# Projects

**Project 1) Quantum Systems in Gravitational Fields**

The aim of this project is to develop a consistent systematic scheme that allows to recursively compute the influence of a background gravitational field upon the dynamical behaviour of a quantum system in a post-Newtonian expansion (in terms of 1/c). Here the conceptual and mathematical challenge lies in the fact that the standard universal coupling scheme only applies to theories and dynamical laws that comply with Special Relativity, (SR) which is not the case for ordinary Quantum Mechanics (QM) and the Schrödinger equation. Given that, and since the incorporation of SR into QM results in Relativistic Quantum Field Theory (RQFT), it may seem necessary to first recourse to the highly complex and abstract theories of RQFT in curved spacetimes in order to answer even the most simple questions concerning quantum systems in gravitational fields beyond the most simple linear coupling to the Newtonian potential. Such higher correction terms become relevant in modern experiments in atom interferometry and allow new "quantum tests" of gravitational phenomena and principles, like Einstein's principle of equivalence.

Recent related publications

A. Alibabaei, P. Schwartz, **D. Giulini**:

Geometric post-Newtonian description of massive spin-half particles

in curved spacetime. Clasical and Quantum Gravity, year 2023

(accepted for publication).

https://www.arxiv.org/abs/2307.04743

A. Bassi, L. Cacciapuoti, S. Capozziello, S. Dell’Agnello, E.

Diamanti, **D. Giulini**, L. Iess, P. Jetzer, S. K. Joshi, A. Landragin,

C. Le Poncin-Lafitte, E. Rasel, A. Roura, C. Salomon, and

H. Ulbricht:

A way forward for fundamental physics in space.

npj Microgravity, year 2022, volume 8, article number 49 (15 pages).

https://www.nature.com/articles/s41526-022-00229-0

**D. Giulini**, A. Großardt, and P. Schwartz:

Coupling Quantum Matter and Gravity. In: C. Lämmerzahl and

C. Pfeifer (editors) "Modified and Quantum Gravity - From Theory to

Experimental Searches on All Scales". Springer Verlag (2022).

https://link.springer.com/book/9783031315190

P. Schwartz and **D. Giulini**:

Post-Newtonian Hamiltonian description of an atom in a weak

gravitational field. Physical Review A, year 2019, volume 100,

issue 5, article 052116 (16 pages).

https://journals.aps.org/pra/abstract/10.1103/PhysRevA.100.052116

P. Schwartz and **D. Giulini**:

Post-Newtonian corrections to Schrödinger equations in gravitational

fields. Classical and Quantum Gravity, year 2019, volume 36, number

9, article 095016 (28 pages).

https://iopscience.iop.org/article/10.1088/1361-6382/ab0fbd

**Project 2) Asymptotic symmetries and charges in gauge theories**

All theories of fundamental interactions are gauge theories. In those theories the concept of "charge" plays a fundamental role. A characterisitic mathematical feature of such charges is that they can be computed as 2-dimensional surface integrals enclosing the 3-dimensional "charged" domain. In case of the gravitational field such charges are energy, momentum, angular momentum, and 3 more quantities associated with the motion of the centre-of-mass. Global charges are associated with asymptotic symmetries. For example, the gravitational field for isolated objects is associated with 10 global charges (energy, momentum, angular momentum, centre-of-mass) corresponding to the 10 generators of asymptotic Poincare transformations. In this project we analyse the structure of asymptotic symmetries and hence the existence of charged stated for classical gauge theories within the precise Hamiltonian formulation. More concretely, we analyse the weakest asymptotic fall-off conditions for fields compatible the existence of a relativistic Hamiltonian structures; that is: phase-space, symplectic structure, smooth Hamiltonian flow, and a proper Hamiltonian action of the Poincare group. So far we already derived hitherto unknown results, like, e.g., the absence of globally charges states in SU(2) pure Yang-Mills theory in d=4 (classical confinement).

Recent related publications

**R. Tanzi** and **D. Giulini**:

Asymptotic symmetries of scalar electrodynamics and of the abelian

Higgs model in Hamiltonian formulation. Journal of High Energy

Physics, year 2021, article number 117 (39 pages).

https://link.springer.com/article/10.1007/JHEP08(2021)117

**R. Tanzi** and **D. Giulini**:

Asymptotic symmetries of Yang-Mills fields in Hamiltonian

formulation. Journal of High Energy Physics, year 2020, article

number 94 (39 pages).

