B. K. Sahoo

We propose a method for measuring parity violation in neutral atoms. It is an adaptation of a seminal work by Fortson [Phys. Rev. Lett. {\bf 70}, 2383 (1993)], proposing a scheme for a single trapped ion. In our version, a large sample of neutral atoms should be localised in an optical lattice overlapping a grid of detection sites, all tailored as the single site in Fortson's work. The methodology is of general applicability, but as an example we estimate the achievable signal in an experiment probing a nuclear spin independent parity violation on the line $6\mathrm{s}\,^2\mathrm{S}_{1/2}$--$5\mathrm{d}\,^2\mathrm{D}_{3/2}$ in $^{133}$Cs. The projected result is based on realistic parameters and \textit{ab initio} calculations of transition amplitudes, using the relativistic coupled-cluster method. The final result is a predicted spectroscopic signature, evidencing parity violation, of the order of 1 Hz, for a sample of $10^8$ atoms. We show that a total interrogation time of 30000 s should suffice for achieving a precision of the order of 0.1\% --- surpassing previous determinations of the weak charge in Cs by at least a factor of five.

We present additional magic wavelengths ($λ_{\rm{magic}}$) 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 ($α_d(ω)$) of the atomic states associated with the clock transitions play major roles in the evaluation of these $λ_{\rm{magic}}$, 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 $λ_{\rm{magic}}$ values in these hyperfine transitions are estimated and found to be different from $λ_{\rm{magic}}$ for the atomic transitions due to different contributions coming from the vector and tensor part of $α_d(ω)$. Importantly, we also present $λ_{\rm{magic}}$ values that depend only on the scalar component of $α_d(ω)$ 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 $α_d(ω)$ 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.

We report the dispersion coefficients for the interacting inert gas atoms with the alkali ions, alkaline earth ions and alkali atoms with their singly charged ions. We use our relativistic coupled-cluster method to determine dynamic dipole and quadrupole polarizabilities of the alkali atoms and singly ionized alkaline earth atoms, whereas a relativistic random phase approximation approach has been adopted to evaluate these quantities for the closed-shell configured inert gas atoms and the singly and doubly ionized alkali and alkaline earth atoms, respectively. Accuracies of these results are adjudged from the comparison of their static polarizability values with their respective experimental results. These polarizabilities are further compared with the other theoretical results. Reason for the improvement in the accuracies of our estimated dispersion coefficients than the data listed in [At. Data and Nucl. Data Tables 101, 58 (2015)] are discussed. Results for some of the atom-ion interacting systems were not available earlier, these results and the other reported improved results will be very useful for the comprehensive understanding of the collisional physics involving these atom-atom and atom-ion interactions in the cold atom and atom-ion hybrid trapping experiments at the low-temperature regime.

We propose a new ion-trap geometry to carry out accurate measurements of the quadrupole shifts in the $^{171}$Yb-ion. This trap will produce nearly ideal harmonic potential where the quadrupole shifts due to the anharmonic components can be reduced by four orders of magnitude. This will be useful to reduce the uncertainties in the clock frequency measurements of the $6s~{^2}S_{1/2} \rightarrow 4f^{13} 6s^2 ~{^2}F_{7/2}$ and $6s~{^2}S_{1/2} \rightarrow 5d ~{^2}D_{3/2}$ transitions, from which we can deduce precise values of the quadrupole moments ($Θ$s) of the $4f^{13} 6s^2 ~{^2}F_{7/2}$ and $5d ~{^2}D_{3/2}$ states. Moreover, it may be able to affirm validity of the measured $Θ$ value of the $4f^{13} 6s^2 ~{^2}F_{7/2}$ state where three independent theoretical studies defer almost by one order in magnitude from the measurement. We also perform calculations of $Θ$s using the relativistic coupled-cluster (RCC) method. We use these $Θ$ values to estimate quadrupole shift that can be measured in our proposed ion trap experiment.

