Magic wavelength of the Ba+138 6s S1/

Abstract

The zero crossing of the dynamic differential scalar polarizability of the S 1/2 −D 5/2 clock transition in 138 Ba + has been determined to be 459.1614(28) THz. Together with previously determined matrix elements and branching ratios, this tightly constrains the dynamic differential scalar polarizability of the clock transition over a large wavelength range ( 700 nm). In particular it allows an estimate of the blackbody radiation shift of the clock transition at room temperature.PACS numbers: 06.30.Ft, 06.20.fb Singly-ionized barium has been well studied over the years with a wide range of precision measurements [1][2][3][4][5][6][7][8] that have provided valuable benchmark comparisons for theory [9][10][11][12][13][14]. It was recently proposed that some of these measurements, specifically high accuracy measurements of transition matrix elements and branching ratios, could be used to construct an accurate representation of the dynamic differential scalar polarizability, ∆α 0 (ω) of the S 1/2 −D 5/2 clock transition over a large wavelength range [15]. Crucial to that proposal was a determination of a zero crossing ∆α 0 (ω 0 ) = 0 near 653 nm, which bounds significant contributions to ∆α 0 (ω) from the ultraviolet (uv) spectrum. Here we determine ω 0 with an inaccuracy of a few GHz.To find ω 0 , a linearly polarized laser beam near 653 nm is focussed onto the ion to induce an ac Stark shift of the clock transition and the shift measured as a function of the laser frequency ω. The ac Stark shift, δ s (M J ), induced by the 653-nm laser is given bywhere M J denotes the applicable eigenstate of D 5/2 , α 2 (ω) is the dynamic tensor polarizability of D 5/2 , and θ is angle between the 653-nm laser polarization and the quantization axis. The tensor component can be eliminated by determining the average ac Stark shiftHence, with the laser intensity fixed, δ 0 (ω) is directly proportional to ∆α 0 (ω), which is approximately linear * phybmd@nus.edu.sg in a neighbourhood of ω 0 . Consequently, ω 0 can be determined from a linear fit to measurements of δ 0 (ω) as a function of ω with an accuracy limited by the projection noise of the measurements, and a small nonlinearity in ∆α 0 (ω), which can be estimated from theory. Although the laser power is actively stabilized outside the experiment chamber, etaloning effects and uncalibrated frequency response of the detector can give rise to a frequency dependence of the resulting laser intensity at the ion. In addition, pointing stability of the laser can also degrade the accuracy of the ac Stark shift measured at a single frequency. To compensate these effects, one can make use of the weighted average δ 2 (ω) = 25 42 δ s (5/2) − 1 5 δ s (3/2) − 4 5 δ s (1/2)which is a measure of the tensor polarizability. The ratio δ 0 (ω)/δ 2 (ω) is then independent of slow variations in the intensity but has the same zero crossing. In addition, setting θ ≈ π/2 minimizes the influence of magnetic field pointing stability, which would compromise the stability of δ 2 (ω). Measurements are carr...

Two-photon polarizability of Ba$^+$ ion: Control of spin-mixing process in an ultracold $^{137}$Ba$^+$--$^{87}$Rb mixture

“…Barrett et al [52] used a linearized coupled-cluster method at levels of single-double excitations (SD), and with additional partial triple contributions (SDpT)) to calculate ∆α 0 and zero-crossing wavelengths. Our estimations have good agreement with them and the experimental estimates [2]. We observe a few additional zero-crossing wavelengths (one of them lies in the optical region) for the 6 .…”

“…α C varies very slowly with the frequency and remains almost invariant in the frequency region chosen here. The static value of core II and compared with the recent values [2,52] available in the literature. We also present the differential static scalar (in the absence of light) polarizabilities, a measure of the BBR shift.…”

“…High-precision theoretical advancement leads to accurate experimental explorations such as optical clock [1,2], processing of quantum information [3,4], measurement of fundamental constants, and other atomic properties [4][5][6][7][8]. Singly charged Barium ion (Ba + ) is one of the ideal candidates for these experiments.…”

“…The ion has been drawing the attention of theorists and experimentalists over the last two decades or so. The recent theoretical and experimental ventures [1,2,9] prove its extant significance and challenges in advancing science and technologies. The laser used to control the ion for experimental purposes shifts (Stark shift) energy levels of the ions.…”

“…Moreover, the scalar part of the differential polarizability measures the black-body radiation (BBR) shift [2], suppressed only by cooling the system. Although challenging, this crucial part of the polarizability is experimentally measured [10] and reported as one of the most significant systematic uncertainty for the present-day International System of Units (SI).…”