Frequency shifts in cesium beam clocks induced by microwave leakages

Abstract

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.

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

“…However, the maximum Doppler shift of the leakage in a typical cesium fountain is of the same order as the Rabi width (∼100 Hz) and under these conditions the theory remains qualitatively correct and is quantitatively correct within a factor of 2, see [2] and [12]. In NIST-F1 and IEN-CSF1, the leakage above the Ramsey cavity is always resonant because, as explained in the Appendix, the drift tube is a high Q, antiresonant microwave cavity.…”

“…This sign change retains Hermiticity of the Hamiltonian. By using "phase factored" probability amplitudes, the exponential time dependence of the off-diagonal elements in (2) can be transformed to a constant contribution to the diagonal elements (cf (9) and (10) of [11]). The resulting Schrödinger equation for the system is:…”

Frequency performances of a miniature optically pumped cesium beam frequency standard

“…However, the delivered frequency suffered from a high sensitivity to the microwave power and unexpected frequency shifts. A thorough study of the encountered problem leads us to identify microwave leakages of the Ramsey cavity as sources of significant frequency shifts [4], [5]. These drawbacks are avoided by means of a new design and a careful achievement of the Ramsey cavity, thus ensuring a very low level of microwave leakage outside the microwave interaction regions.…”

On the power dependence of extraneous microwave fields in atomic frequency standards

“…Microwave leakage induced frequency biases have previously been investigated by several authors [6,7]. Because the earlier work was primarily in the context of thermal beam clocks operation at optimum power was investigated and the power sensitivity of the effect was not elucidated.…”

“…[3][4][5][6][7][8]. Laser-cooled fountain frequency standards pose problems with respect to both distributed cavity phase and microwave leakage different from those associated with thermal beam standards.…”