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Europhysics Letters (EPL)

Third-harmonic signature of linear-GUP kinematics in mesoscopic Aharonov-Bohm rings

Sameer Ahmad Mir

Published Nov 1, 2025• 1 citation

Abstract

Abstract We implement a linear Generalized Uncertainty Principle (GUP) in a phase-coherent Aharonov-Bohm ring and show that it imprints a distinctive mesoscopic signature. The deformation produces a cubic correction to the kinetic energy that skews the equilibrium current-flux sawtooth and turns on a robust third Fourier harmonic whose amplitude grows linearly with the deformation strength. Closed form many-body results at zero temperature yield a symmetry-protected third-to-first harmonic ratio that cleanly isolates the linear-GUP signal while canceling nonuniversal prefactors, making the observable resilient to material specifics, weak disorder, spin, and moderate thermal smearing. Using the harmonic-resolution capabilities of current ring experiments, we translate realistic sensitivities into direct bounds on the deformation parameter and on its standard dimensionless coupling in quantum gravity phenomenology. The framework provides a crisp discriminator between linear and purely quadratic GUP deformations, only the linear case activates an even-under-flux-inversion harmonic sector with a leading third harmonic. Beyond phenomenology, the minimal resolvable length implied by the GUP naturally bounds the information content of the flux-current map and the number of harmonics that can be stably resolved, suggesting a pragmatic analogy without claiming formal equivalence to classical limits on computation and decidability. Taken together, these results establish persistent-current harmonics as a tabletop, symmetry protected probe of minimal-length physics and outline clear routes, i.e. , smaller rings, ring arrays, and low-noise harmonic readout to substantially tighten the resulting constraints.

DOI: 10.1209/0295-5075/ae1b39

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Abstract We implement a linear Generalized Uncertainty Principle (GUP) in a phase-coherent Aharonov-Bohm ring and show that it imprints a distinctive mesoscopic signature. The deformation produces a cubic correction to the kinetic energy that skews the equilibrium current-flux sawtooth and turns on a robust third Fourier harmonic whose amplitude grows linearly with the deformation strength. Closed form many-body results at zero temperature yield a symmetry-protected third-to-first harmonic ratio that cleanly isolates the linear-GUP signal while canceling nonuniversal prefactors, making the observable resilient to material specifics, weak disorder, spin, and moderate thermal smearing. Using the harmonic-resolution capabilities of current ring experiments, we translate realistic sensitivities into direct bounds on the deformation parameter and on its standard dimensionless coupling in quantum gravity phenomenology. The framework provides a crisp discriminator between linear and purely quadratic GUP deformations, only the linear case activates an even-under-flux-inversion harmonic sector with a leading third harmonic. Beyond phenomenology, the minimal resolvable length implied by the GUP naturally bounds the information content of the flux-current map and the number of harmonics that can be stably resolved, suggesting a pragmatic analogy without claiming formal equivalence to classical limits on computation and decidability. Taken together, these results establish persistent-current harmonics as a tabletop, symmetry protected probe of minimal-length physics and outline clear routes, i.e. , smaller rings, ring arrays, and low-noise harmonic readout to substantially tighten the resulting constraints.

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.

Many quantum-gravity scenarios predict a minute modification of the canonical commutator, known as the generalized uncertainty principle (GUP), whose low-energy signatures are, in principle, accessible to state-of-the-art laboratory tests. We compute first-order minimal-length corrections to the quantum speed limit (QSL) for three cases: uniform superpositions in an infinite square well, coherent harmonic-oscillator states, and squeezed-oscillator states. We identify a universal amplification law: for any pure state, the fractional shift of either speed limit scales linearly with

β

and algebraically with the state's effective Hilbert-space size. As the effective Hilbert-space dimension can be exceedingly large, the associated minimal-length signatures are amplified by several orders of magnitude. Using high-precision matter-wave timing data, we set a direct bound on the GUP parameter

β

, which quantifies minimal-length quantum-gravity effects. Our analysis indicates that phase-locked, short-time overlap fits on kilogram-scale optical-spring modes can tighten this bound by orders of magnitude. We outline two implementable measurement pipelines -- continuous back-action-evading single-quadrature readout and stroboscopic, phase-locked pulsed tomography -- that exploit this leverage, making QSL-based timing a practical, near-term probe of minimal-length physics on quantum-optical and optomechanical platforms.

