Accuracy estimation of the O216+ transition frequencies targeting the search for the variation in the proton-electron mass ratio

Abstract

In this paper, we estimate the Stark and Zeeman shifts in the transition frequencies of the 16 O2 + molecular ion, as a step for the search for the variation in the proton-to-electron mass ratio µ. The X 2 Π v = 21 − a 4 Π v = 0 or the X 2 Πv = 21 − a 4 Π v = 1 transition frequencies (THz region) of the 16 O2 + molecular ion have particularly high sensitivity to the variation in µ. Note also that the Stark shift in the 16 O2 + transition frequencies is expected to be much smaller than that for heteronuclear diatomic molecules. However, the actual systematic uncertainties for the 16 O2 + transition frequencies have never been estimated. We estimated the Stark and Zeeman shifts in the different 16 O2 + transition frequencies. When the molecular ions in a string crystal formed in a linear trap (trap electric field < 0.1 V/cm, and Stark shift < 10 -20 ) are used, the X 2 Π 1/2 (v, J) = (0, 1/2) − (v ′ , 1/2)(v ′ ≥ 1) transition frequencies are most advantageous for the search for the variation in µ ∆µ/µ < 10 −17 because the Zeeman shift is easily suppressed to lower than 10 -18 and the electric quadrupole shift is zero. On the other hand, the X 2 Π 1/2 (v, J) = (21, 1/2) − a 4 Π 1/2 (v, J) = (0, 1/2) transition frequency has another merit that the positive Stark shift induced by the trap electric field can be canceled by the quadratic Doppler shift. Therefore, the measurement using molecular ions in a Coulomb crystal broadened in the radial direction is also possible, when the Zeeman shift is effectively eliminated. PACS numbers: 32.60.+i, 06.20.Dk, 33.20Ea

Two-Photon Vibrational Transitions in 16O2+ as Probes of Variation of the Proton-to-Electron Mass Ratio

“…Since the 16 O nuclei are spin-0, there are no Zeeman shifts from nuclear spin or hyperfine structure. Zeeman shifts of each energy level from nuclear rotation [33,110,111] are smaller by approximately 10 3 . They should also largely cancel for transitions that do not change Ω, J, and M J because the nuclear-rotation g factors should be comparable for the two vibrational states.…”

“…The current limit for a molecular experiment iṡ µ/µ = (−3.8 ± 5.6) × 10 −14 yr −1 , which is based on a rovibrational transition in SF 6 and was conducted in a molecular beam [27]. Several proposals exist for next-generation searches in diatomic molecules [24][25][26][28][29][30][31][32][33][34][35]. In this manuscript, we provide additional support for the use of the O + 2 molecule [32,33] in such a search.…”

Two-Photon Vibrational Transitions in O₂⁺ as Probes of Variation of the Proton-to-Electron Mass Ratio

“…Several proposals exist for next-generation searches in diatomic molecules [24][25][26][28][29][30][31][32][33][34][35]. In this manuscript, we provide additional support for the use of the O + 2 molecule [32,33] in such a search. Searches for a change in µ usually involve monitoring the energy difference h f between two energies with different µ dependence, h f = E (µ) − E (µ).…”

“…The X 2 Π g electronic ground state of O + 2 is of Hund's case (a) and has two fine-structure manifolds with electronic angular momentum quantum numbers Ω = 1 2 and 3 2 . For reasons discussed in section 4, systematic effects are more favorable in the J = 1 2 rotational state [33]. Thus, the initial state for any experiment should be…”

Optical Pumping of TeH+: Implications for the Search for Varying mp/me

“…Statistical sensitivity of these species, using probe times set by currently available laser coherence, is shown in Table 2. Stark shifts for nonpolar species are favorably small, and other systematic uncertainties can be low, as well [44][45][46].…”