Abstract
We study the implications of the generalized uncertainty principle (GUP) with a minimal measurable length on some quantum mechanical interferometry phenomena, such as the Aharonov–Bohm, Aharonov–Casher, COW and Sagnac effects. By resorting to a modified Schrödinger equation, we evaluate the lowest-order correction to the phase shift of the interference pattern within two different GUP frameworks: the first one is characterized by the redefinition of the physical momentum only, and the other is a Lorentz covariant GUP which also predicts non-commutativity of spacetime. The obtained results allow us to fix upper bounds on the GUP deformation parameters which may be tested through future high-precision interferometry experiments.
Highlights
Phase factors play a significant role in quantum mechanics (QM)
We study the implications of the generalized uncertainty principle (GUP) with a minimal measurable length on some quantum mechanical interferometry phenomena, such as the Aharonov–Bohm, Aharonov–Casher, COW and Sagnac effects
For the first GUP model, which predicts a redefinition of the high-energy momentum alone, we have shown that a non-trivial correction only appears in the COW experiment, as the characteristic QM phase shift explicitly depends on the momentum of the test particle
Summary
Phase factors play a significant role in quantum mechanics (QM). Broadly speaking, they can be classified into different classes depending on their physical origin and features [1]. In the seminal papers on the generalized uncertainty principle (GUP), deformations of the uncertainty relations stem from the attempt of explaining the divergences appearing in quantum field theory (QFT) without invoking an ad hoc cut-off in the momentum space [12,13] In this context, considerations from string theory [14,15,16,17] and gedanken experiments on micro-black holes [18] have converged to the following proposal for the (one-dimensional) non-relativistic GUP: σXσPx. where σX , σPx are the uncertainties on position and momentum operators, respectively, β is the dimensionless deformation parameter (which is usually assumed to be of order one in the most common quantum gravity formulations) and p denotes the Planck length.
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