Time-Reversal-Violating Generation of Static Magnetic and Electric Fields and a Problem of Electric Dipole Moment Measurement

Abstract

It is shown that in the experiments for search of EDM of an electron (atom, molecule) the T-odd magnetic moment induced by an electric field and the T-odd electric dipole moment induced by a magnetic field will be also measured. It is discussed how to distinguish these contributions.PACS numbers: 32.80. Ys, 11.30.Er, 33.55.Ad Nowadays there is an appreciable progress the in development of methods for ultraweak magnetic and electric field mesurement. Therefore, new experiments for measurement of an electric dipole moment d (EDM) of electrons (atoms, molecules) [1][2][3][4] are being prepared and carried out. The EDM of a particle exists if parity (P) and time-reversal (T) invariance are violated. Investigation of the EDM existence could provide knowledge about physics beyond the Standard Model [1][2][3][4].F.L.Shapiro's idea [5] to measure electron EDM by applying a strong electric field to a subtance that has an unpaired electron spin is being used for EDM search (see [1,6]).Interaction W E of an electric dipole moment d of an electron with an electric field E depends on their orientation:whereis the EDM. Spins of electrons (atoms) at low temperature appear to be polarized similar to the polarization (magnetization) of electrons by a magetic field in paramagnetic subtances due to the interaction W B of an electron (atom) magnetic moment µ with a magnetic field BSpins of electrons (atoms) polarized by an electric field induce the magnetic field B E and change in the magnetic flux Φ at the surface of a flat sheet of material [1]:where χ is the magnetic susceptibility, χ ≈ ρµa 2 3kB T , ρ is the number density of spins of interest, k B is Boltzmann's constant and T is the sample temperature. In the cases where simple Langevin paramagnetism is applicable, E * is the effective electric field at the location of the spins, µ a = g J(J + 1)µ B where µ B is the Bohr magneton, µ a is the atomic or ionic magnetic moment, g is Lande factor and A is the sample area.If an external magnetic field acts on either a para-or a ferromagnetic material, the spins in a substance become polarized due to substance magnetization. Therefore, the electric dipole moments appears polarized too. This results in the induction of an electric field E B (D.DeMille [1]):where P represents the degree that the spins are polarized in the sample. According to the analysis [1], modern methods for measurement of B E and E B provide sensitivity for electric dipole moment measurement about 10−32 e cm and in some cases even 10 −35 e cm. It is important to pay attention to another mechanism of time-reversal violating generation of magnetic and electric fields, which have been discussed in [7,8]. According to the idea of [7,8], an induced magnetic moment µ( E) of a particle appears due to the action of a field E under conditions of violation of P-and T-invariance (and similar, an

Predicting outcomes of electric dipole and magnetic moment experiments

“…might have only EDMs as extensions of standard approach. It was suggested in [3] that all types of particles (atom, molecule, nucleus, neutron, electron) can also have an additional property similar to P/T -odd polarizabilities (in addition to nonzero EDMs). However, a specific implementation of this idea for fermions was missing; this work fills this gap.…”

“…If a system has T -odd polarizabilities and susceptibilities [3,4], see also [5,6], it can generate a magnetic field upon applying the electric one; vice versa, an electric field can be generated by the magnetic one [3,4]. As a direct consequence of admitting nonzero P/T -odd polarizabilities, the magnetic and electric moments that are evaluated without these polarizabilities do acquire additional contributions.…”

MolecularCP-violating magnetic moment

“…A part of this large enhancement lies in a softer excitation spectrum of Bi + and thus smaller energy denominators in Eq. (6). Also, while solving the DHF equations we assumed that the outer shell of Bi + ion has the 6p 2 1/2 electronic configuration.…”

“…The effect of CPviolation on electromagnetic properties of the media has been considered by a number of authors (see, e.g., [6,8,9,10]). In particular, the atomic CP-violating (T,Podd) polarizability β CP relates induced atomic magnetic moment µ CP at to the externally applied electric field E,…”

“…where β CP (Cs + ) is a so-called CP-violating polarizability [6,7] of the Cs + ion. Thus the molecular two-center problem is reduced to computing a one-center property -CP-violating polarizability of the heavier constituent.…”