Cesium Beam Clocks Research Articles

A new magnetic state selection method in high-performance optically detected compact cesium beam clocks

We perform a new scheme of magnetic state selection in optically detected compact cesium beam clocks. Unlike the conventional method, we select atoms in the ground state |F = 4, mF ≠ −4⟩ by pointing the atomic collimator to the convex pole of the magnet realizing the two-wire magnetic field and detect atoms in |F = 3⟩ after interacting with the microwave field using a distributed feedback laser. The fluorescence background is greatly reduced as the inherent residual atoms |F = 4, mF = −4⟩ are avoided in this reversed scheme. The velocity distribution is narrowed, and the most probable velocity is decreased, since atomic trajectories are close to the weak-field region. We also investigate the relationship between the position of the atomic collimator and the distributions of the atomic beam, which is consistent with the Monte Carlo-based simulation model. By applying the reversed scheme and setting the deviated position of the collimator to 1.3 mm, the signal contrast is improved from 0.7 to 3, and the short-term frequency stability reaches 3.0 × 10−12 τ−1/2, nearly three times better than that of the high-performance version of Microsemi 5071A.

Light shift suppression with pulsed light detection in magnetic-state-selected cesium beam clocks.

Light detection is widely used in atomic clocks. The simple detecting structure induces the light shift which influences the clock's long-term stability. We introduce a new method to suppress light shift by using pulsed light instead of continuous light to detect atomic states. Under a suitable pulsed sequence, the part of the atoms which do not simultaneously interact with light and microwave field are detected. We demonstrate the validity of our approach in a magnetic-state-selected cesium beam clock. Using a well-tuned sequence, the light shift coefficient is reduced by a factor of about 10, in comparison with the continuous light detection scheme. In a clock stability test with extra light power noise, the result shows good immunity of the method to laser power fluctuations. We also analyze the sources of the clock short-term stability degradation, including the Dick effect and the fact that a reduced number of atoms is detected in the pulsed detection case.

An overview of the optically detected magnetic-state-selected cesium beam clock

Among all kinds of compact cesium beam clocks, the optically detected magnetic-state-selected cesium beam clock (OMCC) combines the advantages of the magnetic state selecting scheme and fluorescence detecting method. This paper presents an overview of the OMCC. Technical issues, noise sources, frequency shifts and improvements of OMCC are reviewed. Finally, the frequency stability of five OMCC is given, which is better than the stability of the high-performance version of Microsemi 5071A.

Beam optics analysis on magnetic-state-selected atomic clocks with optical detection

In traditional cesium beam clocks, cesium atoms are deflected by strong inhomogeneous magnetic fields. The distribution of the detectable atoms, which is critical to the short-term frequency stability, is hard to describe with analytical functions. In this paper, we numerically analyze the beam optics performance of cesium beam tubes based on the magnetic-state-selected and fluorescence detection scheme. To accurately model the cesium beam tube, we apply the Monte Carlo sampling directly inside the collimator. The finite element method is also applied to model the magnetic field. Upon the high dimensional distribution space, two key parameters are selected as indicators of the short-term performance of the cesium beam tube, the effective velocity distribution, and the normalized density difference of atoms in |F=3,mF=0⟩ and |F=4,mF=0⟩. The influence of the configuration of the collimator is analyzed. Experiments are carried out with two manufactured beam tubes. The results show good agreement with the simulation model. We also discuss limitations of the simulation method when applied to designing cesium beam tubes.

Improving the short-term frequency stability of a magnetic-state-selected cesium beam clock with optical detection.

The microwave spectrum line shape and the signal-to-noise ratio of a compact optically detected magnetic-state-selection cesium beam clock are analyzed in this paper. As the noise analysis shows, the performance is related to the atomic utilization ratio and locking parameters when the laser frequency noise is the dominant noise source. Methods are adopted for realizing better short-term frequency stability of the clock, including using a highly efficient state-selection cesium beam tube, optimizing the locking parameters, and stabilizing the microwave power to maximize the error signal. After optimization, the signal-to-noise ratio of the clock reaches 7.0 × 103 in a bandwidth of 1Hz and the clock demonstrates a short-term stability of 4.1 × 10-12 τ-1/2. The five-day Allan standard deviation reaches 7.7 × 10-15.

A linewidth locking method to control the microwave power in optically pumped cesium-beam clocks.

