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arXiv:1204.4354 · Chinese Physics Letters

Magic Wavelengths for a Lattice Trapped Rubidium Four-Level Active Optical Clock

Xiaorun Zang, Tonggang Zhang, Jingbiao Chen

Published Sep 1, 2012• 19 citations
arXivHTMLPDF

Abstract

After being pumped from the 5 s 1/2 ground state to the 6 p 1/2 state, the population inversion between 6 s 1/2 and 5 p 1/2,3/2 can be established for a rubidium four-level active optical clock. We calculate the ac Stark shift due to lattice trapping laser which dominates the frequency shift of clock transition in a lattice trapped rubidium four-level active optical clock. Several magic wavelengths are found, which can form desired optical lattice trapping potential. By choosing a proper intensity and linewidth of the trapping laser, the fractional frequency uncertainty of clock transition due to the ac Stark shift of the trapping laser, is estimated to be below 10 −18 .

DOI
10.1088/0256-307x/29/9/090601

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Magic wavelengths for laser trapping of barium atoms in the optical lattices are calculated with considering the optical clock transition at 1107 nm between the 6s 2 1 S 0 state and 6s5d 3 D 1 state. Theoretical calculation shows that there are several magic wavelengths with the linearly polarized trapping laser. The trap depths of the optical lattice and the slope of light shift difference with different magic wavelengths are also calculated. Some of these magic wavelengths are selected and recommended as potentially suitable magic wavelengths for the optical lattice trapping laser.

