Accurate determination of black-body radiation shift, magic and tune-out wavelengths for the 6S_1/2$ \rightarrow $ 5D_3/2clock transition in Yb⁺

Abstract

We present precise values of the dipole polarizabilities (α) of the ground [4f 14 6s] 2 S 1/2 and metastable [4f 14 5d] 2 D 3/2 states of Yb + , that are important in reducing systematics in the clock frequency of the [4f 14 6s] 2 S 1/2 → [4f 14 5d] 2 D 3/2 transition. The static values of α for the ground and [4f 14 5d] 2 D 3/2 states are estimated to be 9.8(1)×10 −40 Jm 2 V −2 and 17.6(5)×10 −40 Jm 2 V −2 , respectively, while the tensor contribution to the [4f 14 5d] 2 D 3/2 state as −12.3(3) × 10 −40 Jm 2 V −2 compared to the experimental value −13.6(2.2) × 10 −40 Jm 2 V −2 . This corresponds to the differential scalar polarizability value of the above transition as −7.8(5) × 10 −40 Jm 2 V −2 in contrast to the available experimental value −6.9(1.4) × 10 −40 Jm 2 V −2 . This results in the black-body radiation (BBR) shift of the clock transition as −0.44(3) Hz at the room temperature, which is large as compared to the previously estimated values. Using the dynamic α values, we report the tune-out and magic wavelengths that could be of interest to subdue systematics due to the Stark shifts and for constructing lattice optical clock using Yb + .

Coherent excitation of the highly forbidden electric octupole transition in ${}^{172}$Yb$^+$

“…Using the information provided by Refs. [31][32][33][34], we compute the differential polarizability of the used m J = ±1/2 → ±5/2 transition at 411 nm to be 2.8(1.5)×10 −39 Jm 2 V −2 , leading to a shift of 0.003(2) Hz for the used π-pulses of 1.6 ms.…”

“…The involved differential polarizability for the E2 transition is computed to be −4.5(2.3) × 10 −40 Jm 2 V −2 using Refs. [31][32][33][34], where the static value of −4.3(2.2) × 10 −40 Jm 2 V −2 was corrected for the BBR spectrum [33,38], whereas for the E3 transition the value can be found in Ref. [19].…”

Engineering spin-spin interactions with optical tweezers in trapped ions

“…In order to test the feasibility of changing the local trap frequency on this scale, we estimate the effect of a single tweezer. For 171 Yb + , and an experimentally feasible tweezer power of P = 1 W, a waist of W 0 = 1 µm and wavelength λ = 1070 nm, we find that the local trap frequencies due to the tweezers are ∼ 2π• 200 kHz [31,32].…”

Microwave spectroscopy of the Yb 6s(n+3)d→6sng , 6snh

“…Ref. [29] extracts the Yb + electric dipole matrix elements E1 6s 1/2 |r|6p 3/2,1/2 from the lifetime measurements of the 6p 1/2,3/2 levels in Yb + ion of Ref. [30] and [31] to calculate α d , yielding α d = 59.3(8) a 3 0 .…”