Magnetic field effects in the transitions of the HD⁺molecular ion and precision spectroscopy

Abstract

We analyse the effects of an external magnetic field on the ro-vibrational, rotational and radiofrequency transitions of the HD + molecular ion-an important systematic effect in precision spectroscopy of HD + , which is of interest for metrology of the fundamental constants. The effects of an external magnetic field on the ro-vibrational, rotational and radiofrequency (hyperfine) transitions of the HD + molecular ion are considered, for one-photon and, where relevant, two-photon transitions. The hyperfine structure of the spectrum lines is taken into account. Particular attention has been devoted to those transitions which are most insensitive to the magnetic field and its orientation with respect to the polarization of the radiation field. We identify experimentally accessible two-photon transitions that exhibit no Zeeman shift, one-photon and two-photon transitions that provide symmetrically split doublets, and one-photon transitions that show only a very weak quadratic Zeeman shift. The importance of the spin-stretched states is emphasized. The results can be used to determine the most suitable transitions given the experimental conditions.

High-precision spectroscopy of the HD+ molecule at the 1-p.p.b. level

“…This procedure is similar to that followed in Refs. [10,39] and can readily be done for the case of σ + , σ − and π transitions and superpositions thereof. As the Zeeman splitting is small compared to the Doppler width, the magnetic subcomponents belonging to the same hyperfine component overlap well within the profile of the lineshape function D z , forming a new composite (and Zeeman-shifted) lineshape function D ′ z .…”

Infrared dynamic polarizability of HD+ rovibrational states

“…In both cases spectroscopy of optical transitions is faced with level shifts due to magnetic and electric fields and, to a lesser extent, shifts due to collisions and relativistic effects. The Zeeman effect of HD + was recently considered by Bakalov et al, and level shifts to second order in the magnetic field were given for a large set of rovibrational states 12,13 . Static polarizabilities of vibrational states with rotational quantum number J = 0, 1 were calculated and reported by several authors 14,15 , while dynamic polarizabilities of HD + vibrational states with J = 0 were evaluated for a discrete set of two-photon transition wavelengths in the 1-18 µm wavelength range 15 .…”

H2+ and HD+Karr1 2014Journal of Molecular Spectroscopy53060View full textAdd to dashboardCite

“…As discussed in [17,27], two types of transitions are particularly interesting for clock applications: …”

“…A few J z = 0 → J ′ z = 0 transitions benefit from a relatively low Zeeman shift (below 100 Hz in a magnetic field of 1 G): Table 2 of [27]). However, none of them were found to have interesting properties in terms of systematic effects, and they will not be considered further.…”

“…(6). Estimates of the two other most important systematic effects are also given: the Zeeman shift ∆fZ in a magnetic field of 1 G from [27], and the quadrupole shift ∆fQ in an electric field gradient of 0.67 × 10 8 V/m 2 (see [17] and corrigendum to be published).…”