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arXiv:physics/0610098 · Physical Review Letters

Cancellation of Stark Shifts in Optical Lattice Clocks by Use of Pulsed Raman and Electromagnetically Induced Transparency Techniques

T. Zanon-Willette, Andrew D. Ludlow, Sebastian Blatt, Martin M. Boyd, E. Arimondo, Jun Ye

Published Dec 7, 2006• 49 citations
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Abstract

We propose a combination of electromagnetically induced transparency-Raman and pulsed spectroscopy techniques to accurately cancel frequency shifts arising from electromagnetically induced transparency fields in forbidden optical clock transitions of alkaline earth atoms. At appropriate detunings, time-separated laser pulses are designed to trap atoms in coherent superpositions while eliminating off-resonance ac Stark contributions, achieving efficient population transfer up to 60% with inaccuracy <10(-17). Results from the wave-function formalism are confirmed by the density matrix approach.

DOI
10.1103/physrevlett.97.233001

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Quantum engineering of time-separated Raman laser pulses in three-level systems is presented to produce an ultranarrow optical transition in bosonic alkali-earth clocks free from light shifts and with a significantly reduced sensitivity to laser parameter fluctuations. Based on a quantum artificial complex wave-function analytical model and supported by a full density-matrix simulation including a possible residual effect of spontaneous emission from the intermediate state, atomic phase shifts associated with Ramsey and hyper-Ramsey two-photon spectroscopy in optical clocks are derived. Various common-mode Raman frequency detunings are found in which the frequency shifts from off-resonant states are canceled, while their uncertainties at the ${10}^{\ensuremath{-}18}$ level of accuracy are strongly reduced.
We study analytically the dynamic cancelation of the AC Stark shift in a three-level pulsed optical lattice clock by solving the time-dependent density-matrix equations in the adiabatic following limit. We found an optimum value of the common detuning Δ 0 of two coherent driving fields at which the dynamic AC Stark shift cancelled completely at an arbitrary field strength. The optimum value of Δ 0 for the well-studied Sr atoms agreed well with the values obtained by using other methods, for instance, a numerical calculation and a wave-function formalism. We give an optimum value of common detuning, Δ 0 = 65.3 MHz, for the pulsed Raman Yb optical lattice clock.
We demonstrate the cancellation of the differential ac Stark shift of the microwave hyperfine clock transition in trapped 87 Rb 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 alkalis, 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.
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.
The circular polarized laser beam of the “magic” wavelength used to produce an optical lattice for the time-frequency standard on neutral atoms may mix the 3P 1 state to the long-living metastable state 3P 0 thus providing significant enhancement of the strongly forbidden 1S 0 -3P 0 clock transition in even isotopes of alkaline-earth-like atoms. We present a detailed analysis of various factors influencing resolution and uncertainty for this kind of optical standard, including precise estimations of the “magic” wavelengths, transition matrix elements and field induced second- and fourth-order ac Stark shifts for the ground and metastable alkaline-earth-like atoms.