We developed a theoretical method within the framework of relativistic many-body theory to accurately treat correlation corrections in atoms with few valence electrons. Preliminary results for systems of interest to atomic clock development are reported. We also calculated the blackbody radiation shift of the ground-state hyperfine microwave transition in87Rb using the relativistic all-order method and evaluated the accuracy of our final value. The uncertainty estimate is discussed in detail.
We developed a theoretical method within the framework of relativistic many-body theory to accurately treat correlation corrections in atoms with few valence electrons. Preliminary results for systems of interest to atomic clock development are reported. We also calculated the blackbody radiation shift of the ground-state hyperfine microwave transition in87Rb using the relativistic all-order method and evaluated the accuracy of our final value. The uncertainty estimate is discussed in detail.
We evaluated the static and dynamic polarizabilities of the 5s21S0 and 5s5p3P0o states of Sr using the high-precision relativistic configuration interaction combined with the all-order method. Our calculation explains the discrepancy between the recent experimental $5{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}\ensuremath{-}5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}$ dc Stark shift measurement $\ensuremath{\Delta}\ensuremath{\alpha}=247.379(7)$ [Middelmann et al., Phys. Rev. Lett. 109, 263004 (2012)] and the earlier theoretical result of 261(4) a.u. [Porsev and Derevianko, Phys. Rev. A 74, 020502(R) (2006)]. Our present value of 247.5 a.u. is in excellent agreement with the experimental result. We also evaluated the dynamic correction to the BBR shift with 1 uncertainty; $\ensuremath{-}0.1492(16)Hz.ThedynamiccorrectiontotheBBRshiftisunusuallylargeinthecaseofSr(7%$) and it enters significantly into the uncertainty budget of the Sr optical lattice clock. We suggest future experiments that could further reduce the present uncertainties.
We evaluated the C(6) coefficients of Yb-Yb, Yb-alkali, and Yb-group II van der Waals interactions with 2% uncertainty. The only existing experimental result for such quantities is for the Yb-Yb dimer. Our value, C(6)=1929(39) a.u., is in excellent agreement with the recent experimental determination of 1932(35) a.u. We have also developed a new approach for the calculation of the dynamic correction to the blackbody radiation shift. We have calculated this quantity for the Yb 6s(2) (1)S(0)-6s6p (3)P(0)(o) clock transition with 3.5% uncertainty. This reduces the fractional uncertainty due to the blackbody radiation shift in the Yb optical clock at 300 K to the 10(-18) level.
The advancement of optical atomic clocks in the past two decades has motivated many potential applications in navigation, communication, and science. Accurate optical clocks that outperform the current cesium time standard also trigger a discussion about a possible redefinition of the SI second. The 27Al+ quantum logic clocks developed at the National Institute of Standards and Technology (NIST) were the first to achieve the clock fractional frequency uncertainty below 10-17 in 2010. To date, a few research groups around the world have demonstrated optical clocks based on various atomic transitions with fractional frequency uncertainty in the 10-18 range. The accuracy of the previous 27Al+ clocks was limited by the second order Doppler (time dilation) shift and the blackbody shift. Since 2010, the third 27Al+ optical clock is being developed at NIST to achieve a higher accuracy. The frequency uncertainties dominant in the previous clocks are controlled and reduced in the current optical clock. The new design of the ion trap system has reduced significantly both the blackbody radiation shift uncertainty and the time dilation shift uncertainty due to micromotion, while the time dilation shift uncertainty due to the secular motion has been reduced by more than an order of magnitude by operating the optical clock near the three dimensional zero-point energy. Despite those previously dominant uncertainties, several other systematic effects are being evaluated and some other efforts are being made to achieve a total uncertainty towards 1.0 x 10-18. In this thesis, I will document the detail of the construction and evaluation of the current 27Al+ optical clock developed at NIST.
We carry out relativistic many-body calculations of the static and dynamic dipole polarizabilities of the ground 6s 2 1 S 0 and the first excited 6s6p 3 P o 0 states of Yb. With these polarizabilities, we compute several properties of Yb relevant to optical lattice clocks operating on the 6s 2 1 S 0 –6s6p 3 P o 0 transition. We determine (i) the first four magic wavelengths of the laser field for which the frequency of the clock transition is insensitive to the laser intensity. While the first magic wavelength is known, we predict the second, the third and the fourth magic wavelengths to be 551 nm, 465 nm and 413 nm. (ii) We re-evaluate the effect of black-body radiation on the frequency of the clock transition, the resulting clock shift at T = 300 K being −1.41(17) Hz. (iii) We compute long-range interatomic van der Waals coefficients (in a.u.) C 6 (6s 2 1 S 0 + 6s 2 1 S 0 ) = 1909(160), C 6 (6s 2 1 S 0 + 6s6p 3 P 0 ) = 2709(338) and C 6 (6s6p 3 P 0 + 6s6p 3 P 0 ) = 3886(360). Finally, we determine the atom-wall interaction coefficients (in a.u.), C 3 (6s 2 1 S 0 ) = 3.34 and C 3 (6s6p 3 P 0 ) = 3.68. We also address and resolve a disagreement between previous calculations of the static polarizability of the ground state.
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.
Molecular lattice clocks enable the search for new physics, such as fifth forces or temporal variations of fundamental constants, in a manner complementary to atomic clocks. Blackbody radiation (BBR) is a major contributor to the systematic error budget of conventional atomic clocks and is notoriously difficult to characterize and control. Here, we combine infrared Stark-shift spectroscopy in a molecular lattice clock and modern quantum chemistry methods to characterize the polarizabilities of the Sr_{2} molecule from dc to infrared. Using this description, we determine the static and dynamic blackbody radiation shifts for all possible vibrational clock transitions to the 10^{-16} level. This constitutes an important step toward millihertz-level molecular spectroscopy in Sr_{2} and provides a framework for evaluating BBR shifts in other homonuclear molecules.