# 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 ...Fred Jendrzejewski

Phone: +49 6221 54 5182

fnj@kip.uni-heidelberg.de

Alexander Mil

Phone: +49 6221 54 5175

alexander.mil@kip.uni-heidelberg.de

Markus Oberthaler

Phone: +49 6221 54 5170

markus.oberthaler@kip.uni-heidelberg.de

## Recent publications

### 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 localization bounds Trotter errors in digital quantum simulation

HD-KIP 18-130, 2018, Science Advances, arXiv:1806.11123 PDF-FileA fundamental challenge in digital quantum simulation (DQS) is the control of inherent errors. These appear when discretizing the time evolution generated by the Hamiltonian of a quantum many-body system as a sequence of quantum gates, called Trotterization. Here, we show that quantum localization-by constraining the time evolution through quantum interference-strongly bounds these errors for local observables. Consequently, for generic quantum many-body Hamiltonians, Trotter errors can become independent of system size and total simulation time. For local observables, DQS is thus intrinsically much more robust than what one might expect from known error bounds on the global many-body wave function. This robustness is characterized by a sharp threshold as a function of the Trotter step size. The threshold separates a regular region with controllable Trotter errors, where the system exhibits localization in the space of eigenstates of the time-evolution operator, from a quantum chaotic regime where the trajectory is quickly scrambled throughout the entire Hilbert space. Our findings show that DQS with comparatively large Trotter steps can retain controlled Trotter errors for local observables. It is thus possible to reduce the number of quantum gate operations required to represent the desired time evolution faithfully, thereby mitigating the effects of imperfect individual gate operations.

### 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.

## Theses

- 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: Systematische Verbesserung von Atom Trap Trace Anlaysis für 39Ar und deren Anwendung zur Erstellung einer tausendjährigen Paläotemperaturzeitreihe aus Grundwasser

DFG: ArTTA-10mL: Ein Instrument für die 39Ar-Datierung von kleinen Eis- und Wasserproben