Transient response following frequency or amplitude switching in a cesium beam tube

The transient responses of an optically pumped cesium beam tube to square wave frequency and amplitude modulation is considered. The frequency transient is computed assuming a phase difference phi of either 0 or pi between the two oscillatory fields. We present theoretical and experimental data showing that, contrary to the frequency transient, the amplitude transient depends on the direction of switching. The knowledge of this property is useful for the design of the servo-loop controlling the amplitude of the microwave signal applied to the atomic resonator. A justification of this asymmetrical behavior is given. Experimental results confirm the theoretical predictions in the case phi=pi.     

Implementation of the beam reversal technique on compact cesiumclocks: towards an improvement in accuracy

Reports the evaluation of the residual phase difference ▵φ in a short (18 cm) Ramsey cavity by implementing the beam reversal technique in an optically pumped cesium beam clock. ▵φ is measured to be 21 ±1.5 μrad, allowing a more accurate evaluation of the frequency performance of this small cesium clock. Finally, the clock accuracy is equal to 1.1·10^-13     

A new cavity configuration for cesium beam primary frequencystandards

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^-15 level for a beam tube with a Q of 10⁸     

Controlling the microwave amplitude in optically pumped cesium beam frequency standards

Assuming square wave frequency modulation, the response, versus the amplitude of the microwave field, of an optically pumped cesium beam tube is considered. The properties of the first maximum of this response are analyzed. The effect of the neighboring lines is taken into consideration, and a model of the profile of the microwave field in each interaction region is validated. A symmetry property of the response considered is pointed out. It enables us to implement a feedback control of the microwave amplitude with a large depth of the amplitude modulation. Residual frequency offsets that may occur as a consequence of a spurious amplitude modulation correlated with the frequency modulation are assessed. And, with a cavity designed such that sigma=pi between the two oscillatory fields, it also is possible to measure the microwave amplitude at the first maximum of the sole contribution of the reference atomic line.     

Frequency performances of a miniature optically pumped cesium beam frequency standard

The optically pumped cesium beam clock named Cs IV is operated with a new short Ramsey cavity satisfying strict requirements on the microwave leakage level. The most relevant characteristics of the device are presented. Cs IV is presently driven by standard electronics coming from a HP 5061 B clock that provides a sinusoidal modulation of the interrogation microwave signal and a microwave power stability of about 1% at a temperature of 20+/-1 degrees C. The short- and medium-term frequency stability measurement gives sigma(y)(1 day)=2x10(-14): this value holds up to 3 days. The accuracy evaluation results in an uncertainty of 10(-12), and the repeatability is evaluated to 3x10(-13). It appears that the flicker floor is beginning at 2x10(-14) and is mainly due to both the power fluctuations of the free running microwave interrogating signal and the fluctuations of the external static magnetic field. The accuracy is limited by the lack of knowledge of the end-to-end cavity phase shift.     

Frequency shifts in cesium beam clocks induced by microwave leakages

The anomalous sensitivity of an optically pumped cesium beam clock to microwave power and the unexpected frequency shifts observed are demonstrated to result from microwave leakages outside the arms of the Ramsey cavity. A new design of the cavity associated with a careful realisation provides very weak microwave leakages and negligible related frequency offsets. We have established a theoretical model that allows us to calculate the frequency shifts due to microwave field components propagating along the beam axis in regions which are free-field in an ideal Ramsey cavity. This results in first order Doppler effect shifts. The order of magnitude of the frequency shift can be predicted and agrees with the measured one when the amplitude of the leakage magnetic field is about a 1000 times smaller than the amplitude of the microwave interrogation field in the cavity.     

