Atomic Beam Frequency Standards Research Articles

GNSS-grade space atomic frequency standards: Current status and ongoing developments

We present an overview on the current state of Global Navigation Satellite Systems (GNSS)-grade or better space atomic frequency standards’ (SAFS) technologies and discuss their applications. We estimate that a total of more than 1000 such standards were sent to space so far, the vast majority consisting of rubidium-cell frequency standards, Cs atomic beam frequency standards, and passive hydrogen masers. Finally, we review a variety of ongoing developments in view of future new generations of GNSS-grade SAFSs.

The influence of interatomic collisions on the angular distribution of Cs atomic flow from microchannel

Beams of alkali atoms are typically used in precise quantum devices, such as atomic beam frequency standards. In order to know more exactly parameters of atomic beam tubes and frequency standards (frequency instability), it is necessary to investigate the propagation of Cs atoms after the channel exit. In this work theoretical calculations of angular distribution of Cs atomic flow from a microchannel are carried out. The Monte-Carlo direct numerical simulation of Cs atom propagation is also performed to estimate the influence of interatomic collisions on the atomic flow.

Improvement of Frequency Locking Algorithm for Atomic Frequency Standards

The authors describe a novel method of frequency locking algorithm for atomic frequency standards. The new algorithm for locking the microwave frequency to the Ramsey resonance is compared with the old one that had been employed in the cesium atomic beam frequency standards such as NIST-7 and KRISS-1. Numerical simulations for testing the performance of the algorithm show that the new method has a noise filtering performance superior to the old one by a factor of 1.2 for the flicker signal noise and 1.4 for random-walk signal noise. The new algorithm can readily be used to enhance the frequency stability for a digital servo employing the slow square wave frequency modulation.

Determination of transit time distribution and Rabi frequency by applying regularized inverse on Ramsey spectra

The authors report on a method to determine the Rabi frequency and transit time distribution of atoms that are essential for proper operation of atomic beam frequency standards. Their method, which employs alternative regularized inverse on two Ramsey spectra measured at different microwave powers, can be used for the frequency standards with short Ramsey cavity as well as long ones. The authors demonstrate that uncertainty in Rabi frequency obtained from their method is 0.02%.

Characterization of the main frequency shifts for the brazilian 133Cs atomic beam frequency standard

In order to evaluate an atomic clock, it is important to determine the main frequency shifts caused by external fields, device imperfections, etc. Scanning the frequency of the main oscillator, the Ramsey fringe is obtained and used to determine the main shifts. The gravitational shift (10-17), second order Doppler (1.65×10-13), Black-Body radiation shift (2.9×10-14), quadratic Zeeman effect (5×10-13), Rabi Pulling (1.3×10-13) and cavity pulling (1.3×10-13) have been evaluated. The short term stability, (6.6±0,2)×10-13, was obtained.

Alternating Current Zeeman and Stark Interference Effect inRamsey Separated Oscillating Fields

Analytic expressions have been derived of the alternating current (ac)Zeeman and ac Stark effect in an atomic beam magnetic resonance method using Ramseyseparated oscillating fields. An interesting featurewhich will affect the normal Ramsey pattern is that an interferencefringe is superimposed on the dispersion lineshapes of the normal acZeeman or ac Stark effect. We point out that this new character of ac Zeeman(ac Stark) effect generally exists in all kinds of Ramsey method, forexample, in the optical Ramsey atomic interferometer and atomic beamfrequency standard. An important implication is that, particularlyin an atomic beam frequency standard using Ramsey method, this effecthas an influence on the evaluation of the second-order Doppler frequencyshift.

Asymmetry of microwave spectrum in an optically-pumped Cs atomic beam frequency standard

The asymmetry of microwave spectrum was investigated in an optically pumped Cs atomic beam frequency standard. The asymmetry was measured with the polarization state and the detuning of the pumping beam, and analyzed by the master equation based on the density matrix for the D/sub 2/ transition line. It was found that the pumping transition, F=4/spl rarr/F'=5 can offer a most sensitive detection scheme for the asymmetry. Finally, it was showed that the asymmetry could be compensated by adjusting the state of polarization of the pumping beam as well as the frequency of pumping laser.

