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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)

Distributed cavity phase and the associated power dependence

Ruoxin Li, Kurt Gibble

Published Jan 18, 2006• 9 citations
Publisher

Abstract

We discuss the power dependence of distributed cavity phase errors for cylindrical TE011cavities in laser-cooled atomic fountain clocks. The azimuthally symmetric phase variations produce a surprisingly large distributed cavity phase error for two 2pi, 4pi, and 6pi pulses. This is due to the correlation between the transverse variation of the Rabi frequency over the cavity aperture and a quadratic density variation of the atomic sample, along with the symmetry of the longitudinal phase variation in the cavity. We show that the large azimuthally symmetric fields and phase shifts near the walls of the endcap holes produce very small errors at optimal power for a uniform wall resistance. We also show the power variation for higher order azimuthal variations m=1, 2, and 4. These may be caused by fountain tilts, nonuniform detection of atoms, and asymmetries in the laser trapping and cooling of the atoms. We demonstrate that distributed cavity phase errors in physical cavities may have no variation with the microwave power. A combination of rigorous calculations of cavity losses, measurements of power dependence, the atomic distributions, and fountain tilts, and electrical measurements that show the lower limit of the cavity Q and the cavity symmetry, should provide stringent limits on distributed cavity phase errors for current atomic clocks

DOI
10.1109/freq.2005.1573909

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We discuss the power dependence of distributed cavity phase errors for cylindrical TE011cavities in laser-cooled atomic fountain clocks. The azimuthally symmetric phase variations produce a surprisingly large distributed cavity phase error for two 2pi, 4pi, and 6pi pulses. This is due to the correlation between the transverse variation of the Rabi frequency over the cavity aperture and a quadratic density variation of the atomic sample, along with the symmetry of the longitudinal phase variation in the cavity. We show that the large azimuthally symmetric fields and phase shifts near the walls of the endcap holes produce very small errors at optimal power for a uniform wall resistance. We also show the power variation for higher order azimuthal variations m=1, 2, and 4. These may be caused by fountain tilts, nonuniform detection of atoms, and asymmetries in the laser trapping and cooling of the atoms. We demonstrate that distributed cavity phase errors in physical cavities may have no variation with the microwave power. A combination of rigorous calculations of cavity losses, measurements of power dependence, the atomic distributions, and fountain tilts, and electrical measurements that show the lower limit of the cavity Q and the cavity symmetry, should provide stringent limits on distributed cavity phase errors for current atomic clocks
Examines cylindrical TE/sub 011/ microwave cavities and finds large phase shifts of the microwave field near the edges of the cut-off waveguide apertures, where there are nodes in the field. The phase shifts lead to a potential distributed cavity phase shift for atomic clocks. Using an additional larger diameter cut-off waveguide section can effectively exclude the nodes and the large phase shifts from the atomic trajectories. It has been suggested that recoils from the absorption of microwave photons lead to frequency shift and also a loss of fringe contrast. We present measurements of the contrast for up to 2 19/spl pi//2 pulses and find no loss of contrast beyond that expected from measuring microwave field inhomogeneities with up to 19/spl pi/ Rabi pulses.
We give a review of recent advances in the accuracy of atomic fountain clocks. The new features are improved experimental and theoretical treatments of distributed cavity phase shifts and a full modeling of microwave lensing. Here we highlight that state selection is often highly non-uniform when Rabi flopping is used instead of an interrupted adiabatic frequency chirp. We show that detuning the state-selection microwave field as well as changing its amplitude can give a much more homogeneous state selection. A spatially inhomogeneous state selection corrupts the density extrapolation because the density distribution changes, which also mixes effects from distributed cavity phase and microwave lensing. This is expected to be important for the microgravity clock PHARAO on ACES, and can also improve fountain clocks.
We demonstrate a convenient experimental method, that facilitates faster and more accurate evaluation of the distributed cavity phase, a leading systematic effect in atomic fountain clocks. We expand on earlier work by Nemitz et al., which showed that displacement of the atoms from the microwave cavity axis can lead to an asymmetry in resonances observed for hyperfine transitions with ΔmF= 1. By applying an additional small transverse magnetic field, with controlled magnitude and direction, we are able to extract from the measured asymmetry the atom cloud's crossing position to within a fraction of a millimeter.
A preliminary calculation of the frequency shifts resulting from the distributed phase of a rectangular cavity is used to model frequency measurements of the fountain clock NRC-FCs1. The calculation is based on a numerical evaluation of the cavity field made with a finite element EM solver. The frequency shift is obtained by solving the Bloch-equations numerically along the path of the atoms on the free-fall trajectories through the cavity. We study the frequency shifts as a function of the launch direction, the tilt of the physics package and offsets in the position of the MOT relative to the axis defined by the state-selection cavity and the Ramsey cavity.
Abstract—We demonstrate a prototype of a laser-cooled 87Rb fountain clock. We report a preliminary measurement of the frequency shift due to cold collisions and find the shift to be at least a factor of ten less than that in a laser-cooled Cs clock. We also demonstrate the use of the ac Zeeman shift to measure the response of a microwave cavity. Finally, we have demonstrated a juggling atomic fountain and discuss the application of this technique to fountain and microgravity atomic clocks. Index Terms—Atomic clock, microwave resonators, microwave spectroscopy, rubidium materials/devices. I.
Abstract : The grant as in support of a research program to explore the possibility of a microwave atomic clock based on an atomic fountain of cesium atoms. During the two year granting period, the following work was done: A large magneto-optic trap in a vapor cell was constructed where over 4x 10(exp 10) atoms were trapped at a density on the order of 10(exp 11) atoms/cu cm. This work increased the number of atoms optically trapped by a factor of -400 compared to previous work. The optical density of the atoms in this trap has a peak attenuation of e(-175). In an invited review article we examined the prospects for slow atom frequency standards. Most of the systematic effects that limit the current accuracy today's frequency standards decrease as the velocity of the atoms is reduced. We identified the one possible exception: collisions between ultra-cold atom in an atomic fountain could induce a phase shift that would ultimately limit the accuracy of the fountain clock. We brought the problem to the attention of B. Verhaar, who began a series of calculations on the effects of low energy collisions. jg p.4