# Post-Newtonian Hamiltonian description of an atom in a weak gravitational field

@article{Schwartz2019PostNewtonianHD, title={Post-Newtonian Hamiltonian description of an atom in a weak gravitational field}, author={Philip K Schwartz and Domenico Giulini}, journal={Physical Review A}, year={2019} }

We extend the systematic calculation of an approximately relativistic Hamiltonian for center of mass and internal dynamics of an electromagnetically bound two-particle system by Sonnleitner and Barnett [Phys. Rev. A 98, 042106 (2018)] to the case including a weak post-Newtonian gravitational background field, described by the Eddington-Robertson parametrized post-Newtonian metric. Starting from a proper relativistic description of the situation, this approach allows us to systematically derive…

## 20 Citations

### Post-Newtonian Description of Quantum Systems in Gravitational Fields

- Physics
- 2020

This thesis deals with the systematic treatment of quantum-mechanical systems in post-Newtonian gravitational fields. Starting from clearly spelled-out assumptions, employing a framework of geometric…

### Geometric post-Newtonian description of spin-half particles in curved spacetime

- Physics
- 2022

Einstein Equivalence Principle (EEP) requires all matter components to universally couple to gravity via a single common geometry: that of spacetime. This relates quantum theory with geometry as soon…

### Coupling Quantum Matter and Gravity

- Physics
- 2022

In this contribution we deal with several issues one encounters when trying to couple quantum matter to classical gravitational fields. We start with a general background discussion and then move on…

### Mass-energy equivalence in gravitationally bound quantum states of the neutron

- PhysicsPhysical Review A
- 2022

Gravitationally bound neutrons have become an important tool in the experimental searches for new physics, such as modiﬁcations to Newton’s force or candidates for dark matter particles. Here we…

### Ab initio quantum theory of mass defect and time dilation in trapped-ion optical clocks

- PhysicsPhysical Review A
- 2022

We derive a Hamiltonian for the external and internal dynamics of an electromagnetically bound, charged two-particle system in external electromagnetic and gravitational ﬁelds, including…

### Composite particles with minimum uncertainty in spacetime

- Physics
- 2020

Composite particles---atoms, molecules, or microspheres---are unique tools for testing joint quantum and general relativistic effects, macroscopic limits of quantum mechanics, and searching for new…

### Palatini f(R) gravity in the solar system: Post-Newtonian equations of motion and complete PPN parameters

- PhysicsPhysical Review D
- 2020

We perform a post-Newtonian (PN) solar system analysis for Palatini $f(R)$ theories considering finite volume non-spherical planets and with emphasis to $f(R)$ functions that are analytical about…

### Quantized mass-energy effects in an Unruh-DeWitt detector

- PhysicsPhysical Review D
- 2022

A simple but powerful particle detector model consists of a two-level system coupled to a ﬁeld, where the detected particles are the ﬁeld excitations. This is known as the Unruh–deWitt detector.…

### Atom-interferometric test of the universality of gravitational redshift and free fall

- Physics
- 2020

Light-pulse atom interferometers constitute powerful quantum sensors for inertial forces. They are based on delocalised spatial superpositions and the combination with internal transitions directly…

### Light propagation and atom interferometry in gravity and dilaton fields

- PhysicsPhysical Review D
- 2022

Dark matter or violations of the Einstein equivalence principle inﬂuence the motion of atoms, their internal states as well as electromagnetic ﬁelds, thus causing a signature in the signal of atomic…

## References

SHOWING 1-10 OF 31 REFERENCES

### Post-Newtonian corrections to Schrödinger equations in gravitational fields

- PhysicsClassical and Quantum Gravity
- 2019

In this paper we extend the WKB-like ‘non-relativistic’ expansion of the minimally coupled Klein–Gordon equation after (Kiefer and Singh 1991 Phys. Rev. D 44 1067–76; Lämmerzahl 1995 Phys. Lett. A…

### Gravitational mass of composite systems

- PhysicsPhysical Review D
- 2019

The equivalence principle in combination with the special relativistic equivalence between mass and energy, E = mc(2), is one of the cornerstones of general relativity. However, for composite systems…

### General Relativistic Effects in Atom Interferometry

- Physics
- 2008

Atom interferometry is now reaching sufficient precision to motivate laboratory tests of general relativity. We begin by explaining the non-relativistic calculation of the phase shift in an atom…

### Equations of Motion in Relativistic Gravity

- Physics
- 2015

Preface.- The New Mechanics of Myron Mathisson and its subsequent development.- Multipolar test body equations of motion in generalized gravity theories.- Energy-Momentum Tensors and Motion in…

### Mass-energy and anomalous friction in quantum optics

- PhysicsPhysical Review A
- 2018

The usual multipolar Hamiltonian for atom-light interaction features a nonrelativistic moving atom interacting with electromagnetic fields which inherently follow Lorentzian symmetry. This…

### Quantum formulation of the Einstein equivalence principle

- PhysicsNature Physics
- 2018

The validity of just a few physical conditions comprising the Einstein equivalence principle (EEP) suffices to ensure that gravity can be understood as spacetime geometry. The EEP is therefore…

### Quantum mechanix plus Newtonian gravity violates the universality of free fall

- Physics
- 2017

Classical point particles in Newtonian gravity obey, as they do in general relativity, the universality of free fall. However classical structured particles, (for instance with a mass quadrupole…

### Coulomb gauge in non-relativistic quantum electro-dynamics and the shape of spectral lines

- PhysicsPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
- 1959

An examination is made of the Green dyadic for the propagation functions of non-relativistic quantum electrodynamics in the Coulomb gauge div A = 0. The existence of false precursors is shown to be…

### Derivation of the Power-Zienau-Woolley Hamiltonian in quantum electrodynamics by gauge transformation

- PhysicsProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1983

The different forms of Hamiltonian for the coupled system consisting of the electromagnetic field and a non-relativistic charged particle are considered in the context of gauge-transformation theory.…