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 [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.PACS numbers: 32.10 Dk,31.15.Dv, 31.15 ap State-insensitive trapping techniques have lead to tremendous advancements in the manipulation and control of atoms in far detuned optical traps. In this approach, the atoms are trapped at the wavelengths (related to frequencies) of an external electric field at which the differential light shift of an atomic transition, that is intended to be probed, due to the Stark effects nullify. These wavelengths are specially referred to as magic wavelengths (λ magic s) [1]. It has been demonstrated earlier ability of trapping neutral atoms inside high-Q cavities at λ magic s in the strong coupling regime, which is important in the quantum computation and communication schemes [2]. This technique is now widely used to carry out many high precision measurements by eliminating large systematics due to stray electric fields. Another notable application of these wavelengths is to perform clock frequency measurements [3], especially for optical frequency standards [4], that are in turn useful to probe temporal and spatial variations of the fundamental constants [5] and improving global positioning systems [6]. Knowing λ magic s of atomic systems are also very useful in the field of quantum state engineering [7], extracting out precise values of the oscillator strengths [8], etc. because of which extensive studies, both experimentally and theoretically, have been carried out in many atoms recently [6,[9][10][11][12]. On the other hand, singly charged alkaline earth ions are advantageous to carry out very high precision measurements using ion trapping and laser cooling techniques. Some of the prominent examples are the optical frequency standards [13, 14], probing variation of fundamental constants [3, 5], parity non-conservation effects [15,16] etc. Advantages of these ions owe to their metastable D states that provide longer probe times during interrogation of measurements. To reduce system- * Email: arorabindiya@gmail.com † Email: bijaya@prl.res.in atics in these measurements, state insensitive measurements can be more pertinent that will require knowledge of ...