Multilambda Rabi cavities in atomic beam frequency standards

Multilambda Rabi cavities have been shown to be a viable solution for the reduction of cavity phase shift and other Doppler related effects in atomic beam frequency standards. For this reason they may be advisable to use in devices in which operations that are apt to measure or correct cavity phase shift are impossible or undesirable. These include short sealed (commercial) tubes, possibly some primary standards with vertical beam (because it is not easy to operate an atomic beam directed vertically down), and microgravity clocks. Analytical and numerical results are reported on particular cavity examples. They support the idea that a Ramsey cavity is not always the only solution for guiding microwaves in a beam standard. A comparison of line shapes between experimental results obtained with an atomic beam and numerical calculations is also reported.

Rabi pedestal shifts as a diagnostic tool in primary frequency standards

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/sup 15/ or less.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Feasibility of end to end phase shift correction from the outside of sealed cesium beam tubes

Summary It is well known that a frequency shift mceable to asymmetry of the microwave resonator occurs in atomic beam frequency standards making use of Ramsey’s double interaction technique. The shift is due to the phase difference which then appears between the fields interacting with the atoms in the two regions. The atoms in fact cannot distinguish the latter from the phase accumulated by a frequency offset during the time of flight between the two cavities. Beam reversal experiments can measure such end-to-end phase difference if it can be assumed constant for the two beam directions. In that case in fact a beam reversal simply changes the sign of the effect. However, this technique can only be applied with predisposed laboratory type primary standards, while in the case of unidirectional beams any accuracy assessment on end-toend phase shift has been traditionally made by relying on mechanical specifications and aimming, and on elecmcal length measurements, during cavity manufacturing. That a correction of end-to-end phase shift might be possible by acting from the outside of a sealed tube has been suggested nxently [ 13, by noting that not just the two arms of the Ramsey cavity, but the microwave structure as a whole, contribute with their asymmetry to the occurrence of the problem. A formula for the end-toend phase difference was found, which includes the asymmetry of the feeding junction at the center of the Ramsey structure, and reduces to the traditional formula in the case of a symmetric junction. It was therefore proposed that a correction of arm asymmetry could be tried by introducing a compensating asymmetry in the “symmetric” arm of the feeding T-junction. Such asymmetry should be calibrated so that the asymmemc superior cut-off modes that it excites produce at the junction the desiredphase difference between the waves launched in the two opposite directions. In this paper an electromagnetic calculation is carried out of the asymmetry induced in an E-plane waveguide T-junction by an asymmetric iris in the feeding port. A comparison with experimental results is given. It is shown that compensation of end-to-end phase shift is possible in this way, and that shifts of few parts in A discussion about how well the absolute size of the effect can be judged by measuring the structure in reflection is also given, and the relevance that this has toward accuracy statements on unidirectional beams is underlined. 1013 can be reduced to below iX1013.

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.

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.

Design of an optically pumped silver atomic beam frequency standard

A project of a silver atomic beam frequency standard with optical pumping and Ramsey microwave excitation is presented and the mean features of such a standard are calculated. It seems that the use of optical pumping gives a good perspective for practical application of the silver beam atomic standards.

Limitations of atomic beam frequency standards

Atomic beam frequency standards may be placed into two categories: field standards and laboratory standards. While this distinction is somewhat artificial, because the two types of standards are interdependent, each category does have different requirements of accuracy, size, and cost. Despite this separation, generally the developments which produce the best laboratory standards eventually give rise to improved field standards. Existing field standards are limited in long term fractional frequency stability to σ y (τ) ∼ 3 x 10 -13, for τ ∼ 6 months. A laboratory standard such as NBS-6, the U.S. primary cesium standard, is limited in inaccuracy to Δ y ∼ 8 x 10 -14. Proposed new cesium field standards are expected to yield long term stabilities of σ y (τ) ∼ 1 x 10 -14 (τ = 6 months). Stored ion standards, prime candidates for new laboratory frequency standards, are expected to have better than Δ y = 1 x 10 -15 inaccuracy. As other approaches to atomic beam frequency standards are considered, they should attempt to compete favorably with these emerging technologies.

Cesium atomic-beam frequency standards

Cesium atomic-beam frequency standards

Shift ofS122hyperfine splittings due to blackbody radiation

Frequency shifts of hyperfine splittings of $^{2}S_{\frac{1}{2}}$ states due to the blackbody radiation field are calculated. It is shown that they can be estimated from the dc hyperfine Stark shifts, which have previously been measured in the ground states of hydrogen and the alkali atoms. The shift at 300 K is large enough to be significant in primary Cs atomic beam frequency standards, and should be measurable. A simple method of calculating the hyperfine Stark shifts is described, which is based on the Bates-Damgaard method for determining radial matrix elements and the Fermi-Segr\`e formula for determining the contact hyperfine matrix elements. It is applied to ${\mathrm{Ba}}^{+}$ and ${\mathrm{Hg}}^{+}$, for which no experimental data are yet available, and which are currently of interest for frequency standards.