We present magic wavelengths for the $nS$ - $nP_{1/2,3/2}$ and $nS$ - $mD_{3/2,5/2}$ transitions, with the respective ground and first excited $D$ states principal quantum numbers $n$ and $m$, in the Mg$^+$, Ca$^+$, Sr$^+$ and Ba$^+$ alkaline earth ions for linearly polarized lights by plotting dynamic polarizatbilities of the $nS$, $nP_{1/2,3/2}$ and $mD_{3/2,5/2}$ states of the ions. These dynamic polarizabilities are evaluated by employing a relativistic all-order perturbative method and their accuracies are ratified by comparing their static values with the available high precision experimental or other theoretical results. Moreover, some of the magic wavelengths identified by us in Ca$^+$ concurs with the recent measurements reported in [{\bf Phys. Rev. Lett. 114, 223001 (2015)}]. Knowledge of these magic wavelengths are propitious to carry out many proposed high precision measurements trapping the above ions in the electric fields with the corresponding frequencies.

We perform precision measurements on the 5D$_{5/2}$ manifold hyperfine intervals of a single trapped ion, $^{137}$Ba$^+$. RF spectroscopy is used to measure the hyperfine intervals to an accuracy of a few Hz. Our results provide a three orders of magnitude improvement in accuracy over previous work and also provide a 10-fold improvement in the value of $g_J$ for this level. These results complement our previous work on the 5D$_{3/2}$ manifold of $^{137}$Ba$^+$, providing an independent measurement of the nuclear octupole, and a consistency check on atomic structure calculations.

We present precision measurements of the hyperfine intervals in the 5D3/2 manifold of a single trapped Barium ion, 137 Ba+ . Measurements of the hyperfine intervals are made between mF = 0 sublevels over a range of magnetic fields allowing us to interpolate to the zero field values with an accuracy below a few Hz, an improvement on previous measurements by three orders of magnitude. Our results, in conjunction with theoretical calculations, provide a 30-fold reduction in the uncertainty of the magnetic dipole (A) and electric quadrupole (B) hyperfine constants. In addition, we obtain the magnetic octupole constant (C) with an accuracy below 0.1 Hz. This gives a subsequent determination of the nuclear magnetic octupole moment, Ω, with an uncertainty of 1% limited almost completely by the accuracy of theoretical calculations. This constitutes the first observation of the octupole moment in 137 Ba+ and the most accurately determined octupole moment to date.

We have estimated the size of the light-shifts due to parity nonconservation (PNC) interactions in different isotopes of Ba+ and Ra+ ions based on the work of Fortson [Phys. Rev. Lett. 70, 2383 (1993)]. We have used the nuclear spin independent (NSI) amplitudes calculated earlier by us [Phys. Rev. Lett. 96, 163003 (2006); Phys. Rev. A 78, 050501(R) (2008)] and we have employed the third order many-body perturbation theory (MBPT(3)) in this work to estimate the nuclear spin dependent (NSD) amplitudes in these ions. Ra+ is found to be more favourable than Ba+ for measuring both the NSI and NSD PNC observables.

As an important step towards an atomic parity violation experiment in one single trapped Ra$^+$ ion, laser spectroscopy experiments were performed with on-line produced short-lived $^{212,213,214}$Ra$^+$ ions. The isotope shift of the $6\,^2$D$_{3/2}$\,-\,$7\,^2$P$_{1/2}$ and $6\,^2$D$_{3/2}$\,-\,$7\,^2$P$_{3/2}$ transitions and the hyperfine structure constant of the $7\,^2$S$_{1/2}$ and $6\,^2$D$_{3/2}$ states in $^{213}$Ra$^+$ were measured. These values provide a benchmark for the required atomic theory. A lower limit of $232(4)$ ms for the lifetime of the metastable $6\,^2$D$_{5/2}$ state was measured by optical shelving.