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arXiv:physics/0606214 · Physical Review Letters

Optical Lattice Polarization Effects on Hyperpolarizability of Atomic Clock Transitions

А. В. Тайченачев, Valeriy I. Yudin, Vitalii D Ovsiannikov, Vitalii G Pal'chikov

Published Oct 25, 2006• 31 citations
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Abstract

The light-induced frequency shift due to hyperpolarizability (i.e., terms of second-order in intensity) is studied for a forbidden optical transition, J = 0 --> J = 0. A simple universal dependence on the field ellipticity is obtained. This result allows minimization of the second-order light shift with respect to the field polarization for optical lattices operating at a magic wavelength (at which the first-order shift vanishes). We show the possibility for the existence of a magic elliptical polarization, for which the second-order frequency shift vanishes. The optimal polarization of the lattice field can be either linear, circular, or magic elliptical. The obtained results could improve the accuracy of lattice-based atomic clocks.

DOI
10.1103/physrevlett.97.173601

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The light-induced frequency shift due to hyperpolarizability (i.e., terms of second-order in intensity) is studied for a forbidden optical transition, J = 0 --> J = 0. A simple universal dependence on the field ellipticity is obtained. This result allows minimization of the second-order light shift with respect to the field polarization for optical lattices operating at a magic wavelength (at which the first-order shift vanishes). We show the possibility for the existence of a magic elliptical polarization, for which the second-order frequency shift vanishes. The optimal polarization of the lattice field can be either linear, circular, or magic elliptical. The obtained results could improve the accuracy of lattice-based atomic clocks.
We derive the frequency shift for a forbidden optical transition $J=0\ensuremath{\rightarrow}{J}^{\ensuremath{'}}=0$ caused by the simultaneous actions of an elliptically polarized lattice field and a static magnetic field. We find that a simple configuration of lattice and magnetic fields leads to a cancellation of this shift to first order in lattice intensity and magnetic field. In this geometry, the second-order lattice intensity shift can be minimized as well by use of optimal lattice polarization. Suppression of these shifts could considerably enhance the performance of the next generation of atomic clocks.
We present an experimental study of the lattice-induced light shifts on the (1)S(0) --> (3)P(0) optical clock transition (nu(clock) approximately 518 THz) in neutral ytterbium. The "magic" frequency nu(magic) for the 174Yb isotope was determined to be 394 799 475(35) MHz, which leads to a first order light shift uncertainty of 0.38 Hz. We also investigated the hyperpolarizability shifts due to the nearby 6s6p(3)P(0) --> 6s8p(3)P(0), 6s8p(3)P(2), and 6s5f(3)F(2) two-photon resonances at 759.708, 754.23, and 764.95 nm, respectively. By measuring the corresponding clock transition shifts near these two-photon resonances, the hyperpolarizability shift was estimated to be 170(33) mHz for a linear polarized, 50 microK deep, lattice at the magic wavelength. These results indicate that the differential polarizability and hyperpolarizability frequency shift uncertainties in a Yb lattice clock could be held to well below 10(-17).
We report the observation of a higher-order frequency shift due to the trapping field in a (87)Sr optical lattice clock. We show that, at the magic wavelength of the lattice, where the first-order term cancels, the higher-order shift will not constitute a limitation to the fractional accuracy of the clock at a level of 10(-18). This result is achieved by operating the clock at very high trapping intensity up to 400 kW/cm(2) and by a specific study of the effect of the two two-photon transitions near the magic wavelength.
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
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.
We investigated the properties of optical lattice clocks operated with a repulsive light-shift potential. The magic wavelength, where light-shift perturbation for the clock transition cancels, was experimentally determined to be 389.889(9) nm for 87Sr. The hyperpolarizability effects on the clock transition were investigated theoretically. With minimal trapping field perturbation provided by the blue-detuned lattice, the fractional uncertainty due to the hyperpolarizability effects was found to be 2x10;{-19} in the relevant clock transition.