Optical Lattice Polarization Effects on Hyperpolarizability of Atomic Clock Transitions

Abstract

The light-induced frequency shift due to the 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.PACS numbers: 42.50. Gy, 39.30.+w, 42.62.Fi, 42.62.Eh In recent years significant attention has been devoted to optical lattice atomic clocks [1,2], in part because the prospects for a fractional frequency uncertainty of such a clock could achieve of the level 10 −17 -10 −18 . Apart from obvious practical applications, such improved clocks will be critical for a variety of terrestrial and space-borne applications including improved tests of the basic laws of physics and searches for drifts in the fundamental constants [3]. The crucial ingredient, for achieving such high metrological performance, is the existence of the magic wavelength λ m , at which the first-order (in intensity) light shift of the clock transition 1 S 0 → 3 P 0 cancels for alkaline-earth-like atoms (such as Mg, Ca, Sr, Yb, Zn, Cd). To date in several experiments cold atoms were trapped in optical lattices at the magic wavelength and the clock transition was observed [2,4,5,6]. From the metrological viewpoint even isotopes (with zero nuclear spin) are more attractive. To excite strictly forbidden clock transitions in even isotopes the method of magnetic field-induced spectroscopy was proposed [7] and used [5].Obviously, the achievement of such an extraordinary accuracy in frequency standards is a challenging goal. On the way to this goal it will be necessary to use new approaches and to solve step-by-step the critical physical problems [2]. For example, since at the magic wavelength λ m the first-order shift vanishes, one of the main factors that limits the accuracy of these optical clocks is the second-order shift due to the atomic hyperpolarizability. Indeed, for the formation of optical lattices with the potential depth of order of MHz [2,4,5,6] it is necessary to use laser beams with the intensity at a level of a few tens of kW/cm 2 . According to our numerical estimates for different alkaline-earth-like atoms [8,9] and first experimental observations for Sr [6], the second-order shift can be at a level of 1-10 Hz in such high-intensity fields. In this case to get planned accuracy we need strictly to control the spatially non-uniform optical lattice fields at a level of 10 −3 -10 −5 under conditions of strong focusing, reflections and interference of light beams. Here apart from long-term stabilization of the lase...

Lattice-Induced Frequency Shifts in Sr Optical Lattice Clocks at the10−17Level

“…For ¼ 0, we observe no trap depth dependence of the clock frequency, meaning that the lattice is tuned to the magic wavelength. Though it is not resolved here, the hyperpolarizability shift is expected to depend on the lattice geometry [23]. However, whatever this dependence, there exists at least one configuration where the effect is smaller than the weighted mean of the two data sets:…”

Lattice-based optical clock using an even isotope of Yb

“…This same transition in the even isotopes is even less sensitive to lattice polarization, and could simplify the control requirements of the lattice polarization and allow for even more accurate clocks. 13 In addition, the lack of Zeeman substructure simplifies the spectroscopy and eliminates optical pumping issues. Unfortunately, the mechanism that induces the polarization sensitivity in the odd isotopes, the hyperfine interaction, also generates the non-zero excitation probability between the two states.…”

Present status of the development of an Yb optical lattice clock at NMIJ/AIST (National Metrology Institute of Japan / National Institute of Advanced Industrial Science and Technology)

“…Furthermore, a recent measurement of the higher order light shift by the lattice far off resonant trap (FORT) laser, which has been a great concern due to the closeness of the two-photon transition energy and that of the 'magic' wavelength [2] laser, indicated that its effect is practically negligible [12]. Especially of interest is that by choosing the proper circular polarization of the lattice FORT laser, its higher order light shift is reduced to be less than 4 mHz [12,13].…”