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arXiv:physics/0512244

High-Accuracy Microwave Atomic Clock via Magic Optical Lattice

Xiaoji Zhou, Xuzong Chen, Jingbiao Chen

Published Dec 25, 2005• 3 citations
arXivHTMLPDF

Abstract

A microwave atomic clock scheme based on Rb and Cs atoms trapped in optical lattice with magic wavelength for clock transition is proposed. The ac Stark shift of clock transition due to trapping laser can be canceled at some specific laser wavelengths. Comparing with in fountain clock, the cavity related shifts, the collision shift, and the Doppler effect are eliminated or suppressed dramatically in atomic clock when the magic optical lattice is exploited. By carefully analyzing various sources of clock uncertainty, we conclude that a microwave atomic clock with an accuracy of better than $2\times10^{-17}$ is feasible, which is of the same accuracy as the expected best optical atomic clock.

DOI
10.48550/arxiv.physics/0512244

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A microwave atomic clock scheme based on Rb and Cs atoms trapped in optical lattice with magic wavelength for clock transition is proposed. The ac Stark shift of clock transition due to trapping laser can be canceled at some specific laser wavelengths. Comparing with in fountain clock, the cavity related shifts, the collision shift, and the Doppler effect are eliminated or suppressed dramatically in atomic clock when the magic optical lattice is exploited. By carefully analyzing various sources of clock uncertainty, we conclude that a microwave atomic clock with an accuracy of better than 2×10−172\times10^{-17}2×10−17 is feasible, which is of the same accuracy as the expected best optical atomic clock.
A scheme for a microwave atomic clock is proposed for Cs or Rb atoms trapped in a blue detuned optical lattice. The ac Stark shift of the clock transition due to a trapping laser is calculated. We analyze it at some specific laser wavelength. Compared with the case of the fountain clock, the cavity related shifts, the collision shift and the Doppler effect are eliminated or suppressed dramatically in an atomic lattice clock. By analyzing various sources of clock uncertainty, a microwave atomic lattice clock with a high accuracy and small volume is feasible.
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
We propose a new class of atomic microwave clocks based on the hyperfine transitions in the ground state of aluminum or gallium atoms trapped in optical lattices. For such elements magic wavelengths exist at which both levels of the hyperfine doublet are shifted at the same rate by the lattice laser field, cancelling its effect on the clock transition. A similar mechanism for the magic wavelengths may work in microwave hyperfine transitions in other atoms which have the fine-structure multiplets in the ground state.
We demonstrate the cancellation of the differential ac Stark shift of the microwave hyperfine clock transition in trapped 87Rb^{87}\mathrm{Rb}87Rb atoms. Recent progress in metrology exploits so-called magic wavelengths, whereby an atomic ensemble can be trapped with laser light whose wavelength is chosen so that both levels of an optical atomic transition experience identical ac Stark shifts. Similar magic-wavelength techniques are not possible for the microwave hyperfine transitions in the alkali metals due to their simple electronic structure. We show, however, that ac Stark shift cancellation is indeed achievable for certain values of wavelength, polarization, and magnetic field. The cancellation comes at the expense of a small magnetic-field sensitivity. The technique demonstrated here has implications for experiments involving the precise control of optically trapped neutral atoms.
After being pumped from the 5 s 1/2 ground state to the 6 p 1/2 state, the population inversion between 6 s 1/2 and 5 p 1/2,3/2 can be established for a rubidium four-level active optical clock. We calculate the ac Stark shift due to lattice trapping laser which dominates the frequency shift of clock transition in a lattice trapped rubidium four-level active optical clock. Several magic wavelengths are found, which can form desired optical lattice trapping potential. By choosing a proper intensity and linewidth of the trapping laser, the fractional frequency uncertainty of clock transition due to the ac Stark shift of the trapping laser, is estimated to be below 10 −18 .
We demonstrate the state-of-the-art technique of an active clock to provide a continuous superradiant lasing signal using an ensemble of trapped Cs atoms in an optical lattice. A magic wavelength of the proposed $|7{S}_{1/2};F=4,{M}_{F}=0\ensuremath{\rangle}\ensuremath{\rightarrow}|6{P}_{3/2};F=3,{M}_{F}=0\ensuremath{\rangle}$ clock transition in Cs atoms is identified at 1181 nm for constructing the optical lattice. Pertinent optical lines are also found for pumping and repumping atoms from their ground states. A fractional uncertainty about ${10}^{\ensuremath{-}15}$ in the clock frequency has been predicted by carrying out rigorous calculations of several atomic properties. The bad-cavity operational mode of the active clock is anticipated to improve remarkably its short-term stability by suppressing intrinsic thermal fluctuations. Thus, a composite clock system with better short-term and long-term stabilities can be built by combining the proposed active clock with another high-accuracy passive optical clock.