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European Frequency and Time Forum

Phase modulation for reduced vibration sensitivity in laser-cooled clocks in space

William M. Klipstein, G.J. Dick, Steven R. Jefferts, Fred L. Walls

Published Mar 6, 2001• 5 citations
OpenAlex

Abstract

The standard interrogation technique in atomic beam clocks is square-wave frequency modulation (SWFM), which suffers a first order sensitivity to vibrations as changes in the transit time of the atoms translates to perceived frequency errors. Square-wave phase modulation (SWPM) interrogation eliminates sensitivity to this noise.

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The standard interrogation technique in atomic beam clocks is square-wave frequency modulation(SWFM), which suffers a first-order sensitivity to vibrations as changes in the transit time of the atoms translates to perceived frequency errors. Square-wave phase modulation (SWPM) interrogation eliminates sensitivity to this noise. We present a particular scheme utilizing independent phase control of the two cavities. The technique is being considered for use with the Primary Atomic Reference Clock in Space (PARCS), a laser-cooled cesium clock scheduled to fly aboard the International Space Station in 2005. In addition to eliminating first-order sensitivity to vibrations, the minimum attack time now in this scheme is the Rabi pulse time (t), rather than the Ramsey time (T). This helps minimize dead time and the degradation of stability due to aliasing.

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The standard interrogation technique in atomic beam clocks is square-wave frequency modulation(SWFM), which suffers a first-order sensitivity to vibrations as changes in the transit time of the atoms translates to perceived frequency errors. Square-wave phase modulation (SWPM) interrogation eliminates sensitivity to this noise. We present a particular scheme utilizing independent phase control of the two cavities. The technique is being considered for use with the Primary Atomic Reference Clock in Space (PARCS), a laser-cooled cesium clock scheduled to fly aboard the International Space Station in 2005. In addition to eliminating first-order sensitivity to vibrations, the minimum attack time now in this scheme is the Rabi pulse time (t), rather than the Ramsey time (T). This helps minimize dead time and the degradation of stability due to aliasing.
Optical clock interrogation protocols, based on laser-pulse spectroscopy, are suffering from probe-induced frequency-shifts and their variations induced by laser power. Original Hyper-Ramsey probing scheme, which was proposed to alleviate those issues, does not apply below fractional frequency changes of 10-18when decoherence and relaxation by spontaneous emission or collisions are present. We present a universal interrogation protocol based on composite laser-pulses spectroscopy with phase-modulation for both fermionic and bosonic optical clocks, eliminating probe-induced frequency-shifts at all orders even in presence of various dissipative processes. This scheme, using a magic combination of ±π/4 and ±3π/4 phase-modulated generalized Hyper-Ramsey resonances, extremely robust to errors in laser parameters, can be applied to atomic, molecular and nuclear frequency metrology, mass spectrometry and precision spectroscopy.
Atomic clocks provide a reproducible basis for our understanding of time and frequency. Recent demonstrations of compact optical clocks, employing thermal atomic beams, have achieved short-term fractional frequency instabilities of order ${10}^{\ensuremath{-}16}$, competitive with the best international frequency standards available. However, a serious challenge inherent in compact clocks is the necessarily smaller optical beams, which results in rapid variation in interrogating wave fronts. This can cause inhomogeneous excitation of the thermal beam leading to long-term drifts in the output frequency. Here we develop a model for Ramsey-Bord\'e interferometry using optical fields with curved wave fronts and simulate the 40Ca^{40}\mathrm{Ca}40Ca beam clock experiment described by Olson et al. [Phys. Rev. Lett. 123, 073202 (2019)]. The results of Olson et al. showed surprising and unexplained behavior in the response of the atoms in the interrogation. Our model predicts signals consistent with experimental data and can account for the significant sensitivity to laser geometry that was reported. We find the signal-to-noise ratio is maximized when the laser is uncollimated at the interrogation zones to minimize inhomogeneity and also identify an optimal waist size determined by both laser inhomogeneity and the velocity distribution of the atomic beam. We investigate the shifts and stability of the clock frequency, showing that the Gouy phase is the primary source of frequency variations arising from laser geometry.
The error signal which is used to control the frequency of the quartz crystal oscillator of a passive rubidium cell frequency standard is considered. The value of the slope of this signal, for an interrogation frequency close to the atomic transition frequency is calculated and measured for various phase (or frequency) modulation waveforms, and for several values of the modulation frequency. A theoretical analysis is made using a model which applies to a system in which the optical pumping rate, the relaxation rates and the RF field are homogeneous. Results are given for sine-wave phase modulation, square-wave frequency modulation and square-wave phase modulation. The influence of the modulation frequency on the slope of the error signal is specified. It is shown that the modulation frequency can be chosen as large as twice the non-saturated full-width at half-maximum without a drastic loss of the sensitivity to an offset of the interrogation frequency from center line, provided that the power saturation factor and the amplitude of modulation are properly adjusted.
Atom interferometers that operate in the spatial domain through continuous measurement of an atomic beam provide benefits in the elimination of sensor dead time and reduced sensitivity to certain noise sources. Further improving its operation, time-domain control of a spatial-domain interferometer can provide necessary methods of error suppression and dynamic range improvement. We model numerically and experimentally demonstrate methods of time-domain control in a 3D-cooled atomic beam interferometer. We demonstrate suppression of magnetic-field-induced phase noise through rapid reversal of the direction of inertial sensitivity at a rate faster than the inverse interrogation time of the interferometer.
In atom interferometry the phase evolution of a quantum superposition state is measured with respect to a reference signal. The measurement has a limited unambiguous interval, since not the phase but its projection is measured as a population unbalance on two energetic levels. Resolving phase wrapping brings to a longer interrogation interval and hence instrument sensitivity. We extended the unambiguous probe interval using coherence preserving measurements and phase corrections, and demonstrated the phase lock of the clock oscillator to an atomic superposition state. On this basis we implemented a protocol to improve atomic clocks limited by local oscillator noise, which is the case of optical atomic clocks, nowadays the best frequency standard in terms of both accuracy and precision. The technique could be adopted to enhance the sensitivity of atomic gravimeters.