We employ a three-level Bloch vector model to simulate Ramsey fringes of our Rb vapor-cell atomic clock. The residual inhomogeneity of the microwave magnetic field across the buffer-gas cell is a key ingredient for correctly modelling the behavior at high microwave powers (pulse area > π/2. We add to this model different position-dependent frequency shifts that arise from external fields, and we identify inhomogeneous light-shifts as the dominant contribution for reproducing the measured clock frequency shifts as a function of microwave power. Other frequency shifts give negligible contributions.
We employ a three-level Bloch vector model to simulate Ramsey fringes of our Rb vapor-cell atomic clock. The residual inhomogeneity of the microwave magnetic field across the buffer-gas cell is a key ingredient for correctly modelling the behavior at high microwave powers (pulse area > π/2. We add to this model different position-dependent frequency shifts that arise from external fields, and we identify inhomogeneous light-shifts as the dominant contribution for reproducing the measured clock frequency shifts as a function of microwave power. Other frequency shifts give negligible contributions.
We report on the experimental measurement of the dc and microwave magnetic field distributions inside a recently developed compact magnetron-type microwave cavity mounted inside the physics package of a high-performance vapor-cell atomic frequency standard. Images of the microwave field distribution with sub-100-μm lateral spatial resolution are obtained by pulsed optical-microwave Rabi measurements, using the Rb atoms inside the cell as field probes and detecting with a CCD camera. Asymmetries observed in the microwave field images can be attributed to the precise practical realization of the cavity and the Rb vapor cell. Similar spatially resolved images of the dc magnetic field distribution are obtained by Ramsey-type measurements. The T2relaxation time in the Rb vapor cell is found to be position dependent and correlates with the gradient of the dc magnetic field. The presented method is highly useful for experimental in situ characterization of dc magnetic fields and resonant microwave structures, for atomic clocks or other atom-based sensors and instrumentation.
In this paper we describe a few phenomena that may affect the linewidth and/or the line shape of Ramsey fringes observed in an alkali-metal vapor cell with buffer gas. Experiments are performed on a vapor-cell--microwave-cavity arrangement in which 87Rb atoms successively experience laser pumping preparation (through a D2 line), microwave interrogation with a couple of coherent pulses, and clock signal detection by means of laser absorption. We show that the linewidth of the Ramsey central fringe is influenced by the Rabi pattern produced by a single microwave pulse. Moreover, cycle memory and atomic density effects can modify the shape of the Ramsey central fringe from the common sinusoidal behavior. A simple three-level model well reproduces the experimental observations.
Additive manufacturing (AM) of passive microwave components is of high interest for the cost-effective and rapid prototyping or manufacture of devices with complex geometries. Here, we present an experimental study on the properties of recently demonstrated microwave resonator cavities manufactured by AM, in view of their applications to high-performance compact atomic clocks. The microwave cavities employ a loop-gap geometry using six electrodes. The critical electrode structures were manufactured monolithically using two different approaches: Stereolithography (SLA) of a polymer followed by metal coating and Selective Laser Melting (SLM) of aluminum. The tested microwave cavities show the desired TE011-like resonant mode at the Rb clock frequency of ≈6.835 GHz, with a microwave magnetic field highly parallel to the quantization axis across the vapor cell. When operated in an atomic clock setup, the measured atomic Rabi oscillations are comparable to those observed for conventionally manufactured cavities and indicate a good uniformity of the field amplitude across the vapor cell. Employing a time-domain Ramsey scheme on one of the SLA cavities, high-contrast (34%) Ramsey fringes are observed for the Rb clock transition, along with a narrow (166 Hz linewidth) central fringe. The measured clock stability of 2.2 × 10−13 τ−1/2 up to the integration time of 30 s is comparable to the current state-of-the-art stabilities of compact vapor-cell clocks based on conventional microwave cavities and thus demonstrates the feasibility of the approach.
We report on measurements of frequency shifts in a microwave cesium vapor cell atomic clock based on coherent population trapping (CPT). The dependence of the clock frequency on numerous experimental parameters, such as the laser power, the laser frequency, the microwave power, the cell temperature, the static magnetic field, but also the temperature of some key components, or the translation and rotation of critical wave plates and optical elements, is investigated. The stability budget of the clock frequency at one day is reported and discussed. This study constitutes a solid database for the future demonstration of a CPT-based cell clock with enhanced mid- and long-term stability performances.
Light shift and vapor-cell temperature shift are the two most significant factors dominating the long-term instability of compact atomic clocks. Due to the different physical mechanisms, there is not yet a solution that can effectively suppress the frequency shifts induced by these two effects. Here, we propose a 'resonance-offset' locking approach that compensates for the two physical frequency shifts. In this approach, the additional offset locking shift can effectively counteract the atomic resonance shifts arising from changes in vapor-cell temperature and light power, reducing the net impact on the clock's frequency to nearly zero. We have demonstrated this strategy on the 778 nm Rubidium two-photon optical frequency standard, successfully compensating for light shift and cell-temperature shift, respectively. This general method is particularly appealing for compact vapor-cell microwave and optical atomic clocks designed for the excellent stability rather than accuracy.
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.