In this paper, we present a linewidth locking method to control the microwave power in optically pumped cesium-beam frequency standards. The responses of optically pumped cesium-beam tubes and classical cesium-beam tubes are analyzed and compared against the power of the microwave field. Due to the wide probability distribution of atomic velocity resulting from the optical state preparation and detection, the linewidth of the Ramsey pattern is sensitive to the microwave power. The results can be used to control the microwave power instead of using the traditional extremum method. The advantages of the new method are discussed, and we named this new method the linewidth locking method. When the microwave power is well controlled at a low level by the linewidth locking method, the frequency stability of cesium-beam clocks will be improved to a certain degree for the reduction of the Ramsey pattern linewidth. In experiment, using the linewidth locking method, the Allan deviation of our optically pumped cesium-beam frequency standard is 2.64×10-12/τ and continues until the averaging time exceeds 1 × 105 s, which is 17% better than that using the traditional extremum method.

Design of an atom source collimator for a compact frequency-stabilized laser.

A concise laser system for optically pumped cesium beam clocks is presented. The laser's frequency is locked by a fluorescence signal, produced by the interaction between a cesium atomic beam and laser. A cesium oven with a longer atom source collimator, formed by an array of channels, was used to reduce the divergence angle of the cesium atomic beam. The size of the cesium source collimator is 4 mm×0.6 mm, and the cesium expenditure rate is 2.4×10-1 g per year. A dense cesium atomic flux was used to interact with the laser to generate a fluorescence signal when the oven heating temperature is not too high. The cesium beam tube could have a longer lifetime. The optical structure of the laser system is compact. The measured frequency stability of the laser is ∼4×10-11 at 10,000s when the laser frequency is locked in the F=4→F'=5 transition of the cesium D2 line. The design of an atom oven and atom source may be used in other atomic beam clocks to improve their performance.

Realization of single optical frequency laser system for optically pumped cesium beam frequency standards

Compact laser system for optically pumped cesium beam clocks, which use single optical frequency laser for both Cs atomic state preparation and detection, is presented. The saturation probe laser intensity corresponding to certain Cs flux is researched by using laser, locked in the F = 4 → F′ = 4 transition of the Cs D2 line, to interact with Cs atoms. Light shift produced by laser could be reduced when the laser with small intensity, 0.7 mw/cm2, is used to interact with Cs atoms. High efficiency, 70%, fluorescence collectors are installed in the atom–laser interaction region to collect fluorescence. The frequency stability of the laser system is measured by mixing two output laser lights which are locked by fluorescence signal and it is about 3.2 × 10−11 at 2048 s. The compact laser scheme is beneficial to the miniaturization and industrial production of optically pumped Cs beam clocks. The design is also appropriate and useful for other laser frequency stabilization applications.

Recent progress in optically-pumped cesium beam clock at Peking University

A compact, long-life, and low-drift cesium beam clock is investigated at Peking University, where the atoms are magnetic-state selected and optically detected. Stability close to that of the best commercial cesium clocks has been achieved from 10 to 105 s. As previously shown, the short-term stability is determined by atomic shot noise or laser frequency noise. The stabilizations of microwave power and C-field improve the long-term stability, with the help of a digital servo system based on field-programmable gate array.

Design and test of the microwave cavity in an optically-pumped Rubidium beam frequency standard**Project supported by the National Natural Science Foundation of China (Grant No. 11174015).

We are developing a compact rubidium atomic beam frequency standard with optical pumping and detection. The cavity for microwave interrogation is an important part of the clock. The cavity in our design is a Ramsey-type, E-bend one, which is the same as the conventional method in most cesium beam clocks. Requirements for the design are proposed based on the frequency shift associated with the cavity. The basic structure of the cavity is given by theoretical analysis and detailed dimensions are determined by means of electromagnetic field simulation with the help of commercial software. The cavity is manufactured and fabricated successfully. The preliminary test result of the cavity is given, which is in good agreement with the simulation. The resonant frequency is 6.835 GHz, equal to the clock transition frequency of 87Rb, and the loaded quality factor is 500. These values are adjustable with posts outside the cavity. Estimations on the Ramsey line width and several frequency shifts are made.

Initial atomic coherences and Ramsey frequency pulling in fountain clocks

In the uncertainty budget of primary atomic cesium fountain clocks, evaluations of frequency-pulling shifts of the hyperfine clock transition caused by unintentional excitation of its nearby transitions (Rabi and Ramsey pulling) have been based so far on an approach developed for cesium beam clocks. We re-evaluate this type of frequency pulling in fountain clocks and pay particular attention to the effect of initial coherent atomic states. We find significantly enhanced frequency shifts caused by Ramsey pulling due to sublevel population imbalance and corresponding coherences within the state-selected hyperfine component of the initial atom ground state. Such shifts are experimentally investigated in an atomic fountain clock and quantitative agreement with the predictions of the model is demonstrated.

