Geometric phases in electric dipole searches with trapped spin-1/2 particles in general fields and measurement cells of arbitrary shape with smooth or rough walls

Abstract

The important role of geometric phases in searches for a permanent electric dipole moment of the neutron, using Ramsey separated oscillatory field nuclear magnetic resonance, was first noted by Commins and investigated in detail by Pendlebury et al. Their analysis was based on the Bloch equations. In subsequent work using the spin density matrix Lamoreaux and Golub showed the relation between the frequency shifts and the correlation functions of the fields seen by trapped particles in general fields (Redfield theory). More recently we presented a solution of the Schrödinger equation for spin-$1/2$ particles in circular cylindrical traps with smooth walls and exposed to arbitrary fields [Steyerl et al.] Here we extend this work to show how the Redfield theory follows directly from the Schrödinger equation solution. This serves to highlight the conditions of validity of the Redfield theory, a subject of considerable discussion in the literature [e.g., Nicholas et al.] Our results can be applied where the Redfield result no longer holds, such as observation times on the order of or shorter than the correlation time and non-stochastic systems and thus we can illustrate the transient spin dynamics, i.e. the gradual development of the shift with increasing time subsequent to the start of the free precession. We consider systems with rough, diffuse reflecting walls, cylindrical trap geometry with arbitrary cross section, and field perturbations that do not, in the frame of the moving particles, average to zero in time. We show by direct, detailed, calculation the agreement of the results from the Schrödinger equation with the Redfield theory for the cases of a rectangular cell with specular walls and of a circular cell with diffuse reflecting walls.

20 pages, 8 figures

References in corpus (6)

• An Improved Experimental Limit on the Electric Dipole Moment of the Neutron
• Plans for a Neutron EDM Experiment at SNS
• A measurement of the neutron to 199Hg magnetic moment ratio
• Gravitational Depolarization of Ultracold Neutrons: Comparison with Data
• Universality of spin-relaxation for spin 1/2 particles diffusing over magnetic field inhomogeneities in the adiabatic regime
• Calculation of geometric phases in electric dipole searches with trapped spin-1/2 particles based on direct solution of the Schrödinger equation

Cited by in corpus (8)

• Electric Dipole Moments of the Atoms, Molecules, Nuclei and Particles
• The design of the n2EDM experiment
• Magnetic field uniformity in neutron electric dipole moment experiments
• Spin Dressed Relaxation and Frequency Shifts from Field Imperfections
• A magic magnetic field to measure the neutron electric dipole moment
• Mapping of the magnetic field to correct systematic effects in a neutron electric dipole moment experiment
• The neutron electric dipole moment experiment at the Spallation Neutron Source
• Nonextensive statistics in spin precession