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Physical Review A

Noise-induced dephasing in neutron interferometry

Georg Sulyok, Yuji Hasegawa, Jürgen Klepp, Hartmut Lemmel, H. Rauch

Published May 11, 2010• 5 citations
Publisher

Abstract

Decoherence phenomenona in a neutron interferometer are analyzed by simulation of the effects of an environment with magnetic noise fields. Basic calculations and experiments show the validity and limitations of this model system. In particular, loss and recovery of the interference pattern with controllable noise sources in both interferometer arms are discussed in detail. In addition, the decoherence behavior at high interference order, where Schr\"odinger-cat-like states exist in the interferometer, is investigated. While at low interference order a smearing of the interference pattern is observed, at high interference order a smearing of the modulated momentum distribution occurs.

DOI
10.1103/physreva.81.053609

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Decoherence phenomenona in a neutron interferometer are analyzed by simulation of the effects of an environment with magnetic noise fields. Basic calculations and experiments show the validity and limitations of this model system. In particular, loss and recovery of the interference pattern with controllable noise sources in both interferometer arms are discussed in detail. In addition, the decoherence behavior at high interference order, where Schr"odinger-cat-like states exist in the interferometer, is investigated. While at low interference order a smearing of the interference pattern is observed, at high interference order a smearing of the modulated momentum distribution occurs.
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.
Neutron interferometry provides a powerful tool to investigate particle and wave features in quantum physics. Single particle interference phenomena can be observed with neutrons and the entanglement of degrees of freedom, i.e., contextuality can be verified and used in further experiments. Entanglement of two photons, or atoms, is analogous to a double slit diffraction of a single photon, neutron or atom. Neutrons are proper tools for testing quantum mechanics because they are massive, they couple to electromagnetic fields due to their magnetic moment, they are subject to all basic interactions, and they are sensitive to topological effects, as well. The 4π-symmetry of spinor wave functions, the spin-superposition law and many topological phenomena can be made visible, thus showing interesting intrinsic features of quantum physics. Related experiments will be discussed. Deterministic and stochastic partial absorption experiments can be described by Bell-type inequalities. Neutron interferometry experiments based on post-selection methods renewed the discussion about quantum non-locality 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, but where and when a collapse of the wave-field occurs depends on the level of experiment.
A striking spectral-modulation effect has been observed by means of a proper postselection procedure under conditions where the spatial shift of the wave trains greatly exceeds the coherence length of the neutron beams traversing an interferometer. It is shown that Schr\"odinger-cat-like states are created by the superposition of two coherent states generated in the interferometer. These entangled states exhibit, under certain circumstances, characteristic squeezing phenomena, indicating a highly nonclassical behavior. Analogies with optical experiments are discussed.
Entanglement of two photons, or atoms is a complementary situation to a double slit situation of a single photon, neutron or atom. With neutrons single particle interference phenomena can be observed and the “entanglement of degrees of freedom”, i.e. contextuality can be verified. In this respect, 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 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.
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.
Here we discuss the limits of the recognizability of neutron interference patterns either observed in low-contrast measurements or when collecting very few neutrons only. Low contrast can be caused by a strong beam attenuation or by a large phase shift applied to one beam path. Stochastic and deterministic cases have different influences on the interference pattern, which can be interpreted as a different wavelike or particlelike behavior of the system. Measurements of interference patterns with very few neutrons only are related to the phase--particle-number uncertainty relation, which is discussed on the basis of stochastic and quantum theory arguments. Analogies between coherent-state behavior known in atomic physics and the behavior of neutrons in an interferometer are discussed also.