Measurement of Dipole Matrix Elements with a Single Trapped Ion

Abstract

We demonstrate a method to determine dipole matrix elements by comparing measurements of dispersive and absorptive light ion interactions. We measure the matrix element pertaining to the Ca II H line, i.e. the 4 2 S 1/2 ↔ 4 2 P 1/2 transition of 40 Ca + , for which we find the value 2.8928(43) ea0.Moreover, the method allows us to deduce the lifetime of the 4 2 P 1/2 state to be 6.904(26) ns, which is in agreement with predictions from recent theoretical calculations and resolves a longstanding discrepancy between calculated values and experimental results.PACS numbers: 37.10. Ty, 32.80.Qk, 03.67.Lx Methods for trapping and cooling single or few atoms, molecules or ions and manipulating them at the quantum level have opened up new avenues for precision laser spectroscopy. In particular, quantum logic techniques [1] have enabled a new accuracy regime of timekeeping with optical atomic clocks [2]. In contrast to atomic transition frequencies, dipole matrix elements and radiative lifetimes are still notoriously hard to determine at high accuracy, but are important for the quantification of black body radiation shifts of atomic clocks [3], interpretation of astrophysical spectra [4,5], novel approaches for the search for physics beyond standard model [6,7] and for testing the accuracy of atomic structure calculations [8].Regarding measurements of radiative lifetimes and transition matrix elements, established methods e.g. based on ion beams have been successfully complemented by novel techniques based on trapped particles. For 87 Rb, dipole matrix elements have been determined on the 10 −3 uncertainty level by diffraction in a condensate [9], while for the 6p 2 P o 1/2 state of 174 Yb + , the radiative lifetime has been measured by time-resolved counting of photons emitted from a single trapped ion [10]. A related technique was used for neutral 171 Yb in an optical lattice [11].The species Ca + is widely used in quantum optics experiments, and its II H line led to the discovery of the interstellar medium [12]. For 40 Ca + , branching ratios between different decay channels have been determined at uncertainties approaching the 10 −5 level [13,14], and lifetimes of metastable states have been accurately measured [15]. The radiative lifetime of the 4 2 P 1/2 excited state of 40 In this work, we determine the radiative decay rates and the lifetime of the 4 2 P 1/2 excited state of 40 Ca + together with the dipole matrix element of the 4 2 S 1/2 ↔ 4 2 P 1/2 transition. The cornerstone of our scheme is the comparison between the dispersive and absorptive interactions, which occur upon driving this transition with an off-resonant laser, see Fig. 1. As the method is based on the discrete discrimination of atomic states of a single trapped particle [17,18], it is robust against many systematic error sources which affect other existing methods.The off-resonant laser is characterized by its detuning ∆ from the 4 2 S 1/2 ↔ 4 2 P 1/2 transition, the Rabi frequency Ω and the relative amplitudes q , which characarXiv:1505.025...

Precise determination of the quadrupole transition matrix element ofCa+40via branching-fraction and lifetime measurements

“…A trapped 40 Ca + ion has also been used for precision measurements to test atomic many-body theories [5,6,7]. Such measurements include lifetimes of some low-lying states in 40 Ca + [5,6], branching ratios [8], and dipole transition matrix elements [9]. There are similar developments for 88 Sr + [10].…”

“…Dipole transition matrix elements can also be determined by comparing measurements of dispersive and absorptive light ion interactions [9]. However, for quadrupole transition matrix elements, there have been no experimental measurements for any alkali-metal-like ions, to our knowledge.…”

Precision measurement of the branching fractions of the5pP1/22state inSrLikforman1, Tugayé2, Guibal3 et al. 2016Phys. Rev. A18180View full textAdd to dashboardCite

“…By restricting ourselves to the case of heavier alkali-earth (i.e. species with D metastable states), these techniques have been recently applied to obtain precision measurements of spectroscopical quantities on laser-cooled 40 Ca + ions [9][10][11][12], 138 Ba + ions [13][14][15], and 88 Sr + ions [16][17][18][19]. In this paper we present the precision measurement of the branching fractions for the decay of the 5p 2 P 1/2 state of 88 Sr + .…”

Electromagnetically-induced-transparency ground-state cooling of long ion strings

“…With a linewidth Γ PS /(2π) = 21.57(8) MHz [33], the S 1/2 ⇔ P 1/2 transition enables fast cooling close to the ground state as was shown for a single ion in ref. [19].…”

“…Two different intensity calibration techniques were employed in the experiments. First, light shifts can be precisely determined by measuring the optical pumping rate between S 1/2 Zeeman states [33]. This technique (used in setup 2) relies on a precise knowledge of the laser parameters and the excited state's decay rate.…”