Frequency-Impulse Modulation as a Means of Attaining Accuracy in Cesium Atomic Clocks

An electronic system has been developed which corrects for cavity-detuning errors in cesium atomic-beam frequency standards. The RF signal applied to the beam tube is square-wave phase modulated, i.e., frequency-impulse modulated. The transient response of the beam tube to these phase steps is used as a control signal. When the positive and negative transients are both equal in area and identical in shape, it will be shown that the applied RF signal must be exactly at cesium frequency (for the given magnetic field) and the RF cavities must be exactly in tune. Two feedback loops are needed; one for correcting the crystal oscillator, the other for adjusting the relative phase of the RF cavities. With cavity detuning error greatly reduced by this system, the remaining source of inaccuracy is the uncertainty of the magnetic field in the drift region of the beam tube. An experiment is described which may permit setting a given cesium-beam standard to a frequency that differs by a precisely known amount from the zero-field cesium-resonance frequency.     

A Systems Analysis of the Cesium Beam Atomic Clock

A brief derivation of the transition probability for a two-state atomic system subjected to a phase modulated oscillatory perturbation is presented. This result is used to perform an analysis of a typical cesium beam atomic clock system utilizing a Ramsey (twin cavity) beam tube in order to determine optimum design parameters. It is shown theoretically and experimentally that the optimum modulation frequency for this type of system is higher than has previously been supposed. An additional feedback loop can be incorporated to nearly eliminate cavity phase error.     

Reevaluation of the Optically Pumped Cesium Frequency Standard NRLM-4 With an H-Bend Ring Cavity

The largest source of uncertainty of the optically pumped cesium (Cs) frequency standard (NRLM-4), i.e., the distributed cavity phase shift, was reduced by replacing the microwave cavity with a new ring-type one. An H-bend-type ring cavity is adopted for the first time. Due to the novel cavity and the improvement of the Cs beam alignment, the distributed cavity phase shift was significantly reduced from $2 times 10^{-14}$ to $1.4 times 10^{-15}$. The frequency stability was measured to be $8 times 10^{-13}tau^{-1/2}$ . The total uncertainty was reevaluated to be $6.7 times 10^{-15}$ , which is four times better than the previous value.      

Physical origin of the frequency shifts in cesium beam frequency standards-related environmental sensitivity

When observed in a cesium beam frequency standard, the hyperfine transition frequency of the atoms differs slightly from the invariant transition frequency of the unperturbed atoms at rest. The various physical and technical origins of the frequency offsets are stated. They relate to fundamental physical effects, to the method of probing the atomic resonance and to the frequency control of the slaved oscillator. The variation of the frequency offsets under a change of the value of the internal operating characteristics is considered. The sensitivity to a change of the magnetic induction, the microwave power and the temperature is given. A comparison is made of the sensitivity of cesium beam frequency standards of the commercially available type, making use of magnetic state selection, and of devices under study in which the state preparation and detection is accomplished optically. The pathways between the external stimuli and the physical origin of the frequency offsets are specified.     

Influence of a static magnetic field on the detected atomic velocity distribution in an optically pumped cesium beam frequency standard

Irregularities of the microwave Ramsey patterns in an optically pumped cesium atomic beam frequency standards with a sharp angle incidence detecting laser beam have been diagnosed. They arise from a separated two-peak detected velocity distribution, which is caused by static magnetic fields. Experimentally measured results and theoretical analysis of this phenomenon are presented in this paper.     

Phase noise performance of microwave analog frequency dividers: application to the characterization of oscillators up to the millimeter-wave range

The phase noise performance of two different microwave analog frequency dividers is characterized and compared with the values obtained using simple theories of noise in injection-locked systems. The direct measurement of the divider noise with a low phase noise synthesizer is not accurate enough, and the residual noise technique is used. The noise levels observed using this technique, between -120 and -155 dBc/Hz at a 10 kHz offset frequency, demonstrate that this divider noise is much lower than the phase noise of most microwave free running oscillators, even if this noise is still high with respect to the residual noise of amplifiers realized with the same active devices. The down conversion of microwave sources up to 40 GHz, is proposed as an application example.     

