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Physical Review Letters

Multiphoton Exchange Amplitudes Observed by Neutron Interferometry

Johann Summhammer, Klaus A. Hamacher, Helmut Kaiser, Harald Weinfurter, David L. Jacobson, S. A. Werner

Published Oct 30, 1995• 56 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.75.3206

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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.
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.
The observation of the 4π symmetry of spinor wave functions was one of the first and highly debated neutron interference experiments. Polarized neutrons have been used to verify the spin-superposition principle on a macroscopic level when the spin in one beam path is inverted with respect to the other one. This results in a spin polarization perpendicular to both initial spins. When a Rabi flipper is used the final spin polarization rotates in this perpendicular plane with the Larmor frequency of the flipper field. Thus, it produces a “frozen” Larmor spin rotation in free space. In this case the spin-flip is associated with an energy (photon) transfer which causes this effect. A magnetic Josephson effect-like situation exists when spin-flippers with slightly different resonance frequencies are used in both beam paths. When such a spin reversal is done in both beam paths a magnetic Josephson effect analog has been realized which shows a remarkably high energy resolution. Multiphoton exchange can be achieved when off-resonance fields are used.
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.
The coherent superposition of particle quantum states resulting from different spatial paths shows well-known interference effects. Another type of interference is Larmor precession, which can be described as neutron wave interference in spin space, i.e. interference on the same spatial path. Here we show several new manifestations of interference phenomena of the latter type. The interference is produced by coherent population of different I z = ±½ spin states in a polarized neutron beam between two resonant radio-frequency (RF) spin flippers. Their spin flip probability, and thus the occupation numbers of the spin states, can be tuned between 0 and 1 by changing the RF amplitude. This leads to interference effects in the polarization since the energy exchanged between the RF field and spin yields different phase evolution in the spatial parts of the neutron states. Depending on the preparation of the initial neutron states, five values for the time-independent phase difference between the final neutron states can be observed.
The effect of spin–rotation coupling is measured for the first time with neutrons. The coupling of spin with the angular velocity of a rotating spin turner can be observed as a phase shift in a neutron polarimeter set-up. After the neutron's spin is rotated by 2 π through a rotating magnetic field, different phase shifts are induced for 'up' and 'down' spin eigenstates. This phase difference results in the rotation of the neutron's spin-vector, which turns out to depend solely on the frequency of the rotation of the magnetic field. The experimental results agree well with the solutions acquired by the Pauli–Schrödinger equation.