrate a DR signal with a contrast of 26% and a linewidth of 334 Hz; in Ramsey-DR mode Ramsey signals with higher contrast up to 35% and a linewidth of 160 Hz have been demonstrated.Short-term stabilities of 1.4×10 -13 τ -1/2 and 2.4×10 -13 τ -1/2 are measured for CW-DR and Ramsey-DR schemes, respectively.In the Ramsey-DR operation, thanks to the separation of light and microwave interactions in time, the light-shift effect has been suppressed which allows improving the long-term clock stability as compared to CW-DR operation.Implementations in miniature atomic clocks are considered. IntroductionSince the first invention of lamp-pumped rubidium (Rb) clocks in the 1960's [1,2], the demand for a stable, reliable, and compact Rb frequency standard with low power consumption has been growing, for various applications fields such as industry, telecommunication, navigation, space applications (e.g.GPS [3], GALILEO [4] and COMPASS [5]).Recently, thanks to the semiconductor laser technology, laser-pumped Rb clocks have been considered in several studies, for their better optical pumping efficiency results in short-term frequency stabilities at least one order of magnitude better than their lamp-pumped counterparts [6][7][8][9].This opened up also several new schemes for vapour-cell atomic clocks, such as the continuous-wave (CW) Rb clock [9], coherent population trapping (CPT) Cs clock [10] and pulsed optical pumping (POP) Rb clock [11].In this paper we report our studies on high-performance Rb frequency standards based on the laser-microwave double-resonance (DR) scheme, using both CW and Ramsey interrogation.Both CW-DR and Ramsey-DR schemes require two resonant electromagnetic fields of light and microwave.In the case of CW-DR, the laser optically pumps the vapour of the Rb atoms by creating a polarization of the atomic ground-state; simultaneously the microwave field, generated from a quartz oscillator and is near-resonant with the 87 Rb hyperfine clock transition (energy levels 5 2 S 1/2 │F g =1, m F =0˃ ↔│F g =2, m F =0˃), is applied.The opacity of the Rb vapour to the transmitted light signal as a function of microwave frequency is a measure of the atomic ground state polarization known as CW-DR signal [9].In CW-DR, the steps of optical pumping, microwave interrogation and optical detection are applied simultaneously (figure 1(b)).In the case of Ramsey-DR, these three sequences are separated in time, see figure 1(c): first, during optical pumping a strong laser pulse creates a significant atom population imbalance between
In this paper we report the results we obtained with a prototype of pulsed optically pumped (POP) Rb clock. In terms of frequency stability, an Allan deviation σy(τ)=1.7 ×10-13τ-1/2has been measured, where τ is the integration time. In addition, the long term frequency drift results below 10-14/day. In the paper we also describe a technique to stabilize the amplitude of the microwave signal using the atoms themselves as discriminator. Moreover, an anomalously large temperature sensitivity of the clock frequency and a technique to keep it under control are also reported. Finally, we describe some non linear effects that modify the shape of the clock signal represented by the Ramsey central fringe.