# Dynamical Gauge Fields

Within the Standard Model of Particle Physics, the interaction between fundamental particles is described by gauge theories. These theories have an enormous predictive power, but to compute the dynamics they generate is an extremely hard task. As a consequence, high-energy physics contains many unsolved problems such as quark confinement or the dynamics of quarks and gluons during heavy-ion collisions. Instead of computing them in classical devices or investigating them in enormous accelerator facilities, we aim at implementing lattice gauge theories on the optical table by having atomic gases in optical lattices mimic the interplay between particles, anti-particles, and gauge bosons. In this way, experiments at temperatures just above absolute zero could give insights into unsolved phenomena that in Nature appear at very high energies.

### A short (mathy) introduction

We wrote a blog post to give an introduction into the ideas underlying dynamical gauge fields. If you feel like it please take a look.

more ...Rohit Prasad Bhatt

Phone: +49 6221 54 5175

rohit.prasad@kip.uni-heidelberg.de

Yannick Deller

Phone: +49 6221 54 5175

yannick.deller@kip.uni-heidelberg.de

Lilo Höcker

Phone: +49 6221 54 5175

lilo.hoecker@kip.uni-heidelberg.de

Fred Jendrzejewski

Phone: +49 6221 54 5182

fnj@kip.uni-heidelberg.de

Jolan Kerrien

Phone: +49 6221 54 9176

jolan.kerrien@kip.uni-heidelberg.de

Jan Kilinc

Phone: +49 6221 54 5175

jan.kilinc@kip.uni-heidelberg.de

Robert Ott

Phone: +49-6221-54 9309

ott@thphys.uni-heidelberg.de

Noah Leonardo Wach

Phone: +49 6221 54 5175

noah_leonardo.wach@kip.uni-heidelberg.de

Andy Xiyuan Xia

Phone: +49 6221 54 5175

andy.xia@kip.uni-heidelberg.de

## Recent publications

### From the Jaynes–Cummings model to non-abelian gauge theories: a guided tour for the quantum engineer

HD-KIP 20-88, 2020, New Journal of Physics (22) 103027 PDF-FileThe design of quantum many body systems, which have to fulfill an extensive number of constraints, appears as a formidable challenge within the field of quantum simulation. Lattice gauge theories are a particular important class of quantum systems with an extensive number of local constraints and play a central role in high energy physics, condensed matter and quantum information. Whereas recent experimental progress points towards the feasibility of large-scale quantum simulation of Abelian gauge theories, the quantum simulation of non-Abelian gauge theories appears still elusive. In this paper we present minimal non-Abelian lattice gauge theories, whereby we introduce the necessary formalism in well-known Abelian gauge theories, such as the Jaynes-Cumming model. In particular, we show that certain minimal non-Abelian lattice gauge theories can be mapped to three or four level systems, for which the design of a quantum simulator is standard with current technologies. Further we give an upper bound for the Hilbert space dimension of a one dimensional SU(2) lattice gauge theory, and argue that the implementation with current digital quantum computer appears feasible.

### Direct control of high magnetic fields for cold atom experiments based on NV centers

HD-KIP 20-34, 2020 PDF-FileIn atomic physics experiments, magnetic fields allow to control the interactions between atoms, eg. near Feshbach resonances, or by employing spin changing collisions. The magnetic field control is typically performed indirectly, by stabilizing the current of Helmholtz coils producing the large bias field. Here, we overcome the limitations of such an indirect control through a direct feedback scheme, which is based on nitrogen-vacancy centers acting as a sensor. This allows us to measure and stabilize magnetic fields of 46.6 G down to 1.2 mG RMS noise, with the potential of reaching much higher field strengths. Because the magnetic field is measured directly, we reach minimum shot-to-shot fluctuations of 0.32(4) ppm on a 22 minute time interval, ensuring high reproducibility of experiments. This approach extends the direct magnetic field control to high magnetic fields, which could enable new precise quantum simulations in this regime.

### A scalable realization of local U(1) gauge invariance in cold atomic mixtures

HD-KIP 20-02, 2020, Science, Vol. 367, Issue 6482 PDF-FileIn the fundamental laws of physics, gauge fields mediate the interaction between charged particles. An example is quantum electrodynamics -- the theory of electrons interacting with the electromagnetic field -- based on U(1) gauge symmetry. Solving such gauge theories is in general a hard problem for classical computational techniques. While quantum computers suggest a way forward, it is difficult to build large-scale digital quantum devices required for complex simulations. Here, we propose a fully scalable analog quantum simulator of a U(1) gauge theory in one spatial dimension. To engineer the local gauge symmetry, we employ inter-species spin-changing collisions in an atomic mixture. We demonstrate the experimental realization of the elementary building block as a key step towards a platform for large-scale quantum simulations of continuous gauge theories.

