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arXiv:physics/0504080 · Physical Review A

Optical lattice clock with atoms confined in a shallow trap

P. Lemonde, Peter Wolf

Published Sep 16, 2005• 114 citations
arXivHTMLPDF

Abstract

We study the trap depth requirement for the realization of an optical clock using atoms confined in a lattice. We show that site-to-site tunneling leads to a residual sensitivity to the atom dynamics hence requiring large depths [$(50\text{--}100){E}_{r}$ for Sr] to avoid any frequency shift or line broadening of the atomic transition at the ${10}^{\ensuremath{-}17}\text{--}{10}^{\ensuremath{-}18}$ level. Such large depths and the corresponding laser power may, however, lead to difficulties (e.g., higher-order light shifts, two-photon ionization, technical difficulties) and therefore one would like to operate the clock in much shallower traps. To circumvent this problem we propose the use of an accelerated lattice. Acceleration lifts the degeneracy between adjacents potential wells which strongly inhibits tunneling. We show that using the Earth's gravity, much shallower traps (down to $5{E}_{r}$ for Sr) can be used for the same accuracy goal.

DOI
10.1103/physreva.72.033409

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We study the trap depth requirement for the realization of an optical clock using atoms confined in a lattice. We show that site-to-site tunneling leads to a residual sensitivity to the atom dynamics hence requiring large depths [(50–100)Er(50\text{--}100){E}_{r}(50–100)Er​ for Sr] to avoid any frequency shift or line broadening of the atomic transition at the 10\ensuremath−17–10\ensuremath−18{10}^{\ensuremath{-}17}\text{--}{10}^{\ensuremath{-}18}10\ensuremath−17–10\ensuremath−18 level. Such large depths and the corresponding laser power may, however, lead to difficulties (e.g., higher-order light shifts, two-photon ionization, technical difficulties) and therefore one would like to operate the clock in much shallower traps. To circumvent this problem we propose the use of an accelerated lattice. Acceleration lifts the degeneracy between adjacents potential wells which strongly inhibits tunneling. We show that using the Earth's gravity, much shallower traps (down to 5Er5{E}_{r}5Er​ for Sr) can be used for the same accuracy goal.
We study the trap depth requirement for the realization of an optical clock using atoms confined in a lattice. We show that site-to-site tunnelling leads to a residual sensitivity to the atom dynamics hence requiring large depths (50 to 100 Erfor Sr) to avoid any frequency shift or line broadening of the atomic transition at the 10-17- 10-18level. Such large depths and the corresponding laser power may, however, lead to difficulties (e.g. higher order light shifts, two-photon ionization, technical difficulties) and therefore one would like to operate the clock in much shallower traps. To circumvent this problem we propose the use of an accelerated lattice. Acceleration lifts the degeneracy between adjacents potential wells which strongly inhibits tunnelling. We show that using the Earth's gravity, much shallower traps (down to 5 Erfor Sr) can be used for the same accuracy goal
The quantum metrology with ultra-high precision usually requires the atoms prepared in an ultra-stable environment with well-defined quantum states. Thus, the optical lattice clock system chooses deep lattice potential to trap the ultra-cold atoms. However, building atomic clock in shallow optical lattice can greatly reduce decoherence rate induced by Raman scattering as well as higher order light shift, but tunneling among the lattice sites will cause additional dephasing and strongly broadening of the Rabi spectrum. Here, we periodically drive the shallow 87^{87}87Sr optical lattice clock in the experiment. Counterintuitively, shaking the system can deform the wide broad spectral line into a sharp peak with 5.4Hz line-width. With careful comparison between the theory and experiment, we demonstrate the Rabi frequency and Bloch bands can be simultaneously and independently tuned by adjusting the driving frequency and amplitude. Our work not only provides a different idea for quantum metrology, such as building shallow optical lattice clock in outer space, but also paves the way for quantum simulation of new phase of matter, such as engineering exotic spin orbit coupling Hamiltonian.
Optical clocks benefit from tight atomic confinement enabling extended interrogation times as well as Doppler- and recoil-free operation. However, these benefits come at the cost of frequency shifts that, if not properly controlled, may degrade clock accuracy. Numerous theoretical studies have predicted optical lattice clock frequency shifts that scale nonlinearly with trap depth. To experimentally observe and constrain these shifts in an ^{171}Yb optical lattice clock, we construct a lattice enhancement cavity that exaggerates the light shifts. We observe an atomic temperature that is proportional to the optical trap depth, fundamentally altering the scaling of trap-induced light shifts and simplifying their parametrization. We identify an "operational" magic wavelength where frequency shifts are insensitive to changes in trap depth. These measurements and scaling analysis constitute an essential systematic characterization for clock operation at the 10^{-18} level and beyond.
Progress in atomic optical clocks with total uncertainty of ${10}^{\ensuremath{-}18}$ or below requires a precise estimation of multipolar and higher-order effects due to atom-field interactions. Magnesium is an attractive candidate for optical lattice clocks because it is insensitive to blackbody radiation and has a large quality factor. We employ a combined method of the Dirac-Fock plus core polarization and the relativistic configuration interaction to calculate the dynamic multipolar polarizabilities and the hyperpolarizabilities of the atomic Mg clock. The lattice light shift against variation of the laser detuning and trap depth is also investigated. We find that there exists a distinctive operational magic lattice intensity of 5.33(2)ER5.33(2){E}_{R}5.33(2)ER​ (ER{E}_{R}ER​ is the lattice photon recoil energy) that reduces the total light shift below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ over 1414%14 of the trap depth variation, which will pave the way for the development of a new time-frequency standard of the Mg lattice clock.
Optical lattice clocks in space could improve satellite navigation systems and enable new tests of fundamental physics, including gravitational-wave detection and tests of relativity. In microgravity, atoms can tunnel to degenerate neighboring lattice sites, broadening the clock transition and limiting coherence times. We demonstrate Aubry-André localization in a bichromatic optical lattice formed by two magic-wavelength lasers, suppressing tunneling in a horizontal lattice clock emulating free fall. We recover a Fourier-limited clock Rabi spectrum and measure Ramsey coherence times of up to 2 s in shallow lattices, with up to 100-fold improvement over the delocalized regime. These results establish Aubry-André localization as a practical route to controlling tunneling in future space-based clocks, and open a path to operating terrestrial clocks at shallower lattice depths.