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

Phase modulation with independent cavity-phase control in laser cooled clocks in space

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

Published Nov 13, 2002• 10 citations
Publisher

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. 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.

DOI
10.1109/freq.2001.956155

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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.
In this paper we describe key aspects of the conceptual design of the microwave interrogation structure in the laser-cooled cesium frequency standard that is part of the primary atomic reference clock in space (PARCS) experiment. The PARCS standard uses balls of cold atoms launched in a pulsed beam configuration. The microwave interrogation will take place in two independent high-Q (/spl sim/20,000) cavities operated in the TE/sub 011/ mode. The cavities will be operated off resonance by several linewidths, with a resonant coupling structure delivering the microwave to the two cavities. One persistent problem related to the end-to-end phase shift has been the extreme temperature sensitivity of the phase of inside the cavities to that just outside the cavities. The end-to-end phase shift must ultimately be known to around 3 microradians, and stable long enough to allow measurement of the shift as well as to allow normal clock operation. Operating the cavities off resonance reduces this sensitivity more strongly than reducing the cavity Q.
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.
Sophisticated Ramsey-based interrogation protocols using composite laser pulse sequences have been recently proposed to provide next-generation high-precision atomic clocks with a near perfect elimination of frequency shifts induced during the atom-probing field interaction. We propose here a simple alternative approach to the autobalanced Ramsey interrogation protocol and demonstrate its application to a cold-atom microwave clock based on coherent population trapping (CPT). The main originality of the method, based on two consecutive Ramsey sequences with different dark periods, is to sample the central Ramsey fringes with frequency jumps finely adjusted by an additional frequency-displacement concomitant parameter, scaling as the inverse of the dark period. The advantage of this displaced frequency-jump Ramsey method is that the local oscillator (LO) frequency is used as a single physical variable to control both servo loops of the sequence, simplifying its implementation and avoiding noise associated with controlling the LO phase. When tested using a CPT cold-atom clock, the DFJR scheme reduces the sensitivity of the clock frequency to variations of the light shifts by more than an order of magnitude compared with the standard Ramsey interrogation. This simple method can be applied in a wide variety of Ramsey-spectroscopy based applications including frequency metrology with CPT-based and optical atomic clocks, 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.
We describe a method to stabilize the amplitude of the interrogating microwave field in compact atomic clocks working in a Ramsey approach. In this technique, we take advantage of the pulsed regime to use the atoms themselves as microwave amplitude discriminators. Specifically, in addition to the dependence on the microwave detuning, the atomic signal after the Ramsey interrogation acquires a dependence on the microwave pulse area (amplitude times duration) that can be exploited to implement an active stabilization of the microwave field amplitude, in a similar way in which the Ramsey clock signal is used to lock the local oscillator frequency to the atomic reference. This stabilization results in a reduced sensitivity of the clock frequency to microwave amplitude fluctuations that are transferred to the atoms through the cavity-pulling effect. The proposed technique is then effective to improve the clock stability and drift on medium and long term. We demonstrate the method for a vapor-cell clock working with a hot sample of atoms but it can be extended to cold-atom compact clocks.