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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Multipole, nonlinear and anharmonic contributions to uncertainties of clocks on neutral atoms in optical lattices

Vitaly D. Ovsiannikov, Vitaly G. Palchikov

Published May 1, 2013• 0 citations
Publisher

Abstract

The budget of uncertainties of a time-frequency standard on neutral atoms, trapped in an optical lattice with a “magic wavelength” (MWL), includes a number of shift and broadening corrections, coming from interaction of atoms with different fields of environment. The most important corrections are those arising from interaction with the field of lattice wave. The lattice field is essentially stronger than other fields and may introduce severe perturbations on the standard frequency, despite its tuning to the MWL, which was proposed to compensate these perturbations in a standing-wave lattice, ensuring rigorous equality of the working-level shifts, independently of the atomic motion and the laser intensity. The method of determining MWL, based on measuring the shift of the clock frequency in a weak field of a travelling wave accounts for the Stark shift of energy levels, but only linear in the laser intensity, with inclusion of all multipole-interaction terms.

DOI
10.1109/cleoe-iqec.2013.6801772

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The budget of uncertainties of a time-frequency standard on neutral atoms, trapped in an optical lattice with a “magic wavelength” (MWL), includes a number of shift and broadening corrections, coming from interaction of atoms with different fields of environment. The most important corrections are those arising from interaction with the field of lattice wave. The lattice field is essentially stronger than other fields and may introduce severe perturbations on the standard frequency, despite its tuning to the MWL, which was proposed to compensate these perturbations in a standing-wave lattice, ensuring rigorous equality of the working-level shifts, independently of the atomic motion and the laser intensity. The method of determining MWL, based on measuring the shift of the clock frequency in a weak field of a travelling wave accounts for the Stark shift of energy levels, but only linear in the laser intensity, with inclusion of all multipole-interaction terms.
Magnetic-dipole, electric-quadrupole, and hyperpolarizability effects on clock energy levels are analyzed in detail for Sr atoms in Stark potentials of red-detuned and blue-detuned magic-wavelength optical lattices. A difference between ac Stark shifts in traveling and standing waves is determined numerically. Differences between magic wavelengths for atoms in traveling and standing waves are presented and strategies for minimizing uncertainties of the clock frequency are indicated explicitly. Significant suppression of hyperpolarizability effect is demonstrated analytically for a blue-detuned in comparison with a red-detuned lattice, thus enabling essential deepening of trap potentials, reducing tunneling between lattice wells and collision effects.
In a standing wave of light, a difference in spatial distributions of multipolar atom-field interactions may introduce atomic-motion dependent clock uncertainties in optical lattice clocks. We show that the magic wavelength can be defined so as to eliminate the spatial mismatch in electric dipole, magnetic dipole, and electric quadrupole interactions for specific combinations of standing waves by allowing a spatially constant light shift arising from the latter two interactions. Experimental prospects of such lattices used with a blue magic wavelength are discussed.
Abstract We have assessed the effect of optical lattice laser field parameters (polarisation, intensity, and wavelength) of a cold-ytterbium atomic frequency standard on the systematic uncertainty of precision clock transition frequency measurements. The spectrum and polarisation of the laser field of the lattice have been investigated in detail directly in the spatial region of interaction of cold ytterbium atoms with the laser field. The Stark shift of the clock transition in the vicinity of the magic wavelength of the laser has been estimated as a function of the experimentally measured laser field intensity in the dipole approximation. The estimates have been used to calculate the residual systematic uncertainty in the light shift of the optical lattice laser frequency.
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 Results of theoretical evaluations of uncertainties arising from the atom-lattice interaction effects on the clock frequency are presented for Sr atoms. Possibilities for simultaneous tuning of optical lattice frequency and intensity parameters are discussed aiming at minimizing uncertainties induced by interaction of Sr atoms with the field of magic-wavelength optical lattice. The fractional contributions to the clock-frequency shift from the spontaneous emission of the lattice-beam amplifier after having passed the optical fiber are determined at the level below 10 −18 .