Several approaches to quantum gravity suggest the emergence of a fundamental minimal length at the Planck scale. In quantum mechanics, this feature is naturally encoded through deformations of the Heisenberg algebra, leading to the Generalized Uncertainty Principle (GUP). While the phenomenological implications of GUP have been extensively explored, a consistent characterization of coherent states in minimal-length quantum mechanics remains elusive. In this work, we present a systematic analysis of coherent states for the one-dimensional harmonic oscillator. We show that the canonical equivalence among their standard characterizations - as eigenstates of the annihilation operator, displaced vacuum states and minimum-uncertainty wave packets - is generically lost in the presence of a minimal length. We then investigate the dynamical and semiclassical consequences of this inequivalence by comparing the evolution of generalized coherent states with that of states saturating the GUP. In particular, we demonstrate that minimal-length effects induce nontrivial deformations of phase-space trajectories and give rise to an intrinsic squeezing mechanism with no counterpart in ordinary quantum mechanics. These results establish a unified framework for coherence in GUP-based quantum theories and identify distinctive semiclassical signatures of minimal-length physics, opening a new avenue for probing quantum-gravitational effects.

We discuss classical electrodynamics and the Aharonov–Bohm effect in the presence of the minimal length. In the former, we derive the classical equation of motion and the corresponding Lagrangian. In the latter, we adopt the generalized uncertainty principle (GUP) and compute the scattering cross-section up to the first-order of the GUP parameter [Formula: see text]. Even though the minimal length exists, the cross-section is invariant under the simultaneous change [Formula: see text], [Formula: see text], where [Formula: see text] and [Formula: see text] are azimuthal angle and magnetic flux parameter. However, unlike the usual Aharonv–Bohm scattering, the cross-section exhibits discontinuous behavior at every integer [Formula: see text]. The symmetries, which the cross-section has in the absence of GUP, are shown to be explicitly broken at the level of [Formula: see text].

Several theories of quantum gravity propose the existence of a minimal measurable length and maximum measurable momentum near the Planck scale. When integrated into the framework of quantum mechanics, such restrictions lead to the generalization of the Heisenberg uncertainty principle, which is commonly referred to as the generalized uncertainty principle (GUP). The GUP has been applied to a plethora of physical models in order to provide further insights on our understanding of the Universe, both in the macroscopic and the microscopic regime. Nevertheless, the corrections related to GUP are expected to be extremely small, which thus renders experimental verification a difficult task. Therefore, phenomenological approaches on a qualitative level are typically addressed with the aim of enhancing our possibility of detecting these tiny effects. Motivated by a recent work on a universal decoherence mechanism stemming from the standard formulation of GUP, we extend the ideas contained therein by considering a more general form of GUP which includes linear and quadratic momentum terms to examine its implications. To achieve such a picture, we equip the deformation parameter appearing in front of all momentum terms with a stochastic nature, so that the effective decoherence mechanism emerges by taking the average over fluctuations. We find that, despite the apparently small differences among the two generalizations of the Heisenberg uncertainty principle, the consequences at the level of the universal decoherence mechanism they entail is significant, as they predict decoherence times that are completely uncorrelated and distinct.

We present the coherent states of the harmonic oscillator in the framework of the generalized (gravitational) uncertainty principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop quantum gravity and black-hole physics and implies a minimal measurable length. Using a recently proposed formally self-adjoint representation, we find the GUP-corrected Hamiltonian as a generator of the generalized Heisenberg algebra. Then following Klauder's approach, we construct exact coherent states and obtain the corresponding normalization coefficients, weight functions and probability distributions. We find the entropy of the system and show that it decreases in the presence of the minimal length. These results could shed light on possible detectable Planck-scale effects within recent experimental tests.