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arXiv:physics/0309043 · Physical Review Letters

Ultrastable Optical Clock with Neutral Atoms in an Engineered Light Shift Trap

Hidetoshi Katori, Masao Takamoto, V. G. Pal’chikov, V. D. Ovsiannikov

Published Oct 24, 2003• 576 citations
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Abstract

An ultrastable optical clock based on neutral atoms trapped in an optical lattice is proposed. Complete control over the light shift is achieved by employing the 5s(2) 1S0-->5s5p 3P0 transition of 87Sr atoms as a "clock transition." Calculations of ac multipole polarizabilities and dipole hyperpolarizabilities for the clock transition indicate that the contribution of the higher-order light shifts can be reduced to less than 1 mHz, allowing for a projected accuracy of better than 10(-17).

DOI
10.1103/physrevlett.91.173005

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An ultrastable optical clock based on neutral atoms trapped in an optical lattice is proposed. Complete control over the light shift is achieved by employing the 5s(2) 1S0-->5s5p 3P0 transition of 87Sr atoms as a "clock transition." Calculations of ac multipole polarizabilities and dipole hyperpolarizabilities for the clock transition indicate that the contribution of the higher-order light shifts can be reduced to less than 1 mHz, allowing for a projected accuracy of better than 10(-17).
The authors report the observation of the hyperpolarizability frequency shift due to the trapping field in a87Sr optical lattice clock. The authors show that at the magic wavelength of the lattice, where the first order term cancels, this higher order shift will not constitute a limitation to the fractional accuracy of the clock down to the 10-18level. This result is achieved by operating the clock at very high trapping intensity up to 400 kW/cm2and by a specific study of the effect of the two two-photon transitions near the magic wavelength. The authors also report an accurate frequency measurement of the clock transition. The frequency is determined to be v1S0-3P0= 429 228 004 229 879 (5) Hz with a fractional uncertainty that is comparable to state-of-the-art optical clocks with neutral atoms in free fall
An optical atomic clock scheme is proposed that utilizes two lasers to establish coherent coupling between the 5s2 1S0 ground state of 88Sr and the first excited state, 5s5p 3P0. The coupling is mediated by the broad 5s5p 1P1 state, exploiting the phenomenon of electromagnetically induced transparency. The effective linewidth of the clock transition can be chosen at will by adjusting the laser intensity. By trapping the 88Sr atoms in an optical lattice, long interaction times with the two lasers are ensured; Doppler and recoil effects are eliminated. Based on a careful analysis of systematic errors, a clock accuracy of better than 2 x 10(-17) is expected.
A sharp resonance line that appears in three-photon transitions between the 1S0 and 3P0 states of alkaline earth and Yb atoms is proposed as an optical frequency standard. This proposal permits the use of the even isotopes, in which the clock transition is narrower than in proposed clocks using the odd isotopes and the energy interval is not affected by external magnetic fields or the polarization of trapping light. With this method, the width and the rate of the clock transition can, in principle, be continuously adjusted from the MHz level to sub-mHz without loss of signal amplitude by varying the intensities of the three optical beams. Doppler and recoil effects can be eliminated by proper alignment of the three optical beams or by point confinement in a lattice trap. Light-shift effects on the clock accuracy can be limited to below a part in 10(18).
We report calculations assessing the ultimate precision of an atomic clock based on the 578 nm $6{}^{1}{S}_{0}\ensuremath{\rightarrow}6{}^{3}{P}_{0}$ transition in Yb atoms confined in an optical lattice trap. We find that this transition has a natural linewidth less than 10 mHz in the odd Yb isotopes, caused by hyperfine coupling. The shift in this transition due to the trapping light acting through the lowest order ac polarizability is found to become zero at the magic trap wavelength of about 752 nm. The effects of Rayleigh scattering, multipole polarizabilities, vector polarizability, and hyperfine induced electronic magnetic moments can all be held below 1 mHz (about one part in 1018).{10}^{18}).1018). In the case of the hyperpolarizability, however, larger shifts due to nearly resonant terms cannot be ruled out without an accurate measurement of the magic wavelength.
Optical lattice clocks combine the accuracy and stability required for next-generation frequency standards. At the heart of these clocks are carefully engineered optical lattices tuned to a wavelength where the differential AC Stark shift between ground and excited states vanishes—the so called ‘magic’ wavelength. To date, only alkaline-earth-like atoms utilizing clock transitions with total electronic angular momentum J=0 have successfully realized these magic wavelength optical lattices at the level necessary for state-of-the-art clock operation. In this article, we discuss two additional types of clock transitions utilizing states with J≠0, leveraging hyperfine structure to satisfy the necessary requirements for controlling lattice-induced light shifts. We propose realizing (i) clock transitions between same-parity clock states with total angular momentum F=0 and (ii) M1/E2 clock transitions between a state with F=0 and a second state with J=1/2, mF=0. We present atomic species which fulfill these requirements before giving a detailed discussion of both manganese and copper, demonstrating how these transitions provide the necessary suppression of fine structure-induced vector and tensor lattice light shifts for clock operations. Such realization of alternative optical lattice clocks promises to provide a rich variety of new atomic species for neutral atom clock operation, with applications from many-body physics to searches for new physics.
We experimentally investigate the lattice-induced light shift by the electric-quadrupole (E2) and magnetic-dipole (M1) polarizabilities and the hyperpolarizability in Sr optical lattice clocks. Precise control of the axial as well as the radial motion of atoms in a one-dimensional lattice allows observing the E2-M1 polarizability difference. Measured polarizabilities determine an operational lattice depth to be 72(2)E_{R}, where the total light shift cancels to the 10^{-19} level, over a lattice-intensity variation of about 30%. This operational trap depth and its allowable intensity range conveniently coincide with experimentally feasible operating conditions for Sr optical lattice clocks.