A simple superconductor quantum interference device for testing gravity

Abstract

A simple tabletop setup based on a superconductor quantum interference device is proposed to test 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.

Landau Levels in a Gravitational Field: The Schwarzschild Spacetime Case

“…for some positive integer n, in which case the confluent hypergeometric function in expression (10) becomes a finite-degree polynomial. The condition (11), in turn, implies that,…”

“…In Ref. [11] the effect of gravity on a macroscopic quantum state-the superfluid made of superconducting electrons-has been investigated through the Josephson effect. In both works, the key idea is based on quantum interference induced by gravity (see also Refs.…”

Spin-1/2 Particles under the Influence of a Uniform Magnetic Field in the Interior Schwarzschild Solution

“…For the sake of illustration and simplicity, we display here explicitly the expression we obtain when keeping only the first term of the sum in Equation (23). By substituting the constants ε, κ and τ, as well as the term N 0 = 1 (as given in Appendix A) into Equation ( 23), we find…”

“…As the Landau levels are completely destroyed, we see that even at this order in the approximation the magnetization is completely different from the expression (35). Actually, even Formulas (31) and (32) do not hold anymore, for such formulas were derived by assuming the linear dependence (32) of mi2 n,s on the integer n. As expression (24) of E n, ,s in terms of n displays no such linearity, and since that expression (24) is itself only an approximation for the highly nonlinear full expression (23), we conclude that the Landau-levels-based formalism for computing the magnetization M of neutron stars does not generally apply to the charged plasma in the core of highly dense neutron stars. The condition for the applicability of the formalism is to have the quartic anharmonic oscillator potential term in Equation ( 22) negligible, i.e., to have λ |e|B/h or to apply the formalism only to fermions close to the vicinity of the star's center.…”

“…[17][18][19] based on the Klein-Gordon and Schrödinger equations by considering the gravitational interaction of the particle with a massive sphere as a small perturbation compared to the interaction of the particle with the magnetic field. Although relying on the Schrödinger equation and treating gravity perturbatively as done in these studies might be sufficient for laboratory applications [20][21][22][23], when seeking astrophysical applications, implementing a generalrelativistic and a non-perturbative approach and appealing to the relativistic Dirac equation are highly recommended.…”