Session B6: Focus Session: Precise Atomic Theory and Measurements

Precision physics with few electron atoms and molecules

In the light of the proton charge radius discrepancy [1] and possible existence of extra forces between leptons and hadrons, we search for discrepancies in the spectra of few electron atoms and molecules by comparison of the experimental values with the high accuracy calculations. As a result we observed several unexplained discrepancies, such as in the determination of $^3$He charge radius from different atomic transitions [2], anomalies in the magnetization distribution of $^6$Li nuclei [3], and set bounds on existence of the fifth force from the vibrational spectra of the H$_2$ molecule [4]. Further development of precision tests is currently limited by difficulties in the incorporation of higher order quantum electrodynamics effects in few electron systems. I will describe the recent progress in high precision calculations of atomic energy levels and point out limitations in the current theoretical approaches to the bound state quantum electrodynamics.\\[4pt] [1] R. Pohl, R. Gilman, G.A. Miller and K. Pachucki, Annu. Rev. Nucl. Part. Sci. {\bf 63}, 175 (2013). \\[0pt] [2] P. Cancio Pastor, L. Consolino,P. De Natale, M. Inguscio, V. A. Yerokhin, and K. Pachucki, Phys. Rev. Lett. {\bf 108}, 143001 (2012).\\[0pt] [3] M. Puchalski and K. Pachucki, Phys. Rev. Lett. {\bf 111}, 243001 (2013).\\[0pt] [4] E.J. Salumbides, J.C.J. Koelemeij, J. Komasa, K. Pachucki, K.S.E. Eikema, and W. Ubachs, Phys. Rev. D {\bf 87}, 112008 (2013).   

Atomic Clocks, Fundamental Symmetries, and the Search for New Physics

I will give an overview of theoretical developments related to searches for new physics with atomic systems, including the study of parity violation, search for EDM, and the search for variation of fundamental constants. The study of parity nonconservation in cesium led to a first measurement of the nuclear anapole moment and allowed to place constraints on weak meson-nucleon couplings. I will review the present status of atomic parity violation studies and the implications for searches for physics beyond the standard model and study of weak hadronic interactions. In the second part of my talk, I will discuss the theoretical research related to state-of-the art atomic clock development focusing on the issue of the blackbody radiation shifts as well as application of clocks to the searches for variation of the fine-structure constant.   

Development of new methods of calculation for complicated atoms: application to parity violation in Pb

Measurements of parity nonconserving (PNC) optical rotation in the vicinity of the $6p^2\, ^3\!P_0 - 6p^2\, ^3\!P_1$ magnetic dipole transition in atomic Pb were carried out almost 20 years ago by Meekhof et. al., [1] and by Phipp et. al., [2] giving the ratios of the PNC E1 amplitude to the M1 amplitude, R, to be $(-9.86 \pm 0.12) \times 10^{-8}$ [1] and $(-9.80 \pm 0.33) \times 10^{-8}$ [2]. Due to the complicated electronic structure of Pb, the best calculation of the quantity R was estimated to have 8\% uncertainty [3]. We have developed a new method of calculation based on the combination of configuration interaction and coupled cluster approach that can use different Hartree-Fock potentials as a starting point. We applied it to the calculation of Pb atomic properties, including energy levels, hyperfine structure constants, and E1 transition amplitudes. Many of the properties were calculated for the first time. We also determined the PNC E1 $6p^2\, ^3\!P_0 - 6p^2\, ^3\!P_1$ transition amplitude. An analysis of the results and uncertainties is underway. Final results will be reported at the conference.\\[4pt] [1] D.M. Meekhof et. al, PRL 71, 3442 (1993).\\[0pt] [2] S.J. Phipp et. al., J. Phys. B 29, 1861 (1996).\\[0pt] [3] V.A. Dzuba et. al., Europhys. Lett. 7, 413 (1988).   

Critical Nuclear Charge for Two-electron Atoms

There has been a recent revival of interest in the critical nuclear charge $Z_c$ that is just sufficient to bind a nucleus of charge $Z$ and two electrons in the $1s^2\;^1S$ ground state [1--3]. It is conjectured that the inverse of critical charge is related to the radius of convergence $1/Z^*$ for a $1/Z$ expansion of the energy of the form $E(Z) = Z^2(E_0 + E_1/Z + E_2/Z^2 + \cdots)$. We have performed high precision variational calculations in Hylleraas coordinates, using the double basis set method [4], for values of $Z$ very close to $Z_c$, with basis sets containing up to 2809 terms ($\Omega = 24$). Our preliminary result is $Z_c = 0.911\,028\,224\,077\,260(15)$, corresponding to $1/Z_c = 1.097\,660\,833\,738\,555(18)$. Well-defined eigenvalues continue to appear for $Z < Z_c$, possibly corresponding to quasibound states in the scattering continuum due to a shape resonance induced by the polarization potential of the core.\\[4pt] [1] J.D. Baker et al., Phys.\ Rev.\ A {\bf 41}, 1247 (1990).\newline [2] N.L. Guevara and A.V. Turbiner, Phys. Rev. A {\bf 84}, 064501 (2011).\newline [3] J. Katriel et al. Phys.\ Rev.\ A {\bf 86}, 042508 (2012).\newline [4] G.W.F. Drake and Z.-C. Yan, Phys.\ Rev.\ A {\bf 46}, 2378 (1992).   

