Higher-order perturbation theory is used to study frequency shifts of the spin-forbidden 3 P J - 1 S 0 transitions for Mg, Sr and Yb atoms in an external laser field. Calculations of the higher-order dynamic Stark effect have been performed in connection with precise measurements on cooled and trapped atoms and the design of ultra stable optical clock in an engineered light shift trap. The form of the model potential of the valence electrons suggested by Simons is used for the calculation of atomic dynamic characteristics given by second- and fourth-order perturbation theory for the interaction of the atoms with the electromagnetic field. Dispersion properties of the polarizability and hyperpolarizability components and their behavior in the vicinity of both resonances and so-called magic wavelengths for the upper and lower atomic states, are analyzed. Calculations of ac multipole polarizabilities and dipole hyperpolarizabilities for the 3 P 0 - 1 S 0 clock transition in 87 Sr indicate that the contribution of the higher- order light shifts can be reduced to less than 1 mHz, allowing for a projected accuracy of better than 10 -17 .
Higher-order perturbation theory is used to study frequency shifts of the spin-forbidden 3 P J - 1 S 0 transitions for Mg, Sr and Yb atoms in an external laser field. Calculations of the higher-order dynamic Stark effect have been performed in connection with precise measurements on cooled and trapped atoms and the design of ultra stable optical clock in an engineered light shift trap. The form of the model potential of the valence electrons suggested by Simons is used for the calculation of atomic dynamic characteristics given by second- and fourth-order perturbation theory for the interaction of the atoms with the electromagnetic field. Dispersion properties of the polarizability and hyperpolarizability components and their behavior in the vicinity of both resonances and so-called magic wavelengths for the upper and lower atomic states, are analyzed. Calculations of ac multipole polarizabilities and dipole hyperpolarizabilities for the 3 P 0 - 1 S 0 clock transition in 87 Sr indicate that the contribution of the higher- order light shifts can be reduced to less than 1 mHz, allowing for a projected accuracy of better than 10 -17 .
The light frequency shifts induced by an external laser field are calculated for the spin-forbidden 3 P J — 1 S 0 transitions in Mg, Sr, and Yb atoms. The calculations are performed within the framework of the perturbation theory using experimentally measured transition energies. The calculations of the higher-order dynamic Stark effect were initiated by precision measurements of trapped and cooled atoms as well as by the development of a highly stable optical atomic clock. The dispersion properties of the polarisability and hyperpolarisability components are analysed in the vicinity of resonances and so-called cross points for the ground and excited atomic levels. The radial matrix elements were calculated by the Green function method for the model potential.
The theoretical aspects of the Stark spectroscopy of cold alkaline-earth atoms in a three-dimensional optical lattice related to the development of ultrastable optical frequency standards of a new generation are considered. The main attention is devoted to the dispersion and polarisation properties of the light frequency shift in these atoms, which depend on the power, frequency, and polarisation of lasers forming the optical lattice. The 'light-shift-cancellation' regime is considered in detail, in which the second-order dynamic Stark shifts at the forbidden clock 3 P 0 — 1 S 0 and 3 P 1 — 1 S 0 transitions are mutually compensated. The wavelengths at which this regime takes place ('magic' wavelengths) are calculated for the He, Be, Mg, Ca, Sr, Yb, and Hg atoms. The fourth-order dynamic susceptibilities (hyperpolarisabilities) are calculated for Sr atoms and the contribution of higher-order multipole corrections to the dynamic polarisability of the 3 P 0 and 1 S 0 levels is estimated.
The progress in optical clock with uncertainty at a level of 10−18 requires unprecedented precision in estimating the contribution of multipolar and higher-order effects of atom-field interactions. Previous theoretical and experimental results of dynamic multipolar polarizabilities and hyperpolarizabilities at the 813 nm magic wavelength of the Sr clock differ substantially. We employ the sum-over-states method to calculate dynamic multipolar polarizabilities and hyperpolarizabilities for the Sr and Mg clocks. Our differential dynamic hyperpolarizability at the magic wavelength of 813.4280(5) nm for the Sr clock is −2.09(43)×107 a.u., which agrees well with the recent theoretical and measurement results. Our differential multipolar polarizability of the Sr clock is 2.68(94)×10−5 a.u., which is consistent with the theoretical work of Porsev {\em et al.} [Phys. Rev. Lett. 120, 063204 (2018)], but different from recent measurement of Ushijima {\em et al.} [Phys. Rev. Lett. 121, 263202 (2018)]. In addition, the lattice light shifts as the detuning and trap depth changed are studied in detail by using present multipolar polarizability and hyperpolarizability. It illustrates that for the Mg clock, there exists a distinctive operational lattice depth of 5.3(1)ER that allows the total light shift reduced to less than 1×10−18 over the trap depth variation of 4.1ER<U<6.4ER.
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.
An ultrastable optical clock based on neutral atoms trapped in an optical lattice is proposed. Complete control over the light shift is achieved by employing the 5s(2) 1S0-->5s5p 3P0 transition of 87Sr atoms as a "clock transition." Calculations of ac multipole polarizabilities and dipole hyperpolarizabilities for the clock transition indicate that the contribution of the higher-order light shifts can be reduced to less than 1 mHz, allowing for a projected accuracy of better than 10(-17).
Progress in atomic optical clocks with total uncertainty of ${10}^{\ensuremath{-}18}$ or below requires a precise estimation of multipolar and higher-order effects due to atom-field interactions. Magnesium is an attractive candidate for optical lattice clocks because it is insensitive to blackbody radiation and has a large quality factor. We employ a combined method of the Dirac-Fock plus core polarization and the relativistic configuration interaction to calculate the dynamic multipolar polarizabilities and the hyperpolarizabilities of the atomic Mg clock. The lattice light shift against variation of the laser detuning and trap depth is also investigated. We find that there exists a distinctive operational magic lattice intensity of 5.33(2)ER (ER is the lattice photon recoil energy) that reduces the total light shift below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$ over 14 of the trap depth variation, which will pave the way for the development of a new time-frequency standard of the Mg lattice clock.