Optical clocks based on stimulated emission radiation

Atomic clocks operating at microwave region, are divided into two categories according to the mode of operation, namely the passive mode, in which the standard frequency of a clock signal is locked on to a very narrow atomic spectral line such as in cesium beam and rubidium gas cell clocks, and the active mode, where the atomic ensemble itself can produce a high stable and accurate standard frequency signal such as hydrogen maser. The hydrogen maser has been the most stable atomic clock for nearly half a century, and has been applied in a variety of scientific research fields. The optical clocks, operating at frequency domain by about five orders of magnitudes higher than that of the microwave clocks, have been expected to surpass the performance of microwave clocks both in stability and uncertainty. With the development and maturity of femtosecond optical frequency comb, very recently, the ion optical clock and neutral Sr optical clock have demonstrated better stability and uncertainty than any microwave clocks. However, all the optical clocks realized up to date are based on the “passive mode” of operation, this means that the laser frequency is locked to the very narrow atomic spectral line, but not the lasing light (the stimulated emission radiation) frequency itself which is very stable and can be used as a frequency standard——the active mode. Recently, Chen has proposed the concept of active optical clock (see ref. [6] in this issue), which is an optical clock based on the stimulated emission radiation. This is the first extension of the principle of hydrogen maser from microwave domain to optical domain. There are twofold advantages of this active optical clock. On one hand, the linewidth of the output laser from active optical clock determined by the modified SchawlowTownes formula, is much narrower than the linewidth due to transit time, which is the ultimate limit of absorption laser spectroscopy. On the other hand, utilizing bad cavity in active optical clock, the shift and noise of the centre frequency of active optical clock caused by cavity length change is reduced to a cavity pulling effect. Currently, the cavity length noise is the ultimate limit of existing lasers with coherence time longer than one second, and thus the laser linewidth is at mHz level. Active optical clocks provide several new possibilities of applications: (i) more stable optical clock than any current atomic clocks; (ii) sub-natural linewidth laser spectroscopy; (iii) long coherence time laser with linewidth at mHz level; (iv) Ramsey laser combining stimulated emission process and Ramsey separated oscillatory fields method. Therefore, the prospect of active optical clock is attractive for the research at the field of optical clock, laser spectroscopy and metrology.

The Measurement of Time: Time, Frequency and the Atomic Clock

This book provides an in-depth and comprehensive survey of the current state-of-the-art of the international atomic timescale and its underpinning relationship to practical and legal timescales. The authors are two of the leading figures in French time metrology. Claude Audoin, formerly Director of the Laboratoire de l'Horloge Atomique at Orsay, has had a long and distinguished career in the development of atomic frequency standards and atomic clocks. Bernard Guinot, formerly Director of the Bureau International de l'Heure (now absorbed by the Bureau International des Poids et Mesures, BIPM), has a lifetime's experience in the development of timescales. The work reviewed here is a revised and updated translation of Les fondaments de la mesure du temps (Paris: Masson, 1998). It is written at a level appropriate for an experienced graduate student or postdoctoral scientist entering either the field of time and frequency metrology or that of precise astronomical observation, whilst having sufficient depth to be useful as a work of reference for the established researcher in these fields. The first third of the book discusses the physical foundations of time metrology and introduces key concepts in the use of physical oscillators as clocks. The historical account of the complex process by which mean solar time came to be replaced by Coordinated Universal Time (UTC) will be particularly informative for newcomers to the field. About half of the volume is devoted to atomic frequency standards, with an exposition of the physics of caesium beam clocks and caesium fountains and a review of other commonly used standards such as the hydrogen maser, rubidium cell and stored ion clock. Although thorough, this 127-page chapter does not replace Audoin's earlier work with Jacques Vanier, The Quantum Physics of Atomic Frequency Standards (Bristol: IOP Publishing, 1989, out of print), which will remain the Bible for physicists working on clock development. The present time is one of great excitement in the development of atomic frequency standards. At the time the French edition was published, the first caesium fountain frequency standard, at the BNM-LPTF in Paris, had recently demonstrated 1.5 × 10-15 relative frequency uncertainty. Two such standards, at PTB and NIST, are now contributing to International Atomic Time (TAI). Clocks based on optical transitions in ions or atoms are just beginning to become a reality, thanks to Ted Haensch's breakthrough with the femtosecond optical frequency comb generator, which arrived on the scene just in time to receive a mention in this English edition. In a rapidly evolving field, any general survey is bound to be overtaken by events. Primary caesium frequency standards are designed to realize the SI definition of the second. The relationships between the SI second, TAI and UTC, as well as the national approximations to UTC generated by national standards laboratories such as NPL, the timescale available from GPS and timescales used in astronomy, are carefully set out. Finally, the practical applications of these timescales and frequency standards are reviewed, ranging from ultraprecise determinations of fundamental physical constants to positioning and navigation. The problem of longitude is as pressing as in Harrison's day, but for the foreseeable future, clockmakers will continue to have the upper hand over astronomers! Despite betraying the occasional Gallicism, the English translation reads with the clarity of the French original. The reader is guided painlessly through the multiplicity of acronyms with which the topic abounds. Audoin and Guinot have produced a book that will stand the test of time. Stephen N Lea