An alternative cold cesium frequency standard: the continuous fountain

We report on the primary frequency standard now under construction at the Observatoire de Neuchatel (ON). The design is based on a continuous fountain of laser-cooled cesium atoms, which combines two advantages: the negligible contribution of collisions to the inaccuracy and the absence of stability degradation caused by aliasing effects encountered in pulsed operation. The design is reviewed with special emphasis on the specific features of a continuous fountain, namely the source, the microwave cavity (TE(021) mode), and the microwave modulation scheme. The possible sources of frequency biases and their expected contributions to the error budget are discussed. Based on present data, an accuracy in the low 10(-15) range and a short-term stability of 7.10(-14) are attainable simultaneously under the same operating conditions.     

小型磁选态铯束管的抗振动性能研究

分析了铯束管的固有振动特性,得出了铯束管的危险共振频率和结构的薄弱环节,提出了相应的振动加固措施,这些加固措施可以应用到空间铯束管的研制中。设计了铯束管的正弦扫频试验,通过试验结果与仿真结果之间的对比,验证了有限元模型的合理性和有限元分析的精度。     

The Atomic Beam Tube as an Optical Frequency Standar

It is possible to use the atomic beam tube as an optical frequency standard. Thallium has an advantage over cesium with respect to obtaining narrow spectral lines. The two-cavity method, as applied to the optical region, is analyzed. The construction of the cavity system for the observation of molecular ringing in the optical region is proposed and discussed.     

Digital synchronous detector and frequency control loop for cesiumbeam frequency standard

A setup that includes a digital synchronous detector and a digital frequency control loop and is designed for use in a cesium beam frequency standard is described. It is based on the TMS 32010 signal microprocessor. When associated with a high-quality HP 5061A option four cesium beam tube, it makes it possible to achieve the same levels of short-term and medium-term frequency stability as its original analog counterpart. It is thus expected that the setup will fit the improved short- and long-term frequency stability capability of optically pumped cesium beam tubes     

New design for a high performance optically pumped cesium beam tube

An optically pumped cesium beam resonator has been designed including three successive magnetic field regions. The optical interactions take place in the first and third regions, where the magnetic field has the required value of 3x10(-5) T. The microwave interaction occurs in the intermediate region, where the value of the C-field is typically set to 4x10(-6) T. It has been verified that the magnetic field profile along the cesium beam does not induce Majorana transitions. Using a single laser diode emitting at 852 nm with a linewidth of about 30 MHz, the resonator gives an excellent amplitude signal to noise ratio equal to 20000 in a 1-Hz bandwidth.     

Microwave leakage-induced frequency shifts in the primary frequency standards NIST-F1 and IEN-CSF1

In atomic fountain primary frequency standards, the atoms ideally are subjected to microwave fields resonant with the ground-state, hyperfine splitting only during the two pulses of Ramsey's separated oscillatory field measurement scheme. As a practical matter, however, stray microwave fields can be present that shift the frequency of the central Ramsey fringe and, therefore, adversely affect the accuracy of the standard. We investigate these uncontrolled stray fields here and show that the frequency errors can be measured, and indeed even the location within the standard determined by the behavior of the measured frequency with respect to microwave power in the Ramsey cavity. Experimental results that agree with the theory are presented as well.     

Rabi pedestal shifts as a diagnostic tool in primary frequencystandards

Some of the systematic errors in primary, atomic-beam frequency standards are much larger for the Rabi pedestal part of the lineshape than for the Ramsey fringe part. We have used a digital servo system to measure the frequency offset between the Rabi pedestal and the Ramsey fringe for all seven Zeeman components of the cesium hyperfine transition. The dependence of these shifts on magnetic field, modulation amplitude, and microwave power enables us to separate three distinct causes: Rabi pulling, cavity pulling, and magnetic field inhomogeneity. From the measured pedestal shifts, we infer the corresponding shifts for the clock transition with uncertainties of the order of one part in 10 ¹⁵ or less     

Measurement of dynamic end-to-end cavity phase shifts in cesium-fountain frequency standards

We have measured a previously unobserved systematic frequency shift in our cesium-fountain frequency standard, NIST-F1. This shift, predicted theoretically previously, mimics the well-known end-to-end phase shift in atomic beam standards when synchronous thermal transients are present. Detuning the microwave cavity several megahertz from resonance reduces this effect to the deltaf/f = 1o(-16) level.