Decomposing Magnetic Dark-Field Contrast in Spin Analyzed Talbot-Lau Interferometry: A Stern-Gerlach Experiment without Spatial Beam Splitting

We have recently shown how a polarized beam in Talbot-Lau interferometric imaging can be used to analyze strong magnetic fields through the spin dependent differential phase effect at field gradients. While in that case an adiabatic spin coupling with the sample field is required, here we investigate a nonadiabatic coupling causing a spatial splitting of the neutron spin states with respect to the external magnetic field. This subsequently leads to no phase contrast signal but a loss of interferometer visibility referred to as dark-field contrast. We demonstrate how the implementation of spin analysis to the Talbot-Lau interferometer setup enables one to recover the differential phase induced to a single spin state. Thus, we show that the dark-field contrast is a measure of the quantum mechanical spin split analogous to the Stern-Gerlach experiment without, however, spatial beam separation. In addition, the spin analyzed dark-field contrast imaging introduced here bears the potential to probe polarization dependent small-angle scattering and thus magnetic microstructures.

Figure 1

Setup details. (a) Sketch of the polarized Talbot-Lau interferometer including optional polarization analysis. The setup consists of an adiabatic fast passage spin flipper (AFP), a beryllium filter (Be filter), two V-coils, a source grating ${\mathrm{G}}_0$, a phase grating ${\mathrm{G}}_1$, an analyzer grating ${\mathrm{G}}_2$, a detector, a guide field system, and a polarization analyzer. The probed polarization direction is along the $z$ axis. The sample is placed between ${\mathrm{G}}_0$ and ${\mathrm{G}}_1$. The North and South poles are depicted in red and blue. (b) Hall probe map of the magnetic field between the square-shaped pole shoes. The white line indicates the edges of the magnets, while the green one highlights the region at which the effect is described by the Wigner function calculations.

Figure 2

Results without polarization analysis. (a) DFI and (c) DPCI of the magnetic field prism measured without the spin analyzer. The North and South pole shoes are depicted in blue and red; (a),(c) share the same size scale bar. (b),(d) Horizontal line profiles of the DFI and DPCI along the dashed lines depicted in (a),(c). (e) Illustration of the effect on the as-measured interference pattern $|\uparrow ⟩+|\downarrow ⟩$ (red) according to an ideal open beam modulation ($I_0$) (blues) and the thus-assumed individual and separate interference patterns of the spin-up $|\uparrow ⟩$ (orange) and spin-down $|\downarrow ⟩$ (green) states in the plateau regions where the dark-field contrast is quantified to $V/V_0=0.87$.

Figure 3

Results with polarization analysis. (a) DFI and (c) DPCI of the magnetic field prism measured with the spin analyzer. The North and South pole shoes are depicted in blue and red; (a),(c) share the same size scale bar. (b),(d) Horizontal line profiles of the DFI and DPCI along the dashed lines depicted in (a),(c). The gray areas show the blind region lying outside the field of view of the analyzer. (e) Illustration of the corresponding effect on the as measured interference pattern of the spin-up $|\uparrow ⟩$ (orange), according to an ideal open beam modulation (blue) in the plateau regions where $C_r=0.5\mathrm{rad}$.