[Paper Review] Comment on "Relativistic effects in atom and neutron interferometry and the differences between them" by Greenberger, Schleich and Rasel

Hartmut Lemmel|arXiv (Cornell University)|Jun 5, 2014

Nuclear Physics and Applications9 references3 citations

TL;DR

This paper challenges the interpretation of relativistic effects in neutron and atom interferometers, arguing that while both systems behave similarly under gravity to first order, neutron interferometers exhibit subtle differences due to dynamical diffraction effects. The key result is that momentum transfer in neutron interferometry is not specular but depends on Bragg condition violations, leading to small but measurable changes in flight time and transverse momentum, which affect interference contrast but not the primary phase shift.

ABSTRACT

Bragg diffraction is comparable to a hard-wall reflection if the Bragg condition is exactly fulfilled. However, in a neutron interferometer in the gravitational field (COW experiment) this is not the case and the momentum transfers should not be described by hard wall reflection, as it has been done in the commented article. Instead, and quite similar to the atom case, each mirror or beam splitter creates a constant momentum transfer given by the reciprocal lattice vector of the Bragg crystal. To lowest order there are no differences between the atom and the neutron case.

Motivation & Objective

• To clarify the physical origin of phase shifts in neutron and atom interferometers under gravity.
• To challenge the assumption that neutron reflection in Bragg interferometers is analogous to classical elastic reflection.
• To analyze how dynamical diffraction and Bragg condition violations affect momentum transfer and flight times in neutron interferometers.
• To compare the behavior of atom and neutron interferometers in the near-Bragg regime, focusing on energy and momentum conservation.
• To resolve misconceptions about relativistic effects in neutron interferometry by showing they arise from quantum diffraction, not time dilation.

Proposed method

• Uses dynamical diffraction theory to model neutron reflection in Bragg geometry, treating the crystal as a periodic potential.
• Applies the Laue condition and wavevector conservation to calculate reflected wave vectors under Bragg deviation.
• Models the gravitational momentum change as a small perturbation to the neutron wave vector between crystals.
• Derives expressions for transverse momentum changes (δkₓ) due to vertical momentum shifts (δkᵧ) when the Bragg condition is violated.
• Compares flight times in the two arms of the interferometer, showing asymmetry due to momentum-dependent velocity.
• Uses rigorous coupled wave analysis and Lorentzian acceptance profiles to quantify the range of accepted wave vectors.

Experimental results

Research questions

• RQ1 Do neutron interferometers exhibit relativistic phase shifts due to gravitational time dilation, as claimed in prior work?
• RQ2 How does the Bragg condition violation affect momentum transfer and beam direction in neutron interferometers?
• RQ3 Why do atom and neutron interferometers differ in their response to gravity despite similar phase shifts?
• RQ4 To what extent does dynamical diffraction alter the reflection mechanism compared to classical specular reflection?
• RQ5 How do flight time differences between interferometer arms affect interference contrast in neutron interferometers?

Key findings

• The phase shift in neutron interferometry is not due to relativistic time dilation but arises from dynamical diffraction and Bragg condition deviations.
• Neutron reflection in the symmetric Laue geometry is not specular; the horizontal momentum changes by δkₓ ≈ δkᵧH/kₓ when the Bragg condition is violated.
• The flight time difference between the two arms of the interferometer is ΔT/T ≈ ±1.8×10⁻⁷ for a 5 cm path length, due to momentum-dependent velocity.
• The final wave vectors of the two beams are identical to high precision, ensuring interference is possible and which-way information is not encoded.
• The gravitational momentum change δkᵧ/kᵧ ≈ 2.7×10⁻⁷ is well within the Bragg acceptance width (σₖᵧ/kᵧ ≈ 5×10⁻⁶), ensuring high transmission.
• Higher-order effects from momentum transfer and flight time asymmetry reduce interference contrast but do not affect the primary phase shift.