LASER COOLED, STORED ION EXPERIMENTS AT NBS AND POSSIBLE APPLICATIONS TO MICROWAVE AND OPTICAL FREQUENCY STANDARDS

Research on stored ion frequency standards at the United States National Bureau of Standards is brief 1 y discussed. We summarize past work and indicate directions of future research. Introduction. - The purpose of this paper is to briefly summarize the work at the National Bureau of Standards (NBS) which has been directed towards realizing a frequency standard based on stored ions. The similar work of other groups (I) is not discussed here. This summary briefly describes past work and indicates future directions of research at NBS. The stored ion work at NBS was initiated in the Fall of 1977. The goal of this work has been to devise a technique for realizing a frequency standard whose accuracy would be significantly better than that of the Cs atomic beam frequency standard. With this in mind, the ion storage method (2) was pursued because it can provide long confinement times without the usual perturbations associated with confinement (e.g., the wall shift in the H-maser). The initial work was directed toward realizing laser c ooling of ions 131, since this would provide a way to substantially suppress the frequency shift due to the second-order Doppler or time-di lation effect. For these initial experi- ments, Mg+ ions were stored in a Penning trap. Mg+ ions were chosen, since the electronic s tructure is fairly simple (i.e., like that of neutral alkali atoms) and required a laser source at 280 nm. The Penning trap was chosen because the residual h eating mechanisms (at least for a cloud of ions) are l ess than for the

Second-Order Doppler and Cavity Phase Dependent Frequency Shifts in Atomic Beam Frequency Standards

Theoretical expressions for the second-order Doppler and cavity phase dependent frequency shifts in atomic beam frequency standards are derived, and the concept of momenta of the velocity distribution function is introduced. The effects of frequency modulation of the microwave excitation are also described by analytical expressions. Momenta of the velocity distribution function which can be experimentally derived from the central part of the Ramsey pattern are given for the National Research Council of Canada frequency standards Cs III and Cs V. The values of the frequency shift arising from the second-order Doppler effect obtained for different operating conditions are in close agreement with those calculated from the truncated Maxwellian velocity distributions characteristic of the best fit with the experimental resonance patterns. The frequency shift arising from mistuning of the microwave cavity is also calculated. This shift is dependent on both the velocity distribution and the servo-system frequency modulation employed. The operating conditions required for cancellation of this shift are determined.

Corrections for Second-Order Doppler Shift and Cavity Phase Error in Cesium Atomic Beam Frequency Standards

From the measured static resonance curve of a cesium beam tube, corrections can be derived for second-order Doppler shift and cavity phase error. For the calculation Fourier transforms are used, which also produce the velocity distribution of the atoms. Data are given for the distortion of the resonance curve from which the corrections can be derived applicable in the case of very slow square wave frequency modulation. A method is also given for calculating corrections for faster modulation rates where the time-of-flight effects are no longer negligible. However, quadrature components will now occur in the beam signal, and their effect on the clock servo is discussed.

Improvements in Atomic Cesium Beam Frequency Standards at the National Bureau of Standards

The National Bureau of Standards Frequency Standard, NBS-III, a cesium beam with a 3.66-meter interaction region, has been in operation since 1963. The last published (1966) accuracy capability for NBS-III was 1.1 ? 10-12(l?). Recently, several new solid-state broad-band frequency-multiplier chains have been constructed. Reduction of the random phase noise by more than 20 dB compared to the previous state of the art has been obtained consistently. In addition, a solid-state servo system has been installed to control the frequency of the 5-MHz slave oscillator. Comparisons were made between NBS-III and one of the commercial cesium standards in the NBS clock ensemble. The relative fractional frequency stability ?(N = 2, T = 7 days, ? = 1 day) = 1 ? 10-13 was observed for nine weekly comparisons. The very-long-term frequency stability for this recently improved NBS-III system has not been evaluated fully. Due to the improvements both in electronic systems and evaluative techniques, however, an accuracy of 5 ? 10-13(1?) for a single evaluative experiment is reported. Substantial effort is being expended toward improvement of the accuracy and figure of merit (presently 10) of the NBS cesium standard. The modified system, to be called NBS-5, is expected to be in operation in the latter half of 1970 and to exhibit a figure of merit in excess of 500.