Preliminary results measuring the strongly forbidden magnetic dipole transition moment for the $6S_{1/2} \leftrightarrow 5D_{3/2}$ transitions in Ba$^{+}$

We report the latest results from our effort to measure the magnetic dipole transition moment (M1) between the $6S_{1/2}$ and $5D_{3/2}$ manifolds in Ba$^{+}$. Knowledge of M1 is crucial for a parity-nonconservation experiment in the ion where M1 will be a leading source of systematic errors. To date no measurement of M1 has been made in Ba$^{+}$, however, two calculations were recently reported which found M1 to be 80$\times 10^{-5} \mu_{B}$\footnote{B.K. Sahoo, \emph{ et. al.} Phys. Rev. A 74, 062504 (2006). } and 22$\times 10^{-5} \mu_{B}$\footnote{G.H. Gossel, \emph{ et. al.} Phys. Rev. A 88, 034501 (2013). }. A precise measurement may help to resolve this theoretical discrepancy which originates from their different estimations of many-body effects. To access the transition moment we use a variation of a previously proposed technique\footnote {S.R. Williams, \emph{ et. al.} Phys. Rev. A 88, 012515 (2013).} that allows us to observe the effect of M1 directly in the Rabi frequency of particular Zeeman transitions. In this preliminary experiment we eliminate the electric quadrupole coupling by varying the linear polarization angle of the resonant laser.   

Measurement of the radial matrix elements of the 6s $^{2}$S$_{1/2\, }\to $ 7p $^{2}$P$_{J}$ transitions in atomic cesium

We report measurements of the absorption strength of the cesium 6s $^{2}$S$_{1/2\, }\to $ 7p $^{2}$P$_{3/2}$ and the 6s $^{2}$S$_{1/2\, }\to $ 7p $^{2}$P$_{1/2}$ transitions at $\lambda =$ 456 nm and 459 nm, respectively. We simultaneously measure the absorption strength on the Cs D$_{1}$ line (6s $^{2}$S$_{1/2\, }\to $ 6p $^{2}$P$_{1/2})$ at $\lambda =$ 894 nm, for which the electric dipole transition moment is precisely known, allowing us to precisely determine the reduced dipole matrix elements for these two lines. Our results are $\langle $7P$_{3/2}$\textbar \textbar r\textbar \textbar 6S$_{1/2}\rangle \quad =$ 0.5780 (7) a$_{0}$ and $\langle $7P$_{1/2}$\textbar \textbar r\textbar \textbar 6S$_{1/2}\rangle \quad =$ 0.2789 (16) a$_{0}$, with fractional uncertainties of 0.12{\%} and 0.6{\%}, respectively. These new values allow a more precise determination of the scalar polarizability for the Cs 6s $^{2}$S$_{1/2\, }\to $ 7s $^{2}$S$_{1/2}$ transition, which in turn leads to a more precise value of the vector polarizability for this same transition. The vector polarizability has played a critical role in measurements of the parity nonconserving transition amplitude E$_{PNC}$ in cesium. This revised value of the vector polarizability is in reasonable agreement with the value determined through the nuclear spin dependent component of the transition magnetic dipole moment.   

Measurement of the tensor differential polarizability between Rb clock states

Atoms subjected to intense electric fields experience a shift in their energy levels. This shift, due to the polarizability of atomic states, enables the trapping of atoms in the focus an intense laser beam. Due to the hyperfine interaction the polarizabilities of the two hyperfine levels of $^{\mathrm{87}}$Rb differ on the 10$^{\mathrm{-5}}$ level. In general the atomic polarizability can be decomposed into a scalar and a traceless symmetric tensor parts, the latter being 10$^{\mathrm{-2}}$ that of the former. Any anisotropy of the polarizability is due to its tensor part and the shift depends on the relative angle between the electric field and the quantizing magnetic field. In our experiment we trapped $^{\mathrm{87}}$Rb atoms in an intense quasi-electrostatic field of a, linearly polarized, focused CO$_{\mathrm{2}}$ laser beam and measured the shift in the microwave clock transition frequency using Ramsey spectroscopy. By changing the angle between the electric field of the laser and the magnetic field providing a quantization axis, we were able to isolate the 1 Hz fractional shift caused by the, previously unmeasured, tensor polarizability. The exact knowledge of the scalar and tensor parts of the polarizability are important in order to determine the black body shift of Rb clocks; an important secondary time standard; and can be compared with state-of-the-art atomic structure calculations.