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arXiv:quant-ph/9904086

Wigner function and coherence properties of cold and thermal neutrons

Paolo Facchi A, Angelo Mariano, Saverio Pascazio

Published Apr 26, 1999• 2 citations
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Abstract

We analyze the coherence properties of a cold or a thermal neutron by utilizing the Wigner quasidistribution function. We look in particular at a recent experiment performed by Badurek {\em et al.}, in which a polarized neutron crosses a magnetic field that is orthogonal to its spin, producing highly non-classical states. The quantal coherence is extremely sensitive to the field fluctuation at high neutron momenta. A "decoherence parameter" is introduced in order to get quantitative estimates of the losses of coherence.

DOI
10.48550/arxiv.quant-ph/9904086

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We analyze the coherence properties of a cold or a thermal neutron by utilizing the Wigner quasidistribution function. We look in particular at a recent experiment performed by Badurek {\em et al.}, in which a polarized neutron crosses a magnetic field that is orthogonal to its spin, producing highly non-classical states. The quantal coherence is extremely sensitive to the field fluctuation at high neutron momenta. A "decoherence parameter" is introduced in order to get quantitative estimates of the losses of coherence.
We analyze the coherence properties of polarized neutrons, after they have interacted with a magnetic field or a phase shifter undergoing different kinds of statistical fluctuations. We endeavor to probe the degree of disorder of the distribution of the phase shifts by means of the loss of quantum-mechanical coherence of the neutron. We find that the notion of entropy of the shifts and that of decoherence of the neutron do not necessarily agree. In some cases the neutron wave function is more coherent, even though it has interacted with a more disordered medium.
We analyse the coherence properties of neutron wavepackets, after they have interacted with a phase shifter undergoing different kinds of statistical fluctuation. We give a quantitative (and operational) definition of decoherence and compare it to the standard deviation of the distribution of the phase shifts. We find that in some cases the neutron ensemble is more coherent, even though it has interacted with a wider (i.e. more disordered) distribution of shifts. This feature is independent of the particular definition of decoherence: this is shown by proposing and discussing an alternative definition, based on the Wigner function, that displays a similar behaviour. We briefly discuss the notion of entropy of the shifts and find that, in general, it does not correspond to that of decoherence of the neutron.
Fluctuations of the magnetic field lead to a dephasing of polarized neutron wave packets and to an attenuation of the interference term of the Wigner distribution. It turns out that the Schrödinger equation can be solved exactly by using a constant space-dependent magnetic potential plus an arbitrary number of time-dependent cosine- and sine-shaped potentials with different frequencies and amplitudes. If the time oscillations are not resolved or if frequency fluctuations are taken into consideration, one can work out a procedure to take the damping characteristics of the interference term into account. An arbitrary statistical noise function can be constructed by Fourier's theorem. This potential leads to depolarization due to a loss of phase correlation. One can simulate the transition from coherence to decoherence which can be used in ongoing spin-echo and quantum state reconstruction experiments.
The neutron interferometer set-up S18 at the ILL reactor has been used for the first neutron quantum state reconstruction experiment. By a simultaneous measurement of the coherence function and of the modulated momentum distribution behind the interferometer, the Wigner function of various quantum states can be reconstructed. This is equivalent to knowledge of the particle wavefunction. Its spatial dimension follows from the measurement of the coherence function, which is the autocorrelation function of the wavefunction and the shape in momentum space follows from momentum post-selection experiments. Non-orthogonal traces through the ( x , k )-phase space have to be measured for an unambiguous reconstruction. Nearly classical (coherent) and non-classical states in the form of Schrödinger cat-like states have been identified. Comparisons of calculated and measured Wigner functions will be shown.
Neutrons are proper tools for testing quantum mechanics because they are massive, they couple to electromagnetic fields due to their magnetic moment and they are subject to all basic interactions and they are sensitive to topological effects, as well. Related experiments will be discussed. Recent neutron interferometry experiments based on postselection methods renewed the discussion about quantum nonlocality and the quantum measuring process. It has been shown that interference phenomena can be revived even when the overall interference pattern has lost its contrast. This indicates a persisting coupling in phase space even in cases of spatially separated Schrödinger Cat-like situations. These states are extremely fragile and sensitive against any kind of fluctuations and other decoherence processes. More complete quantum experiments also show that a complete retrieval of quantum states behind an interaction volume becomes impossible in principle.
Neutrons are proper tools for testing quantum mechanics because they are massive, they couple to electromagnetic fields due to their magnetic moment and they are subject to all basic interactions and they are sensitive to topological effects, as well. Related experiments will be discussed. Deterministic and stochastic partial absorption experiments can be described by Bell-type inequalities. Recent neutron interferometry experiments based on postselection methods renewed the discussion about quantum nonlocality and the quantum measuring process. It has been shown that interference phenomena can be revived even when the overall interference pattem has lost its contrast. This indicates a persisting coupling in phase space even in cases of spatially separated Schrödingercat-like situations. These states are extremely fragile and sensitive against any kind of fluctuations and other decoherence processes. More complete quantum experiments also show that a complete retrieval of quantum states behind an interaction volume becomes impossible in principle. First results of neutron quantum state reconstruction experiments will be presented.