A laboratory prototype of a compact quantum frequency standard based on a rubidium vapour cell with pulsed laser pumping is developed. With significantly smaller overall dimensions (a volume of ∼10 L and a mass of ∼10 kg), the frequency standard is expected to have the short-term instability comparable with that of the commercial passive hydrogen masers and even the laboratory fountain-type atomic clocks based on cold atoms. The advantages of the technique of pulsed optical pumping and pulsed excitation of microwave resonances over the traditional techniques of double radio-optical resonance detection are substantiated. The results of the experimental study of pulsed optical pumping of a rubidium cell with a mixture of buffer Ar – Ne gases implemented at the VNIIFTRI are presented, the Ramsey resonances are obtained, and the process of optimising the contrast of the central resonance peak is described.
A laboratory prototype of a compact quantum frequency standard based on a rubidium vapour cell with pulsed laser pumping is developed. With significantly smaller overall dimensions (a volume of ∼10 L and a mass of ∼10 kg), the frequency standard is expected to have the short-term instability comparable with that of the commercial passive hydrogen masers and even the laboratory fountain-type atomic clocks based on cold atoms. The advantages of the technique of pulsed optical pumping and pulsed excitation of microwave resonances over the traditional techniques of double radio-optical resonance detection are substantiated. The results of the experimental study of pulsed optical pumping of a rubidium cell with a mixture of buffer Ar – Ne gases implemented at the VNIIFTRI are presented, the Ramsey resonances are obtained, and the process of optimising the contrast of the central resonance peak is described.
We report the results of experimental investigation of the Raman – Ramsey method of pulsed excitation of coherent population trapping (CPT) resonances in a rubidium vapour cell filled with a mixture of Ar and Ne buffer gases. For the development of compact quantum microwave frequency standards, this method is an alternative to the pulsed optical pumping method recently implemented using the same rubidium cell. Both methods have advantages over the traditional double radio-optical resonance technique, the main of which is the substantial suppression of the light shift of the clock transition frequency, since the evolution of the coherence of atomic states forming the clock transition occurs in the absence of laser radiation in the cell. The narrow (110 – 240 Hz) Raman – Ramsey resonances are obtained using the scheme of pulsed excitation of CPT resonances on the D 1 lines of the 87 Rb atom with the same linear (lin||lin) polarisations of the bichromatic laser radiation components. The process of optimising the central fringe linewidth, its contrast, and the linewidth-to-contrast ratio is described. The magnetic dependence of the Raman – Ramsey line central fringe linewidth is experimentally investigated.
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
The pulsed optically pumped(POP) 87Rb vapor-cell frequency standard was studied based on the detection of free induction microwave signal or optical absorption signal.In POP operation the pumping,interrogation,and detection phases are separated in time,avoiding the coupling between microwave and optical coherence.The theoretical results show that an oscillation period doubled with respect to the classical Ramsey method which leads to a doubled atomic quality factor Q,and the reduction of optical shift and cavity pulling shift will be obtained,when the atoms are submitted to π/2 Ramsey microwave pulse.In experiment Ramsey fringes were obtained with a clock prototype based on 87Rb in buffer gas,with bandwidth of 65 Hz and 150 Hz for microwave and optical signal respectively.The frequency stability achieved was 1.2×10-12 for measurement times up to 100 s.
In this paper we report a laboratory prototype of pulsed optically pumped (POP) rubidium frequency standard. In POP operation the pumping, interrogation, and detection phases are separated in time, avoiding the coupling between microwave and optical coherence. The POP87Rb vapor-cell frequency standard was studied experimentally based on the detection of free induction microwave signal or optical absorption signal. Ramsey fringes were obtained based on87Rb in buffer gas, with FWHM of 65Hz and 150Hz for microwave and optical central Ramsey fringes respectively. The atomic quality factor was on the order of 108. With microwave detection, the achieved frequency stability was 1.2×10-12τ-1/2(τ=1~100s).
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 present a multilevel theoretical approach to describe the behavior of a pulsed optically pumped (POP) 87Rb 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 $1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$ 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 ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})\ensuremath{\approx}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}{\ensuremath{\tau}}^{\ensuremath{-}1∕2}$ is foreseen. This value can be degraded by microwave phase noise and laser fluctuations so that the overall predicted clock stability is ${\ensuremath{\sigma}}_{y}(\ensuremath{\tau})\ensuremath{\approx}1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}{\ensuremath{\tau}}^{\ensuremath{-}1∕2}$.