Resonant Cancellation Effect in Ramsey-type Nuclear Magnetic Resonance Experiments

Abstract

We investigate the response of a Ramsey-type experiment on an additional oscillating magnetic field. This superimposed field is oriented in the same direction as the static main magnetic field and causes a modulation of the original Larmor spin precession frequency. The observable magnitude of this modulation reduces at higher frequencies of the oscillating field. It disappears completely if the interaction time of the particles matches the oscillation period, which we call resonant cancellation. We present an analytical approach that describes the effect and compare it to a measurement using a monochromatic cold neutron beam.

Figures (4)

• Figure 1: Schematic of the experimental apparatus. Neutrons enter the setup from the left. They first pass a polarizer that transmits only one spin state. The neutrons then enter the magnetic field region where a constant magnetic field $B_0$ and an oscillating magnetic field $B_a(t)$ are applied in the vertical direction. Two $6~\mathrm{cm}$-long spin-flip coils with a center-to-center separation of $50~\mathrm{cm}$ allow to flip the spins. After the second spin-flip coil the neutron spin states are analyzed and counted with a $^\text{3}$He detector. There are four apertures to define the beam cross-section and divergence. They also block the reflected beams from the polarizer and analyzer.
• Figure 2: (a) Ramsey frequency scan over the full resonance. The data shows the neutron counts as a function of the spin-flip signal frequency. The solid line serves only as a guide for the eye. (b) Ramsey phase scans were the neutron counts are shown as a function of the relative phase between the two spin-flip signals. The frequency was fixed on resonance at $91.7~\mathrm{kHz}$. Besides a reference measurement (●), we applied various DC offset currents via the auxiliary coil. The measurements with a current of $-100~\mathrm{mA}$ (★), $+100~\mathrm{mA}$ (▼), and $+200~\mathrm{mA}$ (✚) are shown. The solid lines correspond to least-squares fits of a sinusoidal function.
• Figure 3: Neutron signals for oscillating magnetic fields at $f_a$ equal to (a) 252 Hz, (b) 1020 Hz, (c) 1477 Hz, and (d) 2227 Hz. They show the neutron counts as a function of time. The counts are phase-wrapped into two periods of the signal. The data (black) are fitted with a sinusoidal function with a fixed frequency (orange). The fit results are presented in Tab. \ref{['tab:neutronSignalFitResults']}. The measurement time was roughly $100$ seconds for each setting.
• Figure 4: Measurement of the resonant cancellation effect at the Narziss beamline. The normalized ratio of amplitude over offset as a function of the frequency of the oscillating signal is shown. The data (black) are fitted with Eq. (\ref{['eq:resonantCancellationPhase']}) (red). The lower subfigure shows the residuals.