Neutron Spin Echo as a Quantum Interference System

Neutron spin echo systems use the superposition of two longitudinal wave fields with slightly different momenta produced either by the longitudinal Zeeman splitting in the case of dc spin echo systems or by a coherent energy transfer by means of neutron magnetic resonance systems and are, therefore, equivalent to neutron interferometers. The systems are rather similar to the familiar Ramsey-Bordé interferometers used in atom interferometry. Spin rotation and momentum change can be considered as an entanglement of various quantum states and Bell-like inequalities can be formulated. A quantum optical description of the quantum states inside the spin echo devices based on the Wigner formalism will be presented. The difference between the state functions for dc and resonance spin echo systems will be demonstrated and methods for a quantum state reconstruction will be discussed. This provides a new access to basic features of the quantum world. The Wigner functions show the non-classical features of these states and their fragility against any fluctuations of the field parameters. Schrödinger cat-like states can be identified with a spatial separation of up to several micrometers. This spatial separation is directly related to the spin echo time used in spin echo spectroscopy.