Nonclassical effects in geodesic motion

Abstract

Gravity gradient is known as a serious systematic effect in atomic tests of the universality of free fall, where the initial central position and velocity of atoms need to be exactly controlled. In this paper, we study quantum free fall with high-order gravity gradients. It is shown that the cubic terms in the Newtonian potential shall generate a new phase shift in atom interferometers, which depends on the position and velocity uncertainties of the incident atoms. We further investigate the nonclassicality of free fall and show that, due to the cubic potential, the gravitational Wigner equation in phase space of position and velocity is different from the classical Liouville equation. There exists a mass-dependent correction in the dynamical equation regardless of initial state. Nevertheless, this is just a quantum mechanical effect of microparticles, which does not violate equivalence principle that inertia mass is equal to the gravitational mass.

arXiv commentMinor revision for v2

References in corpus (25)

• The fundamental constants and their variation: observational status and theoretical motivations
• Minimal Length Scale Scenarios for Quantum Gravity
• Atomic Interferometer with Amplitude Gratings of Light and its Applications to Atom Based Tests of the Equivalence Principle
• Phase shift in atom interferometry due to spacetime curvature
• A transportable optical lattice clock with $7\times 10^{-17}$ uncertainty
• Quantum test of the equivalence principle for atoms in superpositions of internal energy eigenstates
• MICROSCOPE mission: first constraints on the violation of the weak equivalence principle by a light scalar dilaton
• General Relativistic Effects in Atom Interferometry
• Quantum Tests of the Einstein Equivalence Principle with the STE-QUEST Space Mission
• STE-QUEST - Test of the Universality of Free Fall Using Cold Atom Interferometry
• Fermion-Mediated Interactions Between Bosonic Atoms
• Efficient computation of the Zassenhaus formula
• Testing the equivalence principle through freely falling quantum objects
• Circumventing Heisenberg's uncertainty principle in atom interferometry tests of the equivalence principle
• Does an atom interferometer test the gravitational redshift at the Compton frequency ?
• Manipulation and coherence of ultra-cold atoms on a superconducting atom chip
• Quantum Test of the Equivalence Principle and Space-Time aboard the International Space Station
• Observation of the Spatial Distribution of Gravitationally Bound Quantum States of Ultracold Neutrons and Its Derivation Using the Wigner Function
• On the quantum analogue of Galileo's leaning tower experiment
• Fundamental limitations to high-precision tests of the universality of free fall by dropping atoms
• Gravity gradient suppression in spaceborne atomic tests of the equivalence principle
• The Disconnect Between Quantum Mechanics and Gravity
• Lattice Wigner equation
• Weak values obtained from mass-energy equivalence
• Real-time Quantum evolution in the Classical approximation and beyond

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