Krzysztof Szymaniec

Improved accuracy of the NPL-CsF2 primary frequency standard: evaluation of distributed cavity phase and microwave lensing frequency shifts

We evaluate the distributed cavity phase (DCP) and microwave lensing frequency shifts, which were the two largest sources of uncertainty for the NPL-CsF2 caesium fountain clock. We report measurements that confirm a detailed theoretical model of the microwave cavity fields and the frequency shifts of the clock that they produce. The model and measurements significantly reduce the DCP uncertainty to 1.1 ? 10?16. We derive the microwave lensing frequency shift for a cylindrical cavity with circular apertures. An analytic result with reasonable approximations is given, in addition to a full calculation that indicates a shift of 6.2 ? 10?17. The measurements and theoretical models we report, along with improved evaluations of collisional and microwave leakage induced frequency shifts, reduce the frequency uncertainty of the NPL-CsF2 standard to 2.3 ? 10?16, nearly a factor of two lower than its most recent complete evaluation.

Evaluation of the primary frequency standard NPL-CsF1

A new caesium fountain frequency standard (NPL-CsF1) at the National Physical Laboratory is described. Procedures for evaluation of the systematic frequency shifts are presented. The NPL-CsF1 has a short-term stability σy(τ) = 1.4 × 10−13τ−1/2, predominantly due to the local oscillator phase noise. The accuracy of 1 part in 1015 is limited by the uncertainty of the frequency shift due to collisions between cold atoms.

First accuracy evaluation of the NPL-CsF2 primary frequency standard

An accuracy evaluation of the caesium fountain NPL-CsF2 as a primary frequency standard is reported. The device operates with a simple one-stage magneto-optical trap as the source of cold atoms. Both the uncertainty in and magnitude of the cold collision frequency shift are reduced by taking advantage of the dependence of the cross section on the effective collision energy in an expanding atomic cloud. The combined type B uncertainty (typically 4 ? 10?16) is dominated by an estimate of the frequency shift due to the distributed cavity phase. When operated at single density, the short-term fractional frequency instability of NPL-CsF2 is 1.7 ? 10?13 at 1?s and limited by the noise of the room temperature quartz-based local oscillator. During a typical frequency measurement campaign, the fountain is operated in an alternating mode at high and low density in order to measure and correct for a residual collision shift. This increases the effective fractional frequency instability to 5.4 ? 10?13 at 1?s; consequently the averaging time required for the type A uncertainty level to match that of the type B is 20 days.

An evaluation of the frequency shift caused by collisions with background gas in the primary frequency standard NPL-CsF2

Collisions between cold cesium atoms and background gas atoms at ambient temperature reduce the cold atom signal in a fountain clock and at the same time produce a shift in the measured clock frequency. We evaluate the shift in the NPL-CsF2 cesium fountain primary frequency standard based on measurements of the fractional loss of cold atoms from the atomic cloud during the interrogation time combined with a model by Gibble that quantifies the relationship between the loss and the frequency shift.

Collisions in a ballistically expanding cloud of cold atoms in an atomic fountain

We have employed an intuitive model and 3D Monte Carlo simulations to study the effect of ballistic expansion of the atomic cloud on the collision energies and the resulting frequency shift in a fountain clock. In particular, we show that the energies relevant for collisions contributing to the clock shift correspond to temperatures which may be significantly smaller than the temperature of the cloud at launch. Both the assumptions and predictions of our model are related to realistic parameters of operating caesium fountain clocks.

Initial evaluation of the NPL caesium fountain frequency standard

An initial performance evaluation of the caesium fountain primary frequency standard at the NPL is reported. Improved magnetic shielding has resulted in the inhomogeneity of the C-field being below 1 nT and has enabled the observation of full-contrast Ramsey fringes. A direct evaluation of the fountains stability in comparison to a hydrogen maser is shown to agree with the short-term stability inferred from the signal-to-noise ratio. The stability is consistent with the limit set by the local oscillator. The measurement of the frequency bias due to cold collisions is described, together with the associated uncertainty.

A microwave cavity designed to minimize distributed cavity phase errors in a primary cesium frequency standard

We present the design of the Ramsey cavity to be used in the refurbished cesium primary frequency standard NPL-CsF1. This design is optimized to suppress the distributed cavity phase shift.

Multiple π/2 pulse area operation of caesium fountains and the collisional frequency shift

Typically, primary fountain frequency standards are tested at elevated microwave powers in order to check for potential frequency shifts due to, e.g., microwave leakage or cavity phase gradients. Usually such tests are performed at nπ/2 microwave pulse area (n an odd integer), where the microwave power is set to these values typically by maximizing the contrast of the central Ramsey fringe. We have experimentally demonstrated that in this case for different n a varying clock state composition after the first Ramsey interaction can be obtained, if the average microwave power seen by the expanding atom cloud is different during the first and the second transition through the Ramsey cavity. In the presence of a clock state composition dependent collisional shift, this effect gives rise to different collisional shifts for operation at different nπ/2 pulse area.

Operation of the caesium fountain frequency standard NPL-CsF2 at the collisional shift cancellation point

We report on characterisation of a caesium fountain primary frequency standard NPL-CsF2 operating in a regime where the collisional frequency shift is nearly cancelled by controlling the clock state population ratio and other fountain parameters. We describe in detail the operation protocols possible in this case and their limitations and report on a long-term study of the stability of the parameters defining the cancellation point. Finally, we report on the frequency measurements where NPL-CsF2 was used as a reference, namely, a new measurement of the 87Rb clock transition and several evaluations of the TAI step interval.

Apparent Power-Dependent Frequency Shift Due to Collisions in a Cesium Fountain

We describe a situation where a varying collisional frequency shift in cesium fountain primary frequency standards can be misinterpreted as a power-dependent shift. This misinterpretation may affect analyses of fountains test-operated at multiple pi/2 microwave pulse areas. Such tests are typically performed in the search for microwave- and cavity-related systematic frequency biases.