High-resolution spectroscopy on trapped molecular ions in rotating electric fields: A new approach for measuring the electron electric dipole moment

Abstract

High-resolution molecular spectroscopy is a sensitive probe for violations of fundamental symmetries. Symmetry violation searches often require, or are enhanced by, the application of an electric field to the system under investigation. This typically precludes the study of molecular ions due to their inherent acceleration under these conditions. Circumventing this problem would be of great benefit to the high-resolution molecular spectroscopy community since ions allow for simple trapping and long interrogation times, two desirable qualities for precision measurements. Our proposed solution is to apply an electric field that rotates at radio frequencies. We discuss considerations for experimental design as well as challenges in performing precision spectroscopic measurements in rapidly time-varying electric fields. Ongoing molecular spectroscopy work that could benefit from our approach is summarized. In particular, we detail how spectroscopy on a trapped diatomic molecular ion with a ground or metastable 3 ∆1 level could prove to be a sensitive probe for a permanent electron electric dipole moment (eEDM).

Zeeman interaction in ThOH3Δ1for the electron electric-dipole-moment search

“…Polar molecules have a number of advantages over atoms for eEDM searches [10,11], including a larger E eff and resistance to a number of important systematics. Some molecules, for example, ThO [5,12], lead oxide (PbO) [13,14], HfF + [15,16], and WC [17,18], have additional advantages due to the existence of closely spaced levels of opposite parity, called an doublet. Molecules with doublets can typically be polarized in modest laboratory electric fields ( 1-100 V/cm), and in addition the spin-precession measurement can be carried out in a state where the molecular dipole is either aligned or antialigned with the external laboratory field.…”

“…As discussed in detail elsewhere [5,12,38], the terms in Eq. (15) are determined by performing a spin-precession measurement on a pulsed molecular beam of ThO molecules. By measuring the phase accumulated by a superposition of the M = ±1 Zeeman sublevels (in any level with J 1), we can determine the spin-precession frequency ω = E/ , where E is the energy splitting between the M = ±1 states, and then calculate E. By measuring this frequency with all possible values ofÑ ,Ẽ, andB, we can determine each of the terms in Eq.…”

Broadband velocity modulation spectroscopy of HfF+: Towards a measurement of the electron electric dipole moment

“…Another important value for the eEDM measurements is the size of the Λ-doubling in the 3 ∆ 1 J = 1 level; it is the opposite parity levels in this state that are mixed in an electric field to polarize the molecule. The necessary electric field for full polarization, E pol , is approximately where the Stark energy is larger than the energy difference between the two parity states: thus E pol ≈ ω e f /2πd m f [7], where ω e f is the Λ-doubling splitting (in angular frequency) and d m f is the molecular-frame electric dipole moment of the molecule (4.3 Debye for HfF + [10]). We can use our measurement ofõ ∆ to estimate that ω e f = 2π × 4õ ∆ ≈ 2π × 740 kHz, which is at least an order magnitude larger than previously predicted [10].…”

“…After a free-evolution period a readout pulse will be applied to meaure the accumulated phase difference between the two sublevels, which is proportional to the energy difference between the sublevels. A detailed analysis of the proposed experiment can be found in [10]. For this scheme, optical transitions from the metastable 3 ∆ 1 state will most likely be required for state-selective readout via laser induced fluorescence or resonant multiphoton photodissociation (states (b) or (c) in Figure 1 respectively); in addition, transitions coupling the X 1 Σ + state with the 3 ∆ 1 state via some excited state (state (a) in Figure 1) will be necessary for state preparation in the 3 ∆ 1 state.…”

State-specific detection of trapped HfF+ by photodissociation

“…Quantum-state selective detection of molecular ions is a prerequisite for exciting new experiments in precision measurement [1,2], quantum information science [3], and astrochemistry [4]. Many proposed and ongoing precision measurement experiments utilize carefully chosen properties of molecules to improve previous constraints on fundamental symmetries and variations of constants set by experiments based on atoms [5,6,7,8].…”