Chinese Physics Letters•Mar 1, 2015•2 citations
After being pumped from the 5 s 1/2 ground state to the 6 p 1/2 state, the population inversion between 6 s 1/2 and 5 p 1/2,3/2 can be established for a rubidium four-level active optical clock. We calculate the ac Stark shift due to lattice trapping laser which dominates the frequency shift of clock transition in a lattice trapped rubidium four-level active optical clock. Several magic wavelengths are found, which can form desired optical lattice trapping potential. By choosing a proper intensity and linewidth of the trapping laser, the fractional frequency uncertainty of clock transition due to the ac Stark shift of the trapping laser, is estimated to be below 10 −18 .
Wavelength-dependent AC Stark shifts and magic wavelengths of the terahertz clock transitions between the metastable triplet states 6s5d 3 D 1 and 6s5d 3 D 2 are investigated with considering the optical lattice trapping of barium atoms with the linearly polarized laser. The trap depths and the slopes of light shift difference with distinct magic wavelengths of the optical lattices are also discussed in detail. Several potentially suitable working points for the optical lattice trapping laser are recommended and selected from these magic wavelengths.
A microwave atomic clock scheme based on Rb and Cs atoms trapped in optical lattice with magic wavelength for clock transition is proposed. The ac Stark shift of clock transition due to trapping laser can be canceled at some specific laser wavelengths. Comparing with in fountain clock, the cavity related shifts, the collision shift, and the Doppler effect are eliminated or suppressed dramatically in atomic clock when the magic optical lattice is exploited. By carefully analyzing various sources of clock uncertainty, we conclude that a microwave atomic clock with an accuracy of better than 2×10−172\times10^{-17}2×10−17 is feasible, which is of the same accuracy as the expected best optical atomic clock.
Abstract The energy levels and electric dipole ( E 1 ) matrix elements of the ground state and low-lying excited states of Be atoms are calculated using the relativistic configuration interaction plus core polarization (RCICP) method. The static and dynamic E 1 , magnetic dipole ( M 1 ) and electric quadrupole ( E 2 ) polarizabilities as well as the hyperpolarizabilities of the 2 s 2 1 S 0 and 2 s 2 p 3 P 0 states are determined. Two magic wavelengths, 300.03 and 252.28 nm, of 2 s 2 1 S 0 → 2 s 2 p 3 P 0 clock transition are found. Then, the multipolar and nonlinear Stark shifts of the clock transition at the magic wavelength are discussed in detail. We find that when the laser intensity I is in the range of 14.3–15.9 kW cm−2 and the detuning δ (the frequency detuning of the lattice laser frequency relative to the magic frequency) is in the range of 40.7–40.9 MHz, the fractional Stark shifts of the clock transition are less than 1.0 × 10−18. While, when I is in the range of 15.01–15.46 kW cm−2 and δ is in the range of 40.73–40.76 MHz, the fractional Stark shifts are lower than 1.0 × 10−19.
State-of-the-art optical clocks based on neutral atoms have already surpassed the world's best microwave atomic clocks in both accuracy and stability, paving the way to high-precision measurements of elementary aspects of nature, like the search for the drift of fundamental constants or the application of relativistic geodesy.These clocks operate with ensembles trapped in an optical lattice.Normally, high-power trapping laser fields induce a large AC Stark shift on the clock's transition frequency, as the clock states have different polarizabilities.A key feature of lattice clocks is the magic wavelength, for which the atomic polarizabilities of the clock states are equal, therefore compensating a differential frequency shift on the clock transition.In the periodic potential of the optical lattice, the energy spectrum of motional states features a band structure, analogous to electrons in a crystalline structure well-known from solid state physics.Within this band structure, atoms can tunnel between adjacent lattice sites.As a consequence from tunneling motion, the clock transition experiences a frequency shift and a broadening, which becomes pronounced in the shallow lattice regime.This work presents the first demonstration of a 24 Mg optical lattice clock including the precise determination of the frequency of the clock transition, its magic wavelength and its second-order Zeeman shift.Furthermore, the effect of tunneling in an optical lattice for magnesium has been extensively studied via optical spectroscopy of Bloch bands and substantiated with theoretical models, that were initially developed for a strontium optical lattice clock.Measuring lattice light induced frequency shifts of the clock transition for various lattice wavelengths and intensities, yielded a value of the magic wavelength of the 1 S 0 → 3 P 0 clock transition in 24 Mg of 468.463(207) nm.This value is in well agreement with a recent theoretical calculation of 468.45(23) nm, using a refined atomic structure model.The experimental value for the magic wavelength was independently verified with optical spectroscopy of Bloch bands carried out on the clock transition.Here, the AC Stark modified band structure is directly probed by a single frequency scan of the carrier resonance, featuring an asymmetric line shape, that is strongly dependent on the lattice wavelength.This technique demonstrates a novel method for the determination of the magic wavelength and could also be applied to other atomic species.In bosonic isotopes of alkaline earth(-like) elements, like 24 Mg, optical dipole excitation of the spin-forbidden 1 S 0 → 3 P 0 clock transition can be enhanced, e.g. by applying an external magnetic field.While these bosons are insensitive to first-order Zeeman shifts, the second-order Zeeman effect displays a dominant contribution to the clock's error budget.In this thesis, the magnetic polarizability β is measured to be -206.6(2.0)MHz/T 2 , consistent with a theoretical calculation, and the clock transition frequency was found to be 655 058 646 691(101) kHz.
Abstract We analyze an optical atomic clock using two-photon 5 S 1 / 2 → 4 D J transitions in rubidium. Four one- and two-color excitation schemes to probe the 4 D 3 / 2 and 4 D 5 / 2 fine-structure states are considered in detail. We compare key characteristics of Rb 4 D J and 5 D 5 / 2 two-photon clocks. The 4 D J clock features a high signal-to-noise ratio due to two-photon decay at favorable wavelengths, low dc electric and magnetic susceptibilities, and minimal black-body shifts. Ac Stark shifts from the clock interrogation lasers are compensated by two-color Rabi-frequency matching. We identify a ‘magic’ wavelength near 1060 nm, which allows for in-trap, Doppler-free clock-transition interrogation with lattice-trapped cold atoms. From our analysis of clock statistics and systematics, we project a quantum-noise-limited relative clock stability at the 10 − 13 / τ ( s ) -level, with integration time τ in seconds, and a relative accuracy of ∼ 10 − 13 . We describe a potential architecture for implementing the proposed clock using a single telecom clock laser at 1550 nm, which is conducive to optical communication and long-distance clock comparisons. Our work could be of interest in efforts to realize small and portable Rb clocks and in high-precision measurements of atomic properties of Rb 4 D J -states.
Magic wavelengths for laser trapping of barium atoms in the optical lattices are calculated with considering the optical clock transition at 1107 nm between the 6s 2 1 S 0 state and 6s5d 3 D 1 state. Theoretical calculation shows that there are several magic wavelengths with the linearly polarized trapping laser. The trap depths of the optical lattice and the slope of light shift difference with different magic wavelengths are also calculated. Some of these magic wavelengths are selected and recommended as potentially suitable magic wavelengths for the optical lattice trapping laser.