Quantum simulators to bridge between fields of physics Gauge theories are relevant to many different areas of physics ranging from condensed matter to highenergy physics, yet it remains difficult to study them. Researchers at LMU in Munich are building a quantum simulator that directly implements the properties of specific models of interest, and allows them to study their properties with table-top experiments, as Professor Monika Aidelsburger explains. Array of tightly focused laser beams to manipulate atoms in the lattice
A simplified description that captures the main features of an underlying system can help researchers to understand the complex properties of materials. This can be understood by thinking of it as a crystal. “The ions in the material form a periodic array, and electrons can move around in this potential energy landscape,” explains Monika Aidelsburger, Professor for Synthetic Quantum Matter at LMU in Munich. One of the most important models is the Fermi-Hubbard Model, which boils down the complexity of a material by describing it according to just two parameters in the Hamiltonian. “One parameter is about characterising the tunneling of an electron – how fast can an electron move around? The second one is, how strongly do they interact with each other?” continues Professor Aidelsburger. “Remarkably, even though this model looks extremely simple because there are only two parameters, it is still beyond our abilities to solve it analytically or study its rich properties numerically. These are the two options we typically have.”
Quantum mechanical systems These approaches are not effective, however, in terms of accurately reflecting the overall complexity of quantum mechanical systems. While in a grid-like periodic structure electrons may be configured as spin-up and spin-down particles, there are many more possible
Atoms
Square lattice created by interfering laser beams
configurations in a quantum mechanical system. “In quantum mechanics there are also superpositions, so a particle can be both up and down at the same time or anything in between, which considerably increases the complexity of the problem. Simply writing down the state of the quantum system requires a number of variables that scales exponentially with the number of spins. Because of this exponential scaling we typically cannot handle systems with more than 100 spins,” explains Professor Aidelsburger. Together with her colleagues, Professor Aidelsburger is working on the idea
Laser standing-wave = a periodic potential
of quantum simulation, originally proposed by the American physicist Richard Feynman to gain deeper insights into quantum-mechanical models from different fields of physics. “We aim to build a quantum mechanical system that directly implements the properties of the model that we are interested in,” she outlines.
This is a bottom-up approach, where researchers take ultracold atoms and arrange them in a periodic potential, then they behave in a way analogous to electrons in a material. Lasercooling techniques are used to cool atoms down to very low temperatures, in order to trap them in potentials generated by laser beams. “We have two laser beams that we interfere, and that leads to a standing wave, with nodes and maxima,” says Professor Aidelsburger. The intensity of the laser affects the way that the atoms arrange themselves along the wave relative to the node - the lowest amplitude point on the wave - or the maxima the highest. “This depends on the detuning of the frequency, that’s how we create the crystal potential, which is really just a light interference pattern,” explains Professor Aidelsburger. “Then how the atoms move between neighbouring sites is controlled by a potential barrier in between. By changing the laser intensities, we can increase or decrease that barrier, which affects how easy it is for the atoms to move around.” The laser field in this scenario can be thought of as generating a crystal, while the atoms effectively mimic the electrons, and move around in this potential landscape. Over the last decade or so it has been shown that these
We aim to develop a new experimental platform to study more abstract models, called gauge theories. These gauge theories are very general, and appear in many fields of physics. types of systems can be used to study problems in condensed matter physics, now Professor Aidelsburger is looking to extend this further in the EU-funded LaGaTYb project. “We aim to develop a new experimental platform to study more abstract models, called gauge theories. These are more general, and appear in many other fields of physics as well,” she outlines. The basic idea is to use this new platform to not only directly simulate these condensed matter types of Hamiltonians, but to also make connections to other fields which are loosely connected by gauge theory formulations. “It would be very exciting to provide a link between different fields, and to help establish a general framework,” continues Professor Aidelsburger. “Experts from different fields, like condensed matter physics or from high energy physics, all have their specific language and we would like to bring them together.”
Fermionic ytterbium atoms
Aosense Source chamber
36
EU Research
ytterbium atoms, which are used as atomic clocks. The clock transition essentially allows us to generate more complicated potential energy landscapes, using different wavelengths for the laser beams,” says Professor Aidelsburger. A second important ingredient is local control. “We know how to control the system parameters by changing the intensity of the laser beams, but we don’t have very good control of local tunnelling events, or local state control. This is crucial for implementing gauge theories, because they require local symmetries, and therefore local control,” explains Professor Aidelsburger. “The idea there is to combine these interfering laser beams that generate a potential landscape with, for example, an array of tightly focused laser beams.” This array can then be projected onto the atoms, which allows researchers to locally manipulate how atoms move in this potential landscape. This opens up a wide range of possibilities in terms of studying different models. “This optical clock transition can also be used for high-precision spectroscopy an important tool for studying the properties of quantum systems,” says Professor Aidelsburger. One of the main challenges here is to engineer the local interactions; one specific example
A common language to describe different phenomena would help researchers build a deeper understanding of quantum systems. Researchers in the project are developing a new platform, which differs from the more established experimental frameworks described earlier in two main aspects. “We are working with fermionic
www.euresearcher.com
Professor Aidelsburger points to is the possibility of studying quantum electrodynamics problems. “For example if you have two fermions in a lattice, usually they can move around individually, depending on the potential barrier between sites. Now we can engineer the lattice in such a way that two fermions can only hop together, in what we call a correlated hopping process,” she outlines. “Each individual fermion needs a partner to move around. If we do this in the correct way, then this basic building block can be used to study phenomena known from quantum electrodynamics, such as particleantiparticle pair creation processes.” A number of workshops and conferences have been held over the past few years to bring researchers together and identify the main challenges while also exploring the wider potential of quantum simulations. For the moment however, Professor Aidelsburger’s priority is to develop the experimental platform. “We are starting to assemble our vacuum system and the laser system in the lab. At some point next year, we hope to have fermions in the lattice, which we can arrange individually and look at individually. We also hope to show that we are able to locally control the motion of the fermions in the lattice,” she says.
LaGaTYb Exploring lattice