Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)
Towards a magnesium optical lattice clock
Steffen Rühmann, Matthias Riedmann, Temmo Wübbena, A. P. Kulosa, André Pape, Dominika Fim, Klaus Zipfel, Birte Lampmann, J. Friebe, Hrishikesh Kelkar, Wolfgang A. Ertmer, Ernst Maria Rasel
The authors report on the recent progress in setting up a magic wavelength optical lattice for magnesium. At the magic wavelength for the1S0→3P0transition of Mg, which has been predicted to be at 463 nm, the differential AC Stark shift of the intercombination transition cancels out. Currently, the authors investigate to establish the optical lattice inside an optical resonator to enhance the trap depth and the loading of this lattice. Furthermore, the tight confinement of the atoms in the lattice will enable us to reach the Lamb-Dicke regime, allowing first order Doppler-free spectroscopy.
The authors report on the recent progress in setting up a magic wavelength optical lattice for magnesium. At the magic wavelength for the1S0→3P0transition of Mg, which has been predicted to be at 463 nm, the differential AC Stark shift of the intercombination transition cancels out. Currently, the authors investigate to establish the optical lattice inside an optical resonator to enhance the trap depth and the loading of this lattice. Furthermore, the tight confinement of the atoms in the lattice will enable us to reach the Lamb-Dicke regime, allowing first order Doppler-free spectroscopy.
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.
The primary frequency and time standard, defined via a transition frequency of caesium-133, is realized by microwave clocks reaching relative uncertainties in the 10−^16 level. This performance has been surpassed by state-of-the-art lattice clocks, with transition frequencies in the optical regime, leading to two orders of magnitude lower uncertainties. The key to this performance is the confinement in the Lamb-Dicke regime at the magic wavelength enabling a Doppler- and recoil-free spectroscopy with a first-order suppressed AC Stark shift. In atomic clocks, several effects contribute to the uncertainty of the transition frequency. Through continuous global characterization efforts, the individual uncertainty of these effects have been subsequently reduced. Yet one effect, namely the frequency shift induced by blackbody radiation has been identified as a dominant contribution which is difficult to overcome by technical means. In this regard, magnesium-24 excels as a species of choice as its blackbody radiation sensitivity is one order of magnitude lower than in the most frequently used atomic clock species. Furthermore, magnesium offers a relatively simple electronic structure which enables theoretical support through high-precision calculations. This thesis features the first characterization of a magnesium optical lattice clock operating at the magic wavelength. The characterization of the magnesium frequency standard presented in this thesis depends essentially on the resolution of the transition linewidth, which could be reduced from kHz range to 51(3) Hz in a complementing work. The realization of a transition linewidth with a quality factor of Q = 1.3 × 10^13 has contributed to an improved determination of the magic wavelength within this thesis to 468.4106(2) nm. Compared to earlier work, this represents an improvement of two orders of magnitude. Furthermore, the lower transition linewidth also allowed the first observation of the probe AC Stark shift and thus the first characterization of effects in the lattice that falsify the frequency of the trapped magnesium atoms. Overall, the relative uncertainty of the frequency-related effects influencing the clock transition could be determined to be 7.1 × 10^−15. The dominant contributions can be assigned to tunneling broadening and the lattice and probe AC Stark effects, induced by the probe and lattice light. All these effects can be traced back to technical limitations and are part of future work. Following the characterization, a first frequency comparison between the magnesium lattice clock against the primary frequency standard as well as the ytterbium ion clock at the PTB has been performed and thus a first realization of a lattice based frequency standard with magnesium atoms was demonstrated. The determined transition frequency of 655 058 646 681 864.1(5.3) Hz complies with former measurements. The primary frequency and time standard, defined via a transition frequency of caesium-133, is realized by microwave clocks reaching relative uncertainties in the 10^−16 level. This performance has been surpassed by state-of-the-art lattice clocks, with transition frequencies in the optical regime, leading to two orders of magnitude lower uncertainties. The key to this performance is the confinement in the Lamb-Dicke regime at the magic wavelength enabling a Doppler- and recoil-free spectroscopy with a first-order suppressed AC Stark shift. In atomic clocks, several effects contribute to the uncertainty of the transition frequency. Through continuous global characterization efforts, the individual uncertainty of these effects have been subsequently reduced. Yet one effect, namely the frequency shift induced by blackbody radiation has been identified as a dominant contribution which is difficult to overcome by technical means. In this regard, magnesium-24 excels as a species of choice as its blackbody radiation sensitivity is one order of magnitude lower than in the most frequently used atomic clock species. Furthermore, magnesium offers a relatively simple electronic structure which enables theoretical support through high-precision calculations. This thesis features the first characterization of a magnesium optical lattice clock operating at the magic wavelength. The characterization of the magnesium frequency standard presented in this thesis depends essentially on the resolution of the transition linewidth, which could be reduced from kHz range to 51(3) Hz in a complementing work. The realization of a transition linewidth with a quality factor of Q = 1.3 × 10^13 has contributed to an improved determination of the magic wavelength within this thesis to 468.4106(2) nm. Compared to earlier work, this represents an improvement of two orders of magnitude. Furthermore, the lower transition linewidth also allowed the first observation of the probe AC Stark shift and thus the first characterization of effects in the lattice that falsify the frequency of the trapped magnesium atoms. Overall, the relative uncertainty of the frequency-related effects influencing the clock transition could be determined to be 7.1 × 10^−15. The dominant contributions can be assigned to tunneling broadening and the lattice and probe AC Stark effects, induced by the probe and lattice light. All these effects can be traced back to technical limitations and are part of future work. Following the characterization, a first frequency comparison between the magnesium lattice clock against the primary frequency standard as well as the ytterbium ion clock at the PTB has been performed and thus a first realization of a lattice based frequency standard with magnesium atoms was demonstrated. The determined transition frequency of 655 058 646 681 864.1(5.3) Hz complies with former measurements.
We optically excite the electronic state 3s3p ^{3}P_{0} in ^{24}Mg atoms, laser cooled and trapped in a magic-wavelength lattice. An applied magnetic field enhances the coupling of the light to the otherwise strictly forbidden transition. We determine the magic wavelength, the quadratic magnetic Zeeman shift, and the transition frequency to be 468.46(21) nm, -206.6(2.0) MHz/T^{2}, and 655 058 646 691(101) kHz, respectively. These are compared with theoretical predictions and results from complementary experiments. We also develop a high-precision relativistic structure model for magnesium, give an improved theoretical value for the blackbody radiation shift, and discuss a clock based on bosonic magnesium.
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.