Oriented polar molecules in a solid inert-gas matrix: a proposed method for measuring the electric dipole moment of the electron

We propose a very sensitive method for measuring the electric dipole moment of the electron using polar molecules embedded in a cryogenic solid matrix of inert-gas atoms. The polar molecules can be oriented in the $\hat{\rm{z}}$ direction by an applied electric field, as has recently been demonstrated by Park, et al. [Angewandte Chemie {\bf 129}, 1066 (2017)]. The trapped molecules are prepared into a state which has its electron spin perpendicular to $\hat{\rm{z}}$, and a magnetic field along $\hat{\rm{z}}$ causes precession of this spin. An electron electric dipole moment $d_e$ would affect this precession due to the up to 100~GV/cm effective electric field produced by the polar molecule. The large number of polar molecules that can be embedded in a matrix, along with the expected long coherence times for the precession, allows for the possibility of measuring $d_e$ to an accuracy that surpasses current measurements by many orders of magnitude. Because the matrix can inhibit molecular rotations and lock the orientation of the polar molecules, it may not be necessary to have an electric field present during the precession. The proposed technique can be applied using a variety of polar molecules and inert gases, which, along with other experimental variables, should allow for careful study of systematic uncertainties in the measurement

Displacement operators: the classical face of their quantum phase

In quantum mechanics, the operator representing the displacement of a system in position or momentum is always accompanied by a path-dependent phase factor. In particular, two non-parallel displacements in phase space do not compose together in a simple way, and the order of these displacements leads to different displacement composition phase factors. These phase factors are often attributed to the nonzero commutator between quantum position and momentum operators, but such a mathematical explanation might be unsatisfactory to students who are after more physical insight. We present a couple of simple demonstrations, using classical wave mechanics and classical particle mechanics, that provide some physical intuition for the phase associated with displacement operators.Comment: 14 pages, 4 figures, reorganized and reformatte

Search for the electric dipole moment of the electron with thorium monoxide

The electric dipole moment of the electron (eEDM) is a signature of CP-violating physics beyond the Standard Model. We describe an ongoing experiment to measure or set improved limits to the eEDM, using a cold beam of thorium monoxide (ThO) molecules. The metastable $H {}^3\Delta_1$ state in ThO has important advantages for such an experiment. We argue that the statistical uncertainty of an eEDM measurement could be improved by as much as 3 orders of magnitude compared to the current experimental limit, in a first-generation apparatus using a cold ThO beam. We describe our measurements of the $H$ state lifetime and the production of ThO molecules in a beam, which provide crucial data for the eEDM sensitivity estimate. ThO also has ideal properties for the rejection of a number of known systematic errors; these properties and their implications are described.Comment: v2: Equation (11) correcte

Shot-noise-limited spin measurements in a pulsed molecular beam

Heavy diatomic molecules have been identified as good candidates for use in electron electric dipole moment (eEDM) searches. Suitable molecular species can be produced in pulsed beams, but with a total flux and/or temporal evolution that varies significantly from pulse to pulse. These variations can degrade the experimental sensitivity to changes in spin precession phase of an electri- cally polarized state, which is the observable of interest for an eEDM measurement. We present two methods for measurement of the phase that provide immunity to beam temporal variations, and make it possible to reach shot-noise-limited sensitivity. Each method employs rapid projection of the spin state onto both components of an orthonormal basis. We demonstrate both methods using the eEDM-sensitive H state of thorium monoxide (ThO), and use one of them to measure the magnetic moment of this state with increased accuracy relative to previous determinations.Comment: 12 pages, 6 figure

Magnetic and electric dipole moments of the H 3Δ1H\ {}^3\Delta_1 state in ThO

The metastable $H \ {}^3\Delta_1$ state in the thorium monoxide (ThO) molecule is highly sensitive to the presence of a CP-violating permanent electric dipole moment of the electron (eEDM). The magnetic dipole moment $\mu_H$ and the molecule-fixed electric dipole moment $D_H$ of this state are measured in preparation for a search for the eEDM. The small magnetic moment $\mu_H = 8.5(5) \times 10^{-3} \ \mu_B$ displays the predicted cancellation of spin and orbital contributions in a ${}^3 \Delta_1$ paramagnetic molecular state, providing a significant advantage for the suppression of magnetic field noise and related systematic effects in the eEDM search. In addition, the induced electric dipole moment is shown to be fully saturated in very modest electric fields ($<$ 10 V/cm). This feature is favorable for the suppression of many other potential systematic errors in the ThO eEDM search experiment.Comment: 4 pages, 3 figure

Magnetic and electric dipole moments of the H^3 Δ_1 state in ThO

The metastable H^3 Δ_1 state in the thorium monoxide (ThO) molecule is highly sensitive to the presence of a CP -violating permanent electric dipole moment of the electron (eEDM) [E. R. Meyer and J. L. Bohn, Phys. Rev. A 78, 010502 (2008)]. The magnetic dipole moment μ_H and the molecule-fixed electric dipole moment D_H of this state are measured in preparation for a search for the eEDM. The small magnetic moment μH=8.5(5)×10^(−3)μ_B displays the predicted cancellation of spin and orbital contributions in a ^3Δ_1 paramagnetic molecular state, providing a significant advantage for the suppression of magnetic field noise and related systematic effects in the eEDM search. In addition, the induced electric dipole moment is shown to be fully saturated in very modest electric fields (<10 V/cm). This feature is favorable for the suppression of many other potential systematic errors in the ThO eEDM search experiment

A Dielectric Superfluid of Polar Molecules

We show that, under achievable experimental conditions, a Bose-Einstein condensate (BEC) of polar molecules can exhibit dielectric character. In particular, we derive a set of self-consistent mean-field equations that couple the condensate density to its electric dipole field, leading to the emergence of polarization modes that are coupled to the rich quasiparticle spectrum of the condensate. While the usual roton instability is suppressed in this system, the coupling can give rise to a phonon-like instability that is characteristic of a dielectric material with a negative static dielectric function.Comment: Version published in New Journal of Physics, 11+ pages, 4 figure