A. De Marchi

Pulling by Neighbouring Transitions and its Effects on the Performance of Caesium-Beam Frequency Standards

Pulling by the wings of neighbouring field-dependent lines is usually taken into account in accuracy evaluation of caesium-beam frequency standards. Its magnitude is commonly calculated from the observed asymmetry of the neighbouring lines using a well-known formula in which the shape of all the Rabi lines is approximated with Lorentzian profiles of the same width. In this paper it is shown that use of these approximations yields in most cases grossly underestimated results for the pulling, and that the real shape of the Rabi wings must be computed in order to match experimental data. Line shapes far from Lorentzian and different widths for the different lines are obtained if the real rf field profile and the actual velocity distributions for each state are used. Unexpectedly high values are found in this way, which indicate this kind of frequency pulling as possibly the biggest single cause of inaccuracy in commercial caesium beams and a bias to be re-evaluated in primary laboratory standards. Theoretical computations show good agreement with experimental data and suggest that the well-known average frequency difference of about +1 × 10-12 which is shown by the ensemble of all short commercial standards with respect to long primary tubes may be traced to Rabi pulling. The effect turns out to be dependent on modulation type and parameters. Dependence on rf power is also studied, which may be the primary cause of temperature sensitivity and flicker noise in short tubes, and the roles of source temperature and beam optics variations in relation to long-term drift are indicated.

A new cavity configuration for cesium beam primary frequency standards

In the design of cesium beam frequency standards, the presence of distributed cavity phase shifts (associated with residual running waves) in the microwave cavity, due to the small losses in the cavity walls, can become a significant source of error. To minimize such errors in future standards, it has been proposed that the long Ramsey excitation structure be terminated with ring-shaped cavities in place of the conventional shorted waveguide. The ring cavity will minimize distributed cavity phase variations at the position of the atomic beam, provides only that the two sides of the ring and the T-junction feeding the ring are symmetric. A model is developed to investigate the validity of this concept in the presence of the small asymmetries that inevitably accompany the fabrication of such a cavity. The model, partially verified by laboratory tests, predicts that normal tolerances will allow the frequency shifts due to distributed cavity phase variations to be held at the 10/sup -15/ level for a beam tube with a Q of 10/sup 8/. >

Effects of Servo Loop Modulation in Atomic Beam Frequency Standards Employing a Ramsey Cavity

Some kind of modulation needs to be imposed on the mi- crowave signal to acquire lock in all passive atomic frequency stan- dards. In this way a frequency-discriminating dc signal is obtained by synchronous detection, which allows control of a slave oscillator. Fre- quency stability and frequency biases of the latter under closed-loop operation depend on the type and characteristics of the used modula- tion. The case of atomic beam standards using a Ramsey cavity is stud- ied, and different modulation schemes are considered under the aspects of efficiency (obtainable stability) and insensitivity to systematic effects. Theoretical results for the dependence of these on modulation type and parameters and on microwave power are reported and discussed. schemes and their sensitivity to some systematic effects are given as a function of modulation type and parame- ters, and are calculated numerically for an existing atomic beam tube. In particular, the effects of sine-wave modu- lation and slow square-wave frequency modulation on short-term stability and on various biases are discussed. A perfect realization of these ideal schemes will be as- sumed, and system imperfections like second harmonic distortion will be overlooked in the scope of this paper. 11. SYSTEM ANALYSIS Whatever the particular coherent detection system may be, signal processing of the modulated output Pod from the atomic resonator can be ideally divided in two steps: a filter section with a time-dependent output IF synchron- ous with the modulation, and a __ phase-sensitive detector with a time-independent output Pd.

Frequency pulling by hyperfine σ transitions in cesium beam atomic frequency standards

It is demonstrated that frequency pulling by Δm=±1 hyperfine σ transitions, here called Ramsey pulling, is a real calculable effect in atomic beam frequency standards. An analytic expression for the effects of Ramsey pulling is derived using perturbative techniques for the driving σ transitions, while treating the primary π transitions exactly. It is shown that these Ramsey pulling effects are intrinsically different from Rabi pulling in origin, manifestation, and elimination. These predictions are compared to measurements performed on a cesium beam atomic frequency standard, giving good quantitative verification of the theory and a clear demonstration of the existence of these effects.

Spatial phase variations in a TE/sub 011/ microwave cavity for use in a cesium fountain primary frequency standard

This work deals with the determination of the spatial phase distribution in a cesium fountain microwave cavity, taking into account functional requirements such as beam apertures and feeding holes, and the effect of imperfect metallic walls. >

Phase-coherent synthesis and precision frequency measurements in the far infrared

A short review of the basic concepts and problems in frequency multiplication into the infrared region of the electromagnetic spectrum is given. Results obtained with a multiplier chain starting from 5 MHz are reported. The carrier collapse is found at a frequency of about 15 THz. The present state of technological development is illustrated and the inherent limitations of this technique are indicated. The need for more spectral pure sources than those now available and/or different approaches is underlined in connection with the increasing thrust towards the measurement of visible frequencies.

High-Resolution Mode-Locked Laser Rangefinder With Harmonic Downconversion

The development of new pulsed optical sources with high pulse stability allows the improvement of common contactless measurement techniques. A new two-way optical rangefinder, employing a femtosecond laser, is presented here from design to implementation. The system is based on the evaluation of the phase delay of the returning optical pulse train with respect to the outgoing one. The main idea is to expand the time interval corresponding to the phase delay by harmonic heterodyne downconversion of a high harmonic of the pulse repetition rate (up to 10 GHz), which is applied symmetrically to the two channels. The system has shown 10 repeatability with a resolution that improves proportionally to the number of the employed harmonic.

Rabi Pulling and Long-Term Stability in Cesium Beam Frequency Standards

even within a group of standards of the same model, but no clear description of how this may happen has been given. Experimental measurements on high-performance cesium beam standards are reported which show a direct correlation between long-term frequency stability, long-term stability of the microwave power, and power sensitivity. The latter is shown to vary with the C-field (the dc magnetic field enveloping the microwave cavity) in a way that suggests Rabi pulling as the main-effect coupling microwave power changes to frequency changes. The long-term frequency stability of different standards was measured at various values of the C-field, corresponding to different power sensitivities. The flicker floor level was found to be proportional to the power sensitivity for each setting. This was true all the way down to the low range, in a non-temperature-stabilized environment. At about this level, a limitation appears to be introduced by temperature sensitivity not related to microwave power.

The optically pumped passive cesium frequency standard: Basic theory and experimental results on buffer gas frequency shifts

The theory of the optically pumped passive Cs frequency standard is given. Experimental results confirming qualitatively this theory are presented. The results are also compared to those obtained in the case of Rb. Experimental results on the pressure shift and temperature coefficients of the hyperfine frequency of cesium atoms in four buffer gases, CH4, N2, Ar and Kr are presented. Finally graphs for evaluating a given pressure coefficient and the residual temperature coefficient for mixtures of buffer gases are given.

Frequency stability of cell-based passive frequency standards: reducing the effects of local-oscillator PM noise

Experimental measurements in our present diode-laser-pumped Rb buffer-gas-cell frequency standard show that the sensitivity to microwave PM noise is approximately a factor of 10 lower when square-wave modulation is used in place of the more traditional sine-wave modulation. This result virtually eliminates what had been a serious limitation to the frequency stability attainable in cell-type standards. It also has ramifications for low-cost, commercial standards.