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Register a new userHyperfine-induced quadrupole moments of alkali-metal atom ground states and their implications for atomic clocks
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Andrei Derevianko
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Spherically-symmetric ground states of alkali-metal atoms do not posses electric quadrupole moments. However, the hyperfine interaction between nuclear moments and atomic electrons distorts the spherical symmetry of electronic clouds and leads to non-vanishing atomic quadrupole moments. We evaluate these hyperfine-induced quadrupole moments using techniques of relativistic many-body theory and compile results for Li, Na, K, Rb, and Cs atoms. For heavy atoms we find that the hyperfine-induced quadrupole moments are strongly (two orders of magnitude) enhanced by correlation effects. We further apply the results of the calculation to microwave atomic clocks where the coupling of atomic quadrupole moments to gradients of electric fields leads to clock frequency uncertainties. We show that for $^{133}$Cs atomic clocks, the spatial gradients of electric fields must be smaller than $30 , mathrm{V}/mathrm{cm}^2$ to guarantee fractional inaccuracies below $10^{-16}$.
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The values of nuclear electric quadrupole moment are different by about 7% for 87Sr nucleus between the recommended value [N. J. Stone, At. Data Nucl. Data Tables 111-112, 1 (2016); P. Pyykko, Mol. Phys. 116, 1328 (2018)] and earlier results [e.g. A. M. Matensson-Pendrill, J. Phys. B: At. Mol. Opt. Phys. 35, 917 (2002); K. Z. Yu et al., Phys. Rev. A 70, 012506 (2004)]. In this work, we reported a new value, Q(87Sr) = 328(4) mb, making use of our calculated electric field gradients produced by electrons at nucleus in combination with experimental values for hyperfine structures of the 5s5p 3P1,2 states of the neutral Sr atom. In the framework of the multi-configuration Dirac-Hartree-Fock theory, the electron correlations were taken into account systematically so as to control the uncertainties of the electric field gradient at about 1% level. The present result is different from the recommended value, but in excellent agreement with those by Matensson-Pendrill and Yu et al.. We would recommend the present Q value as a reference for 87Sr.
Simple and efficient lambda-method and lambda/2-method (lambda is the resonant wavelength of laser radiation) based on nanometric-thickness cell filled with rubidium are implemented to study the splitting of hyperfine transitions of 85Rb and 87Rb D_1 line in an external magnetic field in the range of B = 0.5 - 0.7 T. It is experimentally demonstrated from 20 (12) Zeeman transitions allowed at low B-field in 85Rb (87Rb) spectra in the case of sigma+ polarized laser radiation, only 6 (4) remain at B > 0.5 T, caused by decoupling of the total electronic momentum J and the nuclear spin momentum I (hyperfine Paschen-Back regime). The expressions derived in the frame of completely uncoupled basis (J, m_J ; I, m_I) describe very well the experimental results for 85Rb transitions at $B > 0.6 T (that is a manifestation of hyperfine Paschen-Back regime). A remarkable result is that the calculations based on the eigenstates of coupled (F, m_F) basis, which adequately describe the system for low magnetic field, also predict reduction of number of transition components from 20 to 6 for 85Rb, and from 12 to 4 for 87Rb spectrum at B > 0.5 T. Also, the Zeeman transitions frequency shift, frequency interval between the components and their slope versus $B$ are in agreement with the experiment.
In the last ten years extraordinary results in time and frequency metrology have been demonstrated. Frequency-stabilization techniques for continuous-wave lasers and femto-second optical frequency combs have enabled a rapid development of frequency standards based on optical transitions in ultra-cold neutral atoms and trapped ions. As a result, todays best performing atomic clocks tick at an optical rate and allow scientists to perform high-resolution measurements with a precision approaching a few parts in $10^{18}$. This paper reviews the history and the state of the art in optical-clock research and addresses the implementation of optical clocks in a possible future redefinition of the SI second as well as in tests of fundamental physics.
Atomic clocks use atomic transitions as frequency references. The susceptibility of the atomic transition to external fields limits clock stability and introduces systematic frequency shifts. Here, we propose to realize an atomic clock that utilizes an entangled superposition of states of multiple atomic species, where the reference frequency is a sum of the individual transition frequencies. The superposition is selected such that the susceptibilities of the respective transitions, in individual species, destructively interfere leading to improved stability and reduced systematic shifts. We present and analyze two examples of such combinations. The first uses the optical quadrupole transitions in a $^{40}$Ca$^+$ - $^{174}$Yb$^+$ two-ion crystal. The second is a superposition of optical quadrupole transitions in one $^{88}$Sr$^+$ ion and three $^{202}$Hg$^+$ ions. These combinations have reduced susceptibility to external magnetic fields and blackbody radiation.
We have developed an improved scheme for loading atoms into a magneto-optical trap (MOT) from a directed alkali metal dispenser in < 10^-10 torr ultra-high vacuum conditions. A current-driven dispenser was surrounded with a cold absorbing shroud held at < 0 C, pumping rubidium atoms not directed into the MOT. This nearly eliminates background alkali atoms and reduces the detrimental rise in pressure normally associated with these devices. The system can be well-described as a current-controlled, rapidly-switched, two-temperature thermal beam, and was used to load a MOT with 3 x 10^8 atoms.
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