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European Frequency and Time Forum

Fountain clock accuracy

Kurt Gibble

Published Apr 1, 2012• 6 citations
Publisher

Abstract

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.

DOI
10.1109/eftf.2012.6502323

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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

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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 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
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
Our recent work showed the atomic microwave clock configuration beyond fountain is possible by trapped Rb or Cs atoms in optical lattice formed by trapping laser operating at magic wavelength for microwave clock transition where light shifts on both clock levels are matching exactly, and an accuracy of 2 times 10-17at this clock configuration is expected. In this report, we analyze the possibility of 20 s coherent interrogation time of stable Rb or Cs clock transition, which corresponds to a 2 km height atomic fountain. We propose a simple experimental scheme to measure the needed magic wavelengths for atomic microwave clocks in conventional fountain configuration. Moreover, we discuss a new clock scheme combining fountain and lattice configurations, thus provide an easy way to improve fountain clock performance by adding a trapping laser beam in conventional fountain system without any further complicated modifications