Geometric-phase-induced false electric dipole moment signals for particles in traps

Abstract

Theories are developed to evaluate Larmor frequency shifts, derived from geometric phases, in experiments to measure electric dipole moments (EDM's) of trapped, atoms, molecules, and neutrons. A part of these shifts is proportional to the applied electric field and can be interpreted falsely as an electric dipole moment. A comparison is made between our theoretical predictions for these shifts and some results from our recent experiments, which shows agreement to within the experimental errors of 15%. The comparison also demonstrates that some trapped particle EDM experiments have reached a sensitivity where stringent precautions are needed to minimize and control such false EDM's. Computer simulations of these processes are also described. They give good agreement with the analytical results and they extend the study by investigating the influence of varying surface reflection laws in the hard-walled traps considered. They also explore the possibility to suppress such false EDM's by introducing collisions with buffer gas particles. Some analytic results for frequency shifts proportional to the square of the E field are also given and there are results for the averaging of the B field in the absence of an E field.

Ultra-sensitive magnetometry based on free precession of nuclear spins

“…The cohabiting Hg-magnetometer used before at ILL [33] has reached its limits of sensitivity (B 200 fT ). Furthermore, due to a geometric phase effect [34], particles trapped in electric and magnetic fields accumulate a phase shift, which is linear in E and thus cannot be distinguished from a true EDM effect. As a consequence, the magnetometer has to operate in an E-field free region and thus in a separate volume than the ultra cold neutrons (UCN) unless interparticle-collisions suppress these correlated effects [35].…”

Design and performance of an absolute 3He/Cs magnetometer

“…This spoils the direct comparison of the absolute field value given by different sensors and limits the ability to obtain a consistent picture of the magnetic field inside the apparatus necessary to suppress systematic errors in the EDM measurement such as those mentioned in Sec. 1 caused by the geometric phase effects [2].…”

“…Even more severe, a change in the magnitude of the applied mag-netic field that is correlated to the electric field direction would be misinterpreted as an nEDM, if not corrected for. Moreover, magnetic field gradients may lead to geometrical phase effects [2] that could also mimick an nEDM. A high-sensitivity and high-accuracy measurement of the magnetic field and its variation over the neutron storage volume during the free evolution time is therefore of crucial importance for controlling and suppressing several major systematic errors and ensuring good statistics in the nEDM experiment.…”

“…in transverse (perpendicular to I) magnetic fields are given by the sublevel splitting for parallel (↑↑) and antiparallel (↑↓) magnetic and electric fields [2]. In the PSI a Present address: LogrusData, Vienna, Austria experiment the precession frequency of spin-polarized ultracold neutrons is measured by Ramsey's method of (time-) separated oscillatory fields [3].…”

Random walks with thermalizing collisions in bounded regions: Physical applications valid from the ballistic to diffusive regimes

“…Redfield [4], as elucidated by Slichter [5], and McGregor [6] have given formal derivations of the relation between relaxation and the autocorrelation functions of the fields, and the method was applied to a "false EDM" systematic error, effecting searches for time reversal and parity-violating nonzero particle electric dipole moments [7,8]. General methods for obtaining auto-correlation functions for fluctuations produced by particles diffusing in inhomogeneous fields with arbitrary spatial variation have been given by Refs.…”