C. Audoin

Properties of an optically pumped cesium-beam frequency standard with /spl Phi/=/spl pi/ between the two oscillatory fields

The properties of optically pumped cesium-beam resonators showing a phase difference, /spl Phi/, of /spl pi/ between the two oscillatory fields are analyzed. They are compared with those occurring with /spl Phi/=0, when the interrogation signal is slowly square-wave frequency modulated. The value of the operating parameters which optimizes the resonator properties is given for /spl Phi/=0 and /spl pi/,taking into account the effect of the noise sources which perturb the atom detection. It is shown that the design with /spl Phi/=/spl pi/ is superior. It provides a better frequency stability and smaller frequency offsets. The conclusion holds for short as well as long tubes. >

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 /spl sigma/=/spl 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.

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 3*10/sup -5/ T. The microwave interaction occurs in the intermediate region, where the value of the C-field is typically set to 4*10/sup -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.<<ETX>>

Stochastic models of stable frequency and time sources and their relationship

Different stochastic models of a stable frequency and time sources showing white phase noise, white frequency noise, and random walk of frequency noise are considered. A continuous time model of phase fluctuations is associated with the power law model of relative frequency fluctuations. The ARIMA (0,2,2) and the Kalman models of the sampled phase derivations are derived from the continuous model. Equations relating the characteristic parameters of these three representations of the source behavior are given. The Allan variance of relative frequency fluctuations is expressed as a function of the characteristic parameters. The approximation inherent to the simplified Kalman model is discussed, and the limit of validity of this model is stated. >

Frequency stability of an oscillating maser: Analysis of the effect of an external feedback loop

The noise temperature of the microwave cavity of an oscillating maser operated with an external feedback loop is given. The theoretical frequency stability of the signal delivered by the maser is deduced and the effect of the external feedback loop is discussed. Short- and mid-term frequency stabilities achievable with a conventional hydrogen maser with and without an external feedback loop and with a compact hydrogen maser operated either in active or in passive modes are given.

Frequency, phase, and amplitude changes of the hydrogen maser oscillation

The frequency, the phase and the amplitude changes of the hydrogen maser oscillation, which are induced by the modulation of the cavity resonant frequency, are considered. The results obtained apply specifically to one of the H-maser cavity auto-tuning methods which is actually implemented. namely the cavity frequency switching method. The frequency, the phase and the amplitude changes are analyzed theoretically. The phase and the amplitude variations are measured experimentally. It is shown, in particular, that the phase of oscillation is subjected to abrupt jumps at the times of the cavity frequency switching, whose magnitude is specified. The results given can be used for the design of the electronic system associated with the hydrogen maser, with the aim of minimizing the transfer of the phase modulation to the slaved vcxo.

Analysis tools for the accurate evaluation of a small frequency standard

The short, optically pumped cesium beam tube developed at Laboratoire de lHorloge Atomique has been carefully evaluated. For that purpose, we have developed a digital servo system that controls three parameters: the frequency of the ultra stable oscillator (USO), the microwave power of the signal experienced by the cesium atoms, and the static magnetic field applied to the atoms. The frequency standard shows a very satisfactory level of short- and medium-term frequency stabilities. A relative frequency offset, measured to be 4.10/sup -12/, results mainly from the residual phase difference between the oscillatory fields in the two interaction regions, which is due to imperfection in cavity symmetry. We present two different means of analyzing the causes of this spurious frequency offset using theoretical and experimental considerations. First, a numerical simulation of the beam tube response is performed as a function of the microwave field amplitude for different values of the residual phase difference /spl Delta//spl Phi/. Results include the cavity-pulling effect. Compared with the measured frequency offset, the numerical simulation leads to a second-order Doppler shift of -3.3 mHz and a residual phase difference, /spl Delta//spl Phi/, between the fields interacting with the atoms in the second and first regions of the Ramsey cavity, amounting to +150 /spl mu/rad. Second, an experimental method of measurement of /spl Delta//spl Phi/ without beam reversal is implemented. The latter yields /spl Delta//spl Phi/=155/spl plusmn/17 /spl mu/rad. Finally, the clock accuracy is determined. It is equal to /spl plusmn/14.10/sup -13/.

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 /spl phi/ of either 0 or /spl 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 /spl phi/=/spl pi/.

Studies of dielectrically loaded cavities for small size hydrogen masers

A dielectrically loaded cavity made of a hollow alumina cylinder, which is used to reduce hydrogen maser size, is considered. The results of a theoretical study of the effect of the cavity geometry on the frequency stability capability of the maser are reported. The active mode as well as the passive mode of operation are considered and the achievable performances are compared. It is shown that the frequency stability capabilities do not differ very much for both modes of operation with, however, a slight advantage to the active mode. >