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Physical Review A

Neutrons in a time-dependent magnetic field: Photon exchange and decoherence modeling

Georg Sulyok, Hartmut Lemmel, H. Rauch

Published Mar 21, 2012• 6 citations
Publisher

Abstract

If a quantum mechanical particle passes a spatially finite region of a purely time-dependent potential, coherent emission and absorption of energy take place. Due to Zeeman interaction, this situation can be realized with neutrons crossing an oscillating magnetic field. We solve the corresponding Schr\"odinger equation for fields consisting of an arbitrary number of frequencies and measure the calculated transition amplitudes for the quantized energy transfer by means of time-dependent neutron interferometry. Investigating the interferometer contrast for magnetic signals consisting of a high number of modes whose phases are randomly distributed shows that noise fields and therefore decoherence processes can be modeled in this calculation as well.

DOI
10.1103/physreva.85.033624

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If a quantum mechanical particle passes a spatially finite region of a purely time-dependent potential, coherent emission and absorption of energy take place. Due to Zeeman interaction, this situation can be realized with neutrons crossing an oscillating magnetic field. We solve the corresponding Schr"odinger equation for fields consisting of an arbitrary number of frequencies and measure the calculated transition amplitudes for the quantized energy transfer by means of time-dependent neutron interferometry. Investigating the interferometer contrast for magnetic signals consisting of a high number of modes whose phases are randomly distributed shows that noise fields and therefore decoherence processes can be modeled in this calculation as well.
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.
We calculate a neutron's transition amplitudes to various energy and spin states when it interacts with a magnetic field oscillating in time. Two field configurations are analyzed: the oscillating component normal to the static component when the rotating-wave approximation is inapplicable and the oscillating and static components parallel to each other. The two cases require different mechanisms of angular momentum conservation. Experimental tests are proposed including neutron interferometry and double crystal diffraction, the latter permitting observation of quantized energy transfer from fields oscillating at only a few hundred kilohertz.
Polarized neutron interferometry has been used to measure the amplitudes for the exchange of up to five photons between the neutron and an oscillating magnetic field. The Rabi spin flip configuration and a configuration in which spin flip is suppressed were investigated, because they raise different questions on the conservation of angular momentum. Because of the linearity of the time-dependent interference signal in the exchange amplitudes, photon exchange probabilities below 1% could be resolved.
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.
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.