https://link.springer.com/article/10.1007/JHEP10(2020)094

**Project 3) Global inhomogeneous cosmology**

The standard model in relativistic cosmology, the so-called Friedman-Lemaitre-Robertson-Walker (FLRW) Model, is based on the assumption of strict spatial homogeneity and isotropy. This is clearly an idealisation, the approximate validity of which is only meant to apply to structures on the largest observable scales. But the non-linearity of Einstein's equations implies that spacetime averaging Einstein's equations does not result in Einstein's equations for the corresponding averaged field. This feature makes it difficult to find analytic tools by which we can reliably estimate the precise degree to which FLRW models match the actual Universe. This is known as the "fitting problem". A directly related issue is the "backreaction problem", which addresses the question of how to give reliable analytical estimates for the impact of local inhomogeneities upon the global cosmological dynamics. In this project we attempt to develop innovative methods to tacke these problems using methods from global differential geometry and topology. These involve Lie-Sphere-Geometry on one hand, and measures -- like the Hawking Energy -- to investigate the geometric and topological structure of light-cones on the other.

Recent related publications

**D. Stock**, E. Di Dio, R. Durrer:

The Hawking Energy in a Perturbed Friedmann-Lemaitre Universe

Journal of Cosmology and Astroparticle Physics, year 2023, article

033 (27 pages).

https://iopscience.iop.org/article/10.1088/1475-7516/2023/08/033

**D. Stock**:

Applications of the Hawking Energy in Inhomogeneous Cosmology

Classical and Quantum Gravity, year 2021, volume 38, number 7,

article 075019 (14 pages),

https://iopscience.iop.org/article/10.1088/1361-6382/abe882

**D. Stock**:

The Hawking energy on the past lightcone in cosmology

Classical and Quantum Gravity, year 2020, volume 37, number 21,

article 215005 (20 pages).

https://iopscience.iop.org/article/10.1088/1361-6382/aba182

M. Fennen and **D. Giulini**:

Lie sphere geometry in lattice cosmology.

Classical and Quantum Gravity, year 2020, volume 37, number 6,

article 065007 (30 pages).

https://iopscience.iop.org/article/10.1088/1361-6382/ab6a20

Project 4) Optomechanical tests of quantum properties of gravity

A conclusive final answer if gravity and quantum mechanics fit together can only be provided by empirical evidence. The aim of this project is to investigate if evidence for quantum properties of gravity may be obtained in practise by certication of gravity-mediated creation of entanglement between two optomechanical systems. The property of gravity to be a quantum coherent mediator, while widely believed to be necessary for consistency, has not been experimentally tested yet. Proposals for such tests date back to Richard Feynman and have seen a revival and rapid increase in attention in recent years. We have shown that the necessary duration of experiments can be drastically reduced by parametric driving schemes getting into reach with near-term technology. However, our results also suggest that the effect of environmental noise may be a fundamental obstacle. Therefore, we are investigating noise models more carefully to incorporate specific features of potential experimental setups.

**Project 5) Quantum memories in weakly curved spacetime**

Quantum Memories are considered to be a key technology for global quantum communication networks that may be also employed space-based, interest in the community is high to understand gravitational and relativistic effects as potential sources of error. Furthermore, Quantum Memories in space may be used for fundamental research applications, in particular, with storage times >1h available soon comparable to some Earth orbital periods. The aim of this project is to investigate and quantify gravitational effects on Quantum Memories, develop strategies for their mitigation and propose experiments to test theories. In particular, we have investigated the effect of gravitational and relativistic redshift on quantum-memory-assisted Hong-Ou-Mandel interferometry of frequency entangled photons. We have found that the effect denoted as Gravitationally Induced Entanglement Dynamics (GIED) is readily observable with state of the art or near-term Quantum Memories (QMems). If not compensated appropriately, GIED can lead to decoherence.

**Project 6) Gravitational field of ultra-relativistic particle beams**

While many experiments have been performed on the Newtonian gravitational interaction, confirming it down to microscopic scales, the gravitational field of relativistic sources of gravity has not been tested to date in lab-based experiments. For example, laser beams and pulses generate a gravitational field that differs notably from that sourced by slow-moving matter. In particular, General Relativity tells us that the gravitational acceleration of a sensor at rest with respect to an ultra-relativistic particle beam like that at the Large Hadron Collider (LHC) is dominated by the kinetic energy of the particles in the beam (a genuine General Relativity effect) which is a type of gravitational source that has not been used in experiments to date. For example, we have investigated the possibility to measure the gravitational field of the proton bunches at the LHC beam and found that there is a mid-term perspective for such experiments. At the moment, we are exploring the possibility for further efforts in this direction together with researchers at CERN and we investigate the application of cascaded optomechanical sensors arranged around the beam line to enhance the sensitivity beyond the standard quantum limit.

Recent related publications

F. Spengler, **D. Rätzel**, D. Braun:

Perspectives of measuring gravitational effects of laser light

and particle beams.

New Journal of Physics 24.5 (2022): 053021

doi: 10.1088/1367-2630/ac5372 [link] [preprint]