Ultracold neutron energy spectrum and storage properties from magnetically induced spin depolarization

TL;DR

Uncertainty in the ultracold neutron (UCN) energy spectrum within storage traps limits precision measurements such as the neutron electric dipole moment (nEDM). The authors introduce a magnetically induced spin-depolarization approach that uses coil-generated magnetic gradients to simultaneously extract the energy spectrum $n(\epsilon)$ and surface-diffusivity parameters by fitting Ramsey spin-precession data, supported by trajectory simulations. Applied to two n2EDM storage chambers, the method yields consistent spectra and diffuse parameters, validated against a separate magnetic-filter polarization measurement, and provides a prediction for the vertical center-of-mass offset $\langle z\rangle$ relevant to systematic shifts. This non-invasive, self-consistent characterization of UCN traps improves modeling of gravity- and gradient-induced systematics in nEDM analyses and co-magnetometry.

Abstract

We present a novel method for extracting the energy spectrum of ultracold neutrons from magnetically induced spin depolarization measurements using the n2EDM apparatus. This method is also sensitive to the storage properties of the materials used to trap ultracold neutrons, specifically, whether collisions are specular or diffuse. We highlight the sensitivity of this new technique by comparing the two different storage chambers of the n2EDM experiment. We validate the extraction by comparing to an independent measurement for how this energy spectrum is polarized through a magnetic-filter, and finally, we calculate the neutron center-of-mass offset, an important systematic effect for measurements of the neutron electric dipole moment.

Figures (4)

• Figure 1: Measured spin asymmetry $A=(N_\uparrow-N_\downarrow)/(N_\uparrow+N_\downarrow)$ as a function of the driving frequency to induce a $\pi/2$ spin flip pulse, $f_{\pi/2}$, in two magnetic field configurations. (Purple): $B=940$ nT with no vertical gradient. (Orange): $B=940$ nT with a vertical gradient of $G_{1,0}=300$ pTcm. Following Eq. \ref{['eqn:grav_depolarization']}, $\alpha$ decreases with $G$. The statistical uncertainty on the asymmetry is shown but not visible and on the order of $1\%$. In both cases, the precession time is $T=180$ s. The asymmetry is fitted to $A(f_{\pi/2})=-\alpha \cos{\left( \frac{\pi}{\Delta \nu}\left( f_{\pi/2}-f_n\right) \right)}$ in order to extract $\alpha$, where $1/\Delta \nu=2T+8t_{\pi/2}/\pi$ and the duration of the $\pi/2$ pulse is set to $t_{\pi/2}=2$ s. The curves shift in $f_{\pi/2}$ due to an induced frequency shift in $f_n$ proportional to $G$.
• Figure 2: Spin depolarization for different magnetic gradients in the top (red) and bottom (blue) storage chambers of n2EDM. The data points are the extracted visibility from measuring the asymmetry at each gradient (see Figure \ref{['fig:visibility']}). The lower panel in each graph shows the percent residual between the data and theory. The error on the residual points is the normalized data statistical error, whereas the band shows the calculation $\pm1\sigma$ normalized spread from the bootstrapped minimization. (TOP): Gravitationally enhanced depolarization from the vertical gradient $G_{1,0}$. (BOTTOM): Intrinsic depolarization from linear gradient $G_{1,1}$. The fitted gradients $G_{1,-1},G_{2,0}$ are not shown here for brevity, but are in the supplemental and of similar quality.
• Figure 3: (TOP): Extracted energy spectrum for the top (red) storage chamber and bottom (blue) storage chamber. The dashed line is the $50$th percentile and bands demonstrate $16-84$ percentile spread from the bootstrapped minimization. (BOTTOM): Correlation of the diffuse parameters for the electrode and ring surfaces of the bottom storage chamber. The color scale indicates the number of solutions from the bootstrapped minimization in a given bin. Here, $p=0$ would be perfectly specular reflections, while $p=1$ is perfectly diffuse. See text for discussion.
• Figure 4: LFS-HFS neutron asymmetry as a function of polarizing magnet strength $B_\mathrm{polarizer}$ for the top (red) chamber and bottom (blue) chamber. The points are the measured spin-asymmetry after 200 s storage, rescaled to lie between 0-100%. The curves are using the extracted energy spectra from Figure \ref{['fig:results']}. The statistical uncertainty on the asymmetry is shown but not visible and on the order of $1\%$. See text for details.