### Dynamical topological transitions in the massive Schwinger model with a θ-term

HD-KIP 18-131, 2019, Phys. Rev. Lett., arXiv:1808.07885 (122) 050403 PDF-FileAiming at a better understanding of anomalous and topological effects in gauge theories out-of-equilibrium, we study the real-time dynamics of a prototype model for CP-violation, the massive Schwinger model with a θ-term. We identify dynamical quantum phase transitions between different topological sectors that appear after sufficiently strong quenches of the θ-parameter. Moreover, we establish a general dynamical topological order parameter, which can be accessed through fermion two-point correlators and, importantly, which can be applied for interacting theories. Enabled by this result, we show that the topological transitions persist beyond the weak-coupling regime. Finally, these effects can be observed with table-top experiments based on existing cold-atom, superconducting-qubit, and trapped-ion technology. Our work, thus, presents a significant step towards quantum simulating topological and anomalous real-time phenomena relevant to nuclear and high-energy physics.

### Quantum simulation of lattice gauge theories using Wilson fermions

HD-KIP 18-09, 2018, Quantum Sci. Technol., arXiv:1802.06704 (3) 034010 PDF-FileQuantum simulators have the exciting prospect of giving access to real-time dynamics of lattice gauge theories, in particular in regimes that are difficult to compute on classical computers. Future progress towards scalable quantum simulation of lattice gauge theories, however, hinges crucially on the efficient use of experimental resources. As we argue in this work, due to the fundamental non-uniqueness of discretizing the relativistic Dirac Hamiltonian, the lattice representation of gauge theories allows for an optimization that up to now has been left unexplored. We exemplify our discussion with lattice quantum electrodynamics in two-dimensional space-time, where we show that the formulation through Wilson fermions provides several advantages over the previously considered staggered fermions. Notably, it enables a strongly simplified optical lattice setup and it reduces the number of degrees of freedom required to simulate dynamical gauge fields. Exploiting the optimal representation, we propose an experiment based on a mixture of ultracold atoms trapped in a tilted optical lattice. Using numerical benchmark simulations, we demonstrate that a state-of-the-art quantum simulator may access the Schwinger mechanism and map out its non-perturbative onset.

### Implementing quantum electrodynamics with ultracold atomic systems

HD-KIP 17-10, 2017, New Journal of Physics, arXiv:1608.03480 (19) 023030 PDF-FileWe discuss the experimental engineering of model systems for the description of QED in one spatial dimension via a mixture of bosonic

^{23}Na and fermionic^{6}Li atoms. The local gauge symmetry is realized in an optical superlattice, using heteronuclear boson-fermion spin-changing interactions which preserve the total spin in every local collision. We consider a large number of bosons residing in the coherent state of a Bose-Einstein condensate on each link between the fermion lattice sites, such that the behavior of lattice QED in the continuum limit can be recovered. The discussion about the range of possible experimental parameters builds, in particular, upon experiences with related setups of fermions interacting with coherent samples of bosonic atoms. We determine the atomic system's parameters required for the description of fundamental QED processes, such as Schwinger pair production and string breaking. This is achieved by benchmark calculations of the atomic system and of QED itself using functional integral techniques. Our results demonstrate that the dynamics of one-dimensional QED may be realized with ultracold atoms using state-of-the-art experimental resources. The experimental setup proposed may provide a unique access to longstanding open questions for which classical computational methods are no longer applicable.### Observation of the Phononic Lamb Shift with a Synthetic Vacuum

HD-KIP 16-100, 2016, Physical Review X, arXiv:1605.01874 (6) 041041 PDF-FileIn contrast to classical empty space, the quantum vacuum fundamentally alters the properties of embedded particles. This paradigm shift allows one to explain the discovery of the celebrated Lamb shift in the spectrum of the hydrogen atom. Here, we engineer a synthetic vacuum, building on the unique properties of ultracold atomic gas mixtures, offering the ability to switch between empty space and quantum vacuum. Using high-precision spectroscopy, we observe the phononic Lamb shift, an intriguing many-body effect originally conjectured in the context of solid-state physics. We find good agreement with theoretical predictions based on the Fröhlich model. Our observations establish this experimental platform as a new tool for precision benchmarking of open theoretical challenges, especially in the regime of strong coupling between the particles and the quantum vacuum.