Implementation of the beam reversal technique on compact cesium clocks: towards an improvement in accuracy.

We report the evaluation of the residual phase difference deltaphi in a short (18 cm) Ramsey cavity by implementing the beam reversal technique to an optically pumped cesium beam clock. Deltaphi is measured to be 21 +/- 1.5 microrad, allowing a more accurate evaluation of the frequency performances of this small cesium clock. Finally, the clock accuracy is equal to 1.1 x 10(-13).

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.

Investigation of microwave π transitions in cesium beam clocks operated with U-shaped H plane waveguide cavities

In this article, we present the characteristics of the ΔF=±1, ΔmF=±1, π microwave transitions which appear in the response of cesium beam resonators operating with U-shaped waveguide Ramsey cavities bent in the plane of the H field. Such resonances are due to the presence in the cavity of microwave magnetic induction perpendicular to the static field direction. It is shown that the π resonance feature is derived from a pure two-level atomic system interacting with four spatially separated oscillating fields. Good agreement is found between experimental data and theoretical predictions when we take into account the actual transverse microwave field profile in the cavity obtained with tridimensional electromagnetic field computations.

A New Method for the Determination of Velocity Distributions in Cesium Beam Clocks

A new technique for evaluating the velocity distribution in cesium-beam frequency standards is presented. It is based on the dependence of the amplitude of the central maximum of the Ramsey resonance on the exciting microwave power level. The second-order Doppler shift, typically Δf/f ≃ 4 × 10-13 for the NRC primary standards, can be evaluated by this method with an uncertainty of about 10-15, five times the precision attainable previously.

Interplanetary plasma concentration measurements by use of dual frequencies from separated sites

Since 1965 the dual‐frequency method has been used for measuring densities of plasmas near planets and in interplanetary space. Signals at two frequencies are sent from an antenna on the earth to a spacecraft, or vice versa. The speed of the higher‐frequency signal is less affected by plasma than that of the lower‐frequency signal. The difference of delays provides a measure of the integrated effect of plasma along the radio path. In essence, the higher‐frequency signal serves as a benchmark against which the lower‐frequency effect is measured. Two markedly different sets of equipment have thus far been used to perform dual‐frequency observations; their strengths and weaknesses are reviewed, and it shown that many of the weaknesses could be overcome by using separate sites on the earth from which to transmit the low and high frequencies. A survey of the expected error in measurements using separated sites suggests that the critical element is time synchronization between them. The best available device for performing this function is the cesium beam clock; six such clocks were tested under conditions that accurately simulate an operational system. The test results are related to errors that would arise in plasma densities derived by this method. While the feasibility of site separation is dependent upon the specific mission to be accomplished, it appears practicable at the present state of the art for many planetary, solar wind, and comet applications.

The Millman Effect in Cesium Beam Atomic Frequency Standards

A systematic frequency shift which reverses sign with either C field or beam reversal and which can be interpreted as the consequence of the Millman effect has been found in the new NRC cesium beam clock, CsV. A method of calculating the resonance asymmetry resulting from this effect and the dependence on the velocity distribution and exciting microwave power level of the frequency shift caused by it is described. Application of this theory to CsV leads to reasonable agreement with experimental results. Possible origins for the Millman effect in cesium beam standards are discussed, and it is concluded that the most likely source is a very small variation in the direction of the C field over normal beam trajectories within the microwave interaction regions.