Optical clock sensitive to variations of the fine-structure constant based on theHo14+ion

Abstract

We study the Ho 14+ ion as a candidate for extremely accurate and stable optical atomic clock which is sensitive to the time variation of the fine structure constant. We demonstrate that the proposed system has all desired features including relatively strong optical electric dipole and magnetic dipole transitions which can be used for cooling and detection. Zero quadrupole moments for the relevant states in the clock transition allows interrogating multiple ions to improve the clock stability.PACS numbers: 06.30. Ft, 06.20.Jr, 31.15.A, 32.30.Jc Theories unifying gravity with other fundamental interactions suggest a possibility for fundamental constants to vary in space or time (see, e.g. [1]). Searching for variation of the fundamental constants is an important way of testing these theories and finding new physics beyond standard model. Laboratory measurements limit the rate at which the fine structure constant α (α = e 2 /hc) varies in time to about 10 −17 per year [2,3]. On the other hand, the analysis of quasar absorption spectra shows that the fine structure constant may vary on astronomical scale along a certain direction in space forming the so called alpha-dipole [4]. Earth movement in the framework of the alpha-dipole (towards area of bigger alpha) 4f 6 5s 4f 5 s 2~4 0000 cm -1clock hfs-E1 λ~400 nm 6 H 5/2 (5) IonGround state Clock state Energy (cm −1 ) Er 14+ 4f 7 5s J = 4 4f 6 5s 2 J = 0 18555 Dy 10+ 4f 7 5p J = 3 4f 6 5p 2 J = 0 20835 Ho 14+ 4f 6 5s J = 0.5 4f 5 5s 2 J = 2.5 23800 would lead to the local time variation of α on the scale of 10 −19 per year [5]. To test the alpha-dipole hypothesis in terrestrial studies one needs a better accuracy in the laboratory measurements. The current best limit on the local time variation of α has been obtained by comparing Al + and Hg + optical clocks [2]. The result of this comparison limits time variation of alpha to (∂α/∂t)/α = (−1.6±2.3)×10 −17 yr −1 [2]), i.e. about two orders of magnitude improvement in accuracy is needed to test the alpha-dipole hypothesis. Current-best optical-clocks approach fractional uncertainty of ∼ 10 −18 [6][7][8]. However, the transitions used in these clocks are not sufficiently sensitive to the variation of α [9]. If α does change in time, the relative change δω/ω of the clock frequencies in any given period of time would be about an order of magnitude smaller than relative change in δα/α.It has been suggested in [10] to use highly-charged ions (HCI) as extremely accurate atomic clocks to probe possible variation of α. While HCIs are less sensitive to external perturbations due to their compact size, their sensitivity to variation of α is enhanced due to larger relativistic effects. In spite of the general trend of increasing energy intervals in HCIs, it is still possible to find clock transitions which are in optical range. This is due to electron energy level crossing while moving from the Modelung to the Coulomb level ordering with increasing

Hyperfine-induced electric dipole contributions to the electric octupole and magnetic quadrupole atomic clock transitions

“…Measuring the ratio of frequency of this transition to the frequency of the 4f 14 6s 2 S 1/2 − 4f 14 5d 2 D 3/2 transition in the same ion put the strongest limit on the temporal variation of the fine structure constant and (by including the Cs hyperfine transition) on the proton-to-electron mass ratio [8,9,[22][23][24]. The use of the electric octupole transition in Yb + for the search of LLI violation may lead to five orders of magnitude improvement over current best bounds on the LLI violation in the electron-photon sector [11].Many similar opportunities come with the use of optical transitions in highly-charged ions (HCI) [2][3][4][5]10]. For example, the spectrum of the Ir 17+ ion has been recently measured [25] with the prospect of using the 4f 13 5s 3 F o 4 − 4f 12 5s 2 3 H 6 transition for the time keeping and fundamental research.…”

“…Many similar opportunities come with the use of optical transitions in highly-charged ions (HCI) [2][3][4][5]10]. For example, the spectrum of the Ir 17+ ion has been recently measured [25] with the prospect of using the 4f 13 5s 3 F o 4 − 4f 12 5s 2 3 H 6 transition for the time keeping and fundamental research.…”

“…This is may be a fine structure interval for the ground or clock state. The clock transition in 165 Ho 14+ ion [10] is an example.…”

“…They also present unique opportunities for fundamental research by being sensitive to new physics beyond the Standard Model. The transitions are very sensitive to the temporal variation of the fine structure constant α (α = e 2 /hc) [2][3][4][5][6][7][8][9][10], to the local Lorentz invariance (LLI) violation [11], the effect of dark matter [12][13][14][15][16][17][18], etc. For example, the 4f 14 6s 2 S 1/2 − 4f 13 6s 2 2 F o 7/2 transition in Yb + offers opportunities for frequency measurements with fractional accuracy ∼ 10 −18 [1].…”

A tunable low-drift laser stabilized to an atomic reference

“…For example, due to high relativistic contributions to the binding energy of their electrons, some transitions in HCIs are exceptionally sensitive to a change of the fine structure constant [1]. Also, small polarizabilities and high internal fields render HCIs insensitive to external perturbations, promising small systematic shifts in atomic clocks based on optical transitions in HCIs [2,3]. However, laser spectroscopy of HCIs is still in its infancy.…”