Abstract – Niels Geerits

Quantum Contextuality in Neutron Spin Echo Interferometry

Conventional neutron interferometers utilize a perfect silicon crystal to split a neutron beam into two coherent sub beams. The same crystal also reflects and recombines the two beams, resulting in interference of the two partial wavefunctions at the detector.

In instruments which use neutron spin echo interferometry, like Spin Echo Small Angle Neutron Scattering (SESANS), the birefringent properties of polarized neutrons in magnetic fields are exploited [1][2]. Neutrons are prepared in a superposition of both spin states. Upon entering a magnetic field, the Zeeman effect splits the neutron wavefunction into two partial wavefunctions, with different kinetic energies. If the magnetic field interface is inclined with respect to the incoming beam the two sub beams are split spatially as in a conventional interferometer. A second field magnetic field region is responsible for recombining the two partial waves. Resonant spin flippers (RSFs) can be used to change the total energy of each spin state of the neutron [4]. Hence a magnetic field region can be emulated using two RSFs [4] and a spin echo interferometer (like SESANS) can be constructed using four RSFs [5]. This approach results in a spin echo interferometer with an additional degree of freedom, the total neutron energy.

Using the spin echo interferometer, Larmor, at ISIS pulsed neutron source, in SESANS mode, we produce GHZ states using the neutron path, energy and spin states and demonstrate a violation of the Mermin inequality, thus providing evidence against non-contextual hidden variable theories [6]. Furthermore, we demonstrate violations of Bell inequalities for spin-path, path-energy and spin-energy providing more corroborative evidence against hidden variable theories [7].

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[2]: F. Li et al., Rev. of Sci. Instr. 85, (2014) 053303.

[3]: V. K. Ignatovich and F. V. Ignatovich, Am. J. Phys. 71, (2003) 1013-1024.

[4]: R. Golub, et al. Am. J. Phys. 62 (9), (1994) 779-778.

[5]: J. Plomp et al., Thin Solid Films 515, (2007) 5732–5735.

[6]: N. D. Mermin, Phys. Rev. Lett. 65, 1838 (1990).

[7]: J. S. Bell, Physics,1, 195 (1964).