Motional spin relaxation in large electric fields

We discuss the precession of spin-polarized ultracold neutrons (UCNs) and ${}^3\mathrm{He}$ atoms in uniform and static magnetic and electric fields and calculate the spin relaxation effects from motional $\mathbf{v}\times \mathbf{E}$ magnetic fields. Particle motion in an electric field creates a motional $\mathbf{v}\times \mathbf{E}$ magnetic field, which when combined with collisions produces variations of the total magnetic field and results in spin relaxation of neutron and ${}^3\mathrm{He}$ samples. The spin relaxation times $T_1$ (longitudinal) and $T_2$ (transverse) of spin-polarized UCNs and ${}^3\mathrm{He}$ atoms are important considerations in a new search for the neutron electric dipole moment at the Spallation Neutron Source $n\mathrm{EDM}$ experiment. We use a Monte Carlo approach to simulate the relaxation of spins due to the motional $\mathbf{v}\times \mathbf{E}$ field for UCNs and for ${}^3\mathrm{He}$ atoms at temperatures below $600\mathrm{mK}$. We find the relaxation times for the neutron due to the $\mathbf{v}\times \mathbf{E}$ effect to be long compared to the neutron lifetime, while the ${}^3\mathrm{He}$ relaxation times may be important for the $n\mathrm{EDM}$ experiment.

Figure 1

(a) Total magnetic field $B$ as the superposition of the holding field $B_0$ and the $\mathbf{v}\times \mathbf{E}$ motional field $B_v$. (b) Rotation of motional field $B_v$ due to wall collision.

Figure 2

(Color online) Simulation results for the longitudinal polarization $P_z$ for a ${}^3\mathrm{He}$ sample in a thermal bath at $T=100\mathrm{mK}$ vs time. An exponential fit to the simulation data is also shown. The fit yields the relaxation time $T_1$.

Figure 3

(Color online) Spin relaxation times $T_1$ and $T_2$ for ${}^3\mathrm{He}$ atoms as a function of temperature, plotted together with the theoretical formulas derived from Eq. (8).

Figure 4

(Color online) Simulation results for longitudinal spin relaxation times $T_1$ for UCNs as a function of velocity and with different electric field strengths. The simulation data agree with the theoretical formalism described by Eq. (11).