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

Distributed cavity phase shifts and microwave photon recoils

Chad Fertig, Ruoxin Li, J.I. Rees, Kurt Gibble

Published Jun 25, 2003• 10 citations
Publisher

Abstract

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.

DOI
10.1109/freq.2002.1075928

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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 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
We investigate theoretically and by numerical simulations the effects of the atomic recoil on the frequency and fringe contrast of microwave atomic frequency standards. Such effects arise because of the influence of external degrees of freedom on the phases and the spatial positions of the interfering wave packets. We show under which conditions such effects lead to a frequency shift and examine the loss of contrast of the interference signal (Ramsey fringes). We use an interferometric description to model the frequency standards, treating simultaneously internal and external degrees of freedom. We consider multiple momentum exchanges in 3D between the atoms and the standing microwave field inside the cavity leading to a large number of wave packets that leave the cavity with different momenta. At detection, these wave packets interfere giving rise to Ramsey fringes that are modulated by the interference of the external states of the wave packets. Similar treatments have proved efficient when treating ID recoil effects in standing laser waves. We apply this theoretical model numerically to laser cooled atomic fountain frequency standards and investigate the behaviour of the observed signal as a function of the frequency standard parameters (microwave power, launching height, etc.). Finally, we discuss possible experimental methods that could be used to observe such effects.
We report on a theoretical analysis of the phase-shift in compact atomic clocks working either with cold or thermal atoms. It is well known that in a microwave cavity with electromagnetic losses, a traveling wave adds to the standing wave of a given resonant mode. We calculate the spatial varying phase related to this travelling wave for two geometries of interest in clock applications, the cylindrical cavity and the spherical cavity. Due to their motion, the atoms probe different regions of the cavity and then experience different phases of the interrogating microwave field. We show that this combination of atomic motion and spatial changing phase results in a phase-shift of the clock frequency, well known in primary frequency standards, that can affect the metrological performances also of vapor cell and compact cold-atom clocks. In the latter case, we evaluate the phase-shift for a space clock and a ground clock.
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 employ a three-level Bloch vector model to simulate Ramsey fringes of our Rb vapor-cell atomic clock. The residual inhomogeneity of the microwave magnetic field across the buffer-gas cell is a key ingredient for correctly modelling the behavior at high microwave powers (pulse area > π/2. We add to this model different position-dependent frequency shifts that arise from external fields, and we identify inhomogeneous light-shifts as the dominant contribution for reproducing the measured clock frequency shifts as a function of microwave power. Other frequency shifts give negligible contributions.