A Simulation Framework for Ramsey Interferometry

Abstract

The sensitivity of Ramsey interferometry experiments is governed by the interplay between the beam phase-space distribution and the magnetic field environment through which the spins propagate. Quantitative optimisation thus requires a consistent treatment of optics, magnetics and spin dynamics. We present a simulation framework that enables such an analysis by combining neutron optics simulations in McStas, magnetic field modelling in COMSOL and spin-dynamics simulation in the new RamseyProp program. We describe how important experimental parameters such as adiabaticity, flip angle distributions and Ramsey fringe contrast can be studied. The code is being applied to design an experiment to search for axion-like particles at the European Spallation Source (ESS). We examine how the pulsed time structure of the ESS can be exploited to perform Ramsey interferometry on a broad neutron velocity spectrum. In the absence of velocity or timing restrictions, the standard deviation of the spin flip angle at zero detuning can be reduced from 0.67 to 0.17 radians using time-dependent amplitude modulation. Similarly, the phase sensitivity can be improved by a factor of 4 for a 10 m long setup starting 15 m from the ESS moderator.

Figures (7)

• Figure 1: Conceptual sketch of an experiment to search for axion-like particles at the European Spallation Source. Neutrons emanating from the moderator are focussed, chopped and collimated before entering a 10 m long magnetic shield. Inside the magnetic shield is a neutron polarizer, a Ramsey setup with constant $B_0$ field and RF coils, which is followed by an analyser and a neutron detector.
• Figure 2: Example outputs from RamseyProp. In this simulation, the magnetic field distributions are interpolated from COMSOL, with an applied $B_0=100µT$ in the central region, higher fields exceeding $1mT$ close to the edges and an effective $B_1=28.6µT$ from two coils located at $z=2m$ and $z=8m$. This particular trajectory has zero detuning, hence an outgoing polarisation of $-1$ is achieved after the second coil. Panel (a) shows the magnetic field distribution in Cartesian components and the adiabaticity experienced along the trajectory. Panel (b) shows the corresponding evolution of the spin components as calculated from the Bloch equation.
• Figure 3: The Ramsey fringes obtained for an interferometry setup with free precession length $L=8cm$, coil length $\ell=1cm$, $B_0=10mT$, and $B_1=600µT$ for a single neutron velocity $v=700m/s$. The blue line indicates the analytical Ramsey equation while the 500 orange points correspond to individual neutrons simulated in RamseyProp.
• Figure 4: Spectral distributions of the HIBEAM beamline at the ESS E5 beam port as used for simulation in RamseyProp. Panel (a) shows the time distribution in the MCPL file (15 m from the moderator) as well as the extrapolated distributions at the moderator and at 25 m. Panel (b) shows the velocity distribution and Panel (c) shows the divergence distribution relative to the longitudinal axis of the Ramsey setup.
• Figure 5: The distribution of flip angles, defined as the arccosine of the projection on the direction of incident spin, after passage through a 0.3 m coil located 16 m from the moderator. Panel (a) shows the distribution for the full spectrum without velocity compensation or acceptance cuts, while Panel (b) is the same result when including a time-dependent amplitude modulation of the $B_1$ amplitude. Panel (c) places additional time restrictions on the beam, assuming passage through a 0.3 ms window at 6.7 m from the moderator. In each case, 10 000 neutrons are simulated at $\mathrm{d}t = e-6s$.