Prospects for testing the inverse-square law and gravitomagnetism using quantum interference

Hammad, Fayçal; Landry, Alexandre; Mathieu, Kaleb

doi:10.48550/arxiv.1910.13814

Cited by 3 publications

(14 citation statements)

References 52 publications

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“…The gravitational potential inside a full sphere of radius R and mass density ρ due to the Yukawa-like correction term has already been found in Ref. [40]. The result is This potential cannot be of any use in the form given here so we need to expand it in powers of x/λ.…”

Section: The Possibility Of Testing the Islmentioning

confidence: 88%

“…The gravitational potential correction at a distance x from the center of a sphere of radius R and mass density ρ for such a case has already been computed in detail in Ref. [40]. Therefore, we just pick up here the result found there and expand in powers of x/R.…”

Section: The Possibility Of Testing the Islmentioning

confidence: 94%

“…Finally, we have examined the possibility for the QHE to play an eventual role in the modern investigations of gravity based on mesoscopic systems [36] or those based on the use of ultracold neutrons [37][38][39][40]. We came to the conclusion that, even though gravity does influence the Hall resistivity, the Landau levels and their degeneracy, and hence also the QHE, the latter cannot really allow to differentiate between an ISL of gravity and another law that deviates from the latter.…”

Section: The Possibility Of Testing the Islmentioning

confidence: 99%

“…Let us denote by V n D (x) the power-law correction to the gravitational potential at a distance x from the center of a full uniform disk of radius R and thickness 2a, having the uniform mass density ρ. Only for the case n = 1 do we have a converging potential inside the sphere [40]. Therefore, we only focus here on that case.…”

Section: The Possibility Of Testing the Islmentioning

confidence: 99%

“…The calculation of V N S (x) has been done in detail in Ref. [40], so we are only displaying here the final expression of that potential. It is given by,…”

Section: Engineering Research Council Of Canada (Nserc) Discovery Gra...mentioning

confidence: 99%

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A fresh look at the influence of gravity on the quantum Hall effect

Hammad,

Landry,

Mathieu

2020

Preprint

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We study the quantum Hall effect inside a gravitational field. First, we review the influence of the gravitational field of the Earth on the quantum Hall effect. Taking the gravitational field of the Earth to be uniform along the vertical direction, we compute the affected quantized Hall resistivity. Then, we investigate how the gravitational field modifies the Landau levels of a particle moving between two massive hemispheres in the presence of a constant and uniform magnetic field perpendicular to the plane of motion. We find that the familiar degeneracy of the Landau levels is removed and the spacing between the latter becomes dependent on the mass density of the hemispheres and on the gravitational constant G. We use this result to show that the quantum Hall effect in a thin conductor, sandwiched between two massive hemispheres, should yield a slightly different variation of the Hall resistivity with the applied magnetic field. We then argue that the well-known problem of the gravitationally induced electric field, that might a priori be thought to hinder the effect of gravity, has actually a beneficial role as it amplifies the latter. We finally discuss whether there is a possibility of using the quantum Hall effect to probe the inverse-square law of gravity.

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Section: The Possibility Of Testing the Islmentioning

confidence: 88%

Section: The Possibility Of Testing the Islmentioning

confidence: 94%

Section: The Possibility Of Testing the Islmentioning

confidence: 99%

Section: The Possibility Of Testing the Islmentioning

confidence: 99%

“…The calculation of V N S (x) has been done in detail in Ref. [40], so we are only displaying here the final expression of that potential. It is given by,…”

Section: Engineering Research Council Of Canada (Nserc) Discovery Gra...mentioning

confidence: 99%

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A fresh look at the influence of gravity on the quantum Hall effect

Hammad,

Landry,

Mathieu

2020

Preprint

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Landau levels in a gravitational field: the Levi-Civita and Kerr spacetimes case

Hammad

Landry

2020

Eur. Phys. J. Plus

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We have recently found that the gravitational field of a static spherical mass removes the Landau degeneracy of the energy levels of a particle moving around the mass inside a magnetic field by splitting the energy of the Landau orbitals. In this paper we present the second part of our investigation of the effect of gravity on Landau levels. We examine the effect of the gravitational fields created by an infinitely long massive cylinder and a rotating spherical mass. In both cases, we show that the degeneracy is again removed thanks to the splitting of the particle's orbitals. The first case would constitute an experimental test -which is quantum mechanical in nature -of the gravitational field of a cylinder. The approach relies on the Newtonian approximation of the gravitational potential created by a cylinder but, in view of self-consistency and for future higher-order approximations, the formalism is based on the full Levi-Civita metric. The second case opens up the possibility for a novel quantum mechanical test of the well-known rotational frame-dragging effect of general relativity. * Electronic address: fhammad@ubishops.ca † Electronic address: alexandre.landry.1@umontreal.ca

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A simple superconductor quantum interference device for testing gravity

Hammad,

Landry

2020

Preprint

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A simple tabletop setup based on a superconducting quantum interference device is proposed for testing the gravitational interaction. A D-shaped superconducting loop has the straight segment immersed inside a massive sphere while the half-circle segment is wrapped around the sphere. The superconducting condensate within the straight arm of the loop thus bathes inside a gravitational simple harmonic oscillator potential while the condensate in the half-circle arm bathes in the constant gravitational potential around the sphere. The resulting phase difference at the Josephson junctions on both sides of the straight arm induces a sinusoidal electric current that has a frequency determined by the precise gravitational potential due to the massive sphere.

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Prospects for testing the inverse-square law and gravitomagnetism using quantum interference

Cited by 3 publications

References 52 publications

A fresh look at the influence of gravity on the quantum Hall effect

A fresh look at the influence of gravity on the quantum Hall effect

Landau levels in a gravitational field: the Levi-Civita and Kerr spacetimes case

A simple superconductor quantum interference device for testing gravity

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