### Schwinger pair production with ultracold atoms

HD-KIP 16-72, 2016, Physics Letters B, arXiv:1506.01238 (760) 742-746 PDF-FileWe consider a system of ultracold atoms in an optical lattice as a quantum simulator for electron–positron pair production in quantum electrodynamics (QED). For a setup in one spatial dimension, we investigate the nonequilibrium phenomenon of pair production including the backreaction leading to plasma oscillations. Unlike previous investigations on quantum link models, we focus on the infinite-dimensional Hilbert space of QED and show that it may be well approximated by experiments employing Bose–Einstein condensates interacting with fermionic atoms. Numerical calculations based on functional integral techniques give a unique access to the physical parameters required to realize QED phenomena in a cold atom experiment. In particular, we use our approach to consider quantum link models in a yet unexplored parameter regime and give bounds for their ability to capture essential features of the physics. The results suggest a paradigmatic change towards realizations using coherent many-body states for quantum simulations of high-energy particle physics phenomena.

## Theses

- Constructing U(1) gauge symmetry in electronic circuits

Hannes Riechert, Masterarbeit, 2020 PDF-File - Exploring and Benchmarking Quantum-assisted Neural Networks with Qubit Layers

Manuel Rudolph, Masterarbeit, 2020 PDF-File - Experimental realization of U(1) gauge invariance in ultracold atomic mixtures

Alexander Mil, Dissertation, 2020 PDF-File - A NV center based magnetic field stabilization for atomic physics experiments

Alexander Hesse, Masterarbeit, 2020 PDF-File - Building up a modular Na-K quantum gas
experiment

Lilo Höcker, Masterarbeit, 2019 PDF-File - Starting a Na-K experiment for simulating
quantum many-body phenomena

Jan Kilinc, Masterarbeit, 2019 PDF-File - Implementing an Optical Accordion Lattice for the Realization of a Quantized Otto Cycle

Kai-Niklas Schymik, Masterarbeit, 2018 - Nitrogen Vacancy Center Magnetometry as a New Approach for an Active Magnetic Field Control

Kerim Köster, Bachelorarbeit, 2018 PDF-File - Simulation and Measurements of Single and Coupled Coaxial Qubits

Tanja Behrle, Masterarbeit, 2018 PDF-File - Design and Implementation of a Versatile Imaging Objective for Imaging of Ultracold Mixtures of Sodium and Lithium

Alexander Mil, Masterarbeit, 2016 PDF-File - Spin Dynamics and Feshbach Resonances in Ultracold Sodium-Lithium Mixtures

Arno Trautmann, Dissertation, 2016 PDF-File - Observation of the Phononic Lamb Shift in a Synthetic Vacuum

Tobias Rentrop, Dissertation, 2016 PDF-File - Active Magnetic Field Stabilisation for Ultracold
Sodium Lithium Mixtures

Marcell Gall, Masterarbeit, 2015 PDF-File - Dynamics and Motional Coherence of Fermions Immersed in a Bose Gas

Raphael Scelle, Dissertation, 2013 PDF-File - Feshbach Resonances and Periodic Potentials in Ultracold Bose-Fermi Mixtures

Tobias Schuster, Dissertation, 2012 PDF-File - Immersed Quantum Systems: A Sodium Bose-Einstein Condensate for Polaron Studies

Jens Appmeier, Dissertation, 2010 PDF-File - Zeeman-Slower und Experimentsteuerung für das NaLi-Experiment

Jan Krieger, Diplomarbeit, 2008 PDF-File - Setup of a Laser System for Ultracold Sodium - Towards a Degenerate Gas of Ultracold Fermions

Stefan Weis, Diplomarbeit, 2007

**DFG Excellence**

**Initiative**: Simulating high-energy physics in small atomic systems.

*Emmy-Noether research program*of the

**DFG**since 2018. It is focused on the Kondo effect in cold atoms.

*CRC IsoQuant*, funded by the

**DFG**, since 2016. In close collaboration with the group of Jürgen Berges we work on the implementation of lattice gauge theories with effect in cold atoms

*.*

*FOR 2724*, funded by the

**DFG**, the since 2018. It focuses on thermal machines in the quantum world.

EnerQuant, funded by the

**BMWI**, since 2020. In close collaboration with the group of Philipp Hauke, Fraunhofer Institute for Industrial Mathematics (ITWM), and JoS QUANTUM GmbH, we investigate possible quantum simulators for the energy market.

Honda Research Institute (

**HRI**) since 2021 to investigate quantum machine learning with cold atoms.