Kurt Gibble

Improved magneto-optic trapping in a vapor cell

We have captured 3.6 x 10(10) cesium atoms in a magneto-optic trap loaded from a vapor cell. The 300-fold increase in the number of trapped atoms compared with that of previous research was accomplished by using larger laser intensities and 4-cm-diameter laser beams. The loading time constant was as short as 0.2 s.

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.

Distributed cavity phase frequency shifts of the caesium fountain PTB-CSF2

We evaluate the frequency error from distributed cavity phase in the caesium fountain clock PTB-CSF2 at the Physikalisch-Technische Bundesanstalt with a combination of frequency measurements and ab initio calculations. The associated uncertainty is 1.3 × 10 −16 , with a frequency bias of 0.4 × 10 −16 . The agreement between the measurements and calculations explains the previously observed frequency shifts at elevated microwave amplitude. We also evaluate the frequency bias and uncertainty due to the microwave lensing of the atomic wave packets. We report a total PTB-CSF2 systematic uncertainty of 4.1 × 10 −16 .

Evaluation of Doppler shifts to improve the accuracy of primary atomic fountain clocks.

We demonstrate agreement between measurements and ab initio calculations of the frequency shifts caused by distributed cavity phase variations in the microwave cavity of a primary atomic fountain clock. Experimental verification of the finite element models of the cavities gives the first quantitative evaluation of this leading uncertainty and allows it to be reduced to δν/ν=±8.4×10(-17). Applying these experimental techniques to clocks with improved microwave cavities will yield negligible distributed cavity phase uncertainties, less than ±1×10(-17).

Future Slow-atom Frequency Standards

Potential frequency standards based on laser cooled atoms are evaluated. We estimate that a standard based on an atomic fountain of cesium atoms can have an accuracy of Δν/ν = 10-16. Frequency standards based on ion traps are also evaluated.

Evaluating and minimizing distributed cavity phase errors in atomic clocks

We perform 3D finite element calculations of the fields in microwave cavities and analyse the distributed cavity phase (DCP) errors of atomic clocks that they produce. The fields of cylindrical cavities are treated as an azimuthal Fourier series. Each of the lowest components produces clock errors with unique characteristics that must be assessed to establish a clocks accuracy. We describe the errors and how to evaluate them. We prove that sharp structures in the cavity do not produce large frequency errors, even at moderately high powers, provided the atomic density varies slowly. We model the amplitude and phase imbalances of the feeds. For larger couplings, these can lead to increased phase errors. We show that phase imbalances produce a novel DCP error that depends on the cavity detuning. We also design improved cavities by optimizing the geometry and tuning the mode spectrum so that there are negligible phase variations, allowing this source of systematic error to be dramatically reduced.

Phase variations in microwave cavities for atomic clocks

We analyse the phase variations of the microwave field in a TE011 microwave cavity and how these variations affect the frequency of an atomic clock. We analytically solve for the microwave fields in a TE011 cavity. These analytic solutions show significant new terms that are not present in previous two-dimensional treatments. The new terms show that cavities with small radii, near 2.1 cm for a 9.2 GHz cavity, have smaller phase shifts than cavities with larger radii. We also show that the three-dimensional phase variations near the axis of the cavity can be efficiently calculated with a rapidly converging series of two-dimensional finite element calculations. The cavities used in atomic clocks have holes in the endcaps, and we use finite element methods to study the large fields and phase shifts near these holes. The effects of the phase variations on atoms traversing a cavity are analysed using the sensitivity function, and we present a cavity design that has small phase shifts for all atomic trajectories. For two π/2 pulses, the proposed cavity has transverse variations of the effective phase that are within ±0.1 µrad and produce no systematic frequency error for a nearly homogeneous and expanding cloud of atoms.

Laser-cooled Rb clocks

We demonstrate a prototype of a laser-cooled /sup 87/Rb fountain clock and measure the frequency shift due to cold collisions. The shift is fractionally 30 times smaller than that in a laser-cooled Cs clock. We observe a density dependent pulling by the microwave cavity and use it to cancel the collision shift. We have also demonstrated a juggling atomic fountain to study cold collisions and we discuss the importance of juggling for future fountain clocks.

Scattering of cold-atom coherences by hot atoms: frequency shifts from background-gas collisions.

Frequency shifts from background-gas collisions currently contribute significantly to the inaccuracy of atomic clocks. Because nearly all collisions with room-temperature background gases that transfer momentum eject the cold atoms from the clock, the interference between the scattered and unscattered waves in the forward direction dominates these frequency shifts. We show they are ≈ 10 times smaller than in room-temperature clocks and that van der Waals interactions produce the cold-atom background-gas shift. General considerations allow the loss of the Ramsey fringe amplitude to bound this frequency shift.

Rydberg spectroscopy in an optical lattice: blackbody thermometry for atomic clocks.

We show that optical spectroscopy of Rydberg states can provide accurate in situ thermometry at room temperature. Transitions from a metastable state to Rydberg states with principal quantum numbers of 25-30 have 200 times larger fractional frequency sensitivities to blackbody radiation than the strontium clock transition. We demonstrate that magic-wavelength lattices exist for both strontium and ytterbium transitions between the metastable and Rydberg states. Frequency measurements of Rydberg transitions with 10(-16) accuracy provide 10 mK resolution and yield a blackbody uncertainty for the clock transition of 10(-18).