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Register a new userStatic and dynamic polarizabilities of Yb-ion]{Accurate determination of black-body radiation shift, magic and tune-out wavelengths for the $rm 6S_{1/2} rightarrow 5D_{3/2}$ clock transition in Yb$^+$
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We present precise values of the dipole polarizabilities ($alpha$) of the ground $rm [4f^{14}6s] ~ ^2S_{1/2}$ and metastable $rm [4f^{14} 5d] ~ ^2D_{3/2}$ states of Yb$^+$, that are %vital {bf important} in reducing systematics in the clock frequency of the $rm[4f^{14}6s] ~ ^2S_{1/2} rightarrow [4f^{14}5d] ~ ^2D_{3/2}$ transition. The static values of $alpha$ for the ground and $rm [4f^{14} 5d] ~ ^2D_{3/2}$ states are estimated to be $9.8(1) times 10^{-40} ,,rm Jm^2V^{-2}$ and $17.6(5) times 10^{-40},, rm Jm^2V^{-2}$, respectively, while the tensor contribution to the $rm [4f^{14} 5d] ~ ^2D_{3/2}$ state as $- 12.3(3) times 10^{-40},, rm Jm^2V^{-2}$ compared to the experimental value $-13.6(2.2) times 10^{-40},,rm Jm^2V^{-2}$. This corresponds to the differential scalar polarizability value of the above transition as $-7.8$(5)$,times, 10^{-40},rm Jm^2 V^{-2}$ in contrast to the available experimental value $-6.9$(1.4)$,times, 10^{-40}$,, $rm Jm^2V^{-2}$. This results in the black-body radiation (BBR) shift of the clock transition as $-0.44(3)$ Hz at the room temperature, which is large as compared to the previously estimated values. Using the dynamic $alpha$ values, we report the tune-out and magic wavelengths that could be of interest to subdue %major systematics due to the Stark shifts and for constructing lattice optical clock using Yb$^+$.
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The Stark shift of the ytterbium optical clock transition due to room temperature blackbody radiation is dominated by a static Stark effect, which was recently measured to high accuracy [J. A. Sherman et al., Phys. Rev. Lett. 108, 153002 (2012)]. However, room temperature operation of the clock at 10^{-18} inaccuracy requires a dynamic correction to this static approximation. This dynamic correction largely depends on a single electric dipole matrix element for which theoretically and experimentally derived values disagree significantly. We determine this important matrix element by two independent methods, which yield consistent values. Along with precise radiative lifetimes of 6s6p 3P1 and 5d6s 3D1, we report the clocks blackbody radiation shift to 0.05% precision.
The blackbody radiation shift of the Ga$^+$ $4s^2 ^1S^e_0 to 4s4p ^3P^o_0$ clock transition is computed to be $-$$0.0140 pm 0.0048$ Hz at 300 K. The small shift is consistent with the blackbody shifts of the clock transitions of other group III ions which are of a similar size. The polarizabilities of the Ga$^+$ $4s^2 ^1S^e_0$, $4s4p ^3P^o_0$, and $4s4p ^1P^o_1$ states were computed using the configuration interaction method with an underlying semi-empirical core potential. A byproduct of the analysis involved large scale calculations of the low lying spectrum and oscillator strengths of the Ga$^{2+}$ ion.
The frequency dependent polarizabilities of the francium atom are calculated from the available data of energy levels and transition rates. Magic wavelengths for the state insensitive optical dipole trapping are identified from the calculated light shifts of the $7s~^2S_{1/2}$, $7p~^2P_{1/2, 3/2}$ and $8s~^{2}S_{1/2}$ levels of the $7s~^{2}S_{1/2}-7p~^{2}P_{1/2,3/2}$ and $7s~^{2}S_{1/2}-8s~^{2}S_{1/2}$ transitions, respectively. Wavelengths in the ultraviolet, visible and near infrared region is identified that are suitable for cooling and trapping. Magic wavelengths between 600-700~nm and 700-1000~nm region, which are blue and red detuned with the $7s-7p$ and $7s-8s$ transitions are feasible to implement as lasers with sufficient power are available. In addition, we calculated the tune-out wavelengths where the ac polarizability of the ground $7s~^{2}S_{1/2}$ state in francium is zero. These results are beneficial as laser cooled and trapped francium has been in use for fundamental symmetry investigations like searches for an electron permanent electric dipole moment in an atom and for atomic parity non-conservation.
The workhorse of atomic physics, quantum electrodynamics, is one of the best-tested theories in physics. However recent discrepancies have shed doubt on its accuracy for complex atomic systems. To facilitate the development of the theory further we aim to measure transition dipole matrix elements of metastable helium (He*) (the ideal 3 body test-bed) to the highest accuracy thus far. We have undertaken a measurement of the `tune-out wavelength which occurs when the contributions to the dynamic polarizability from all atomic transitions sum to zero; thus illuminating an atom with this wavelength of light then produces no net energy shift. This provides a strict constraint on the transition dipole matrix elements without the complication and inaccuracy of other methods. Using a novel atom-laser based technique we have made the first measurement of the tune-out wavelength in metastable helium between the $3^{3}P_{1,2,3}$ and $2^{3}P_{1,2,3}$ states at 413.07(2) nm which compares well with the predicted valuecite{Mitroy2013} of 413.02(9) nm. We have additionally developed many of the methods necessary to improve this measurement to the 100 fm level of accuracy where it will form the most accurate determination of transition rate information ever made in He* and provide a stringent test for atomic QED simulations. We believe this measurement to be one of the most sensitive ever made of an optical dipole potential, able to detect changes in potentials of $sim$200 pK and is widely applicable to other species and areas of atom optics.
We present additional magic wavelengths ($lambda_{rm{magic}}$) for the clock transitions in the alkaline-earth metal ions considering circular polarized light aside from our previously reported values in [J. Kaur et al., Phys. Rev. A {bf 92}, 031402(R) (2015)] for the linearly polarized light. Contributions from the vector component to the dynamic dipole polarizabilities ($alpha_d(omega)$) of the atomic states associated with the clock transitions play major roles in the evaluation of these $lambda_{rm{magic}}$, hence facilitating in choosing circular polarization of lasers in the experiments. Moreover, the actual clock transitions in these ions are carried out among the hyperfine levels. The $lambda_{rm{magic}}$ values in these hyperfine transitions are estimated and found to be different from $lambda_{rm{magic}}$ for the atomic transitions due to different contributions coming from the vector and tensor part of $alpha_d(omega)$. Importantly, we also present $lambda_{rm{magic}}$ values that depend only on the scalar component of $alpha_d(omega)$ for their uses in a specially designed trap geometry for these ions so that they can be used unambiguously among any hyperfine levels of the atomic states of the clock transitions. We also present $alpha_d(omega)$ values explicitly at the 1064 nm for the atomic states associated with the clock transitions which may be useful for creating high-field seeking traps for the above ions using the Nd:YAG laser. The tune out wavelengths at which the states would be free from the Stark shifts are also presented. Accurate values of the electric dipole matrix elements required for these studies are given and trends of electron correlation effects in determining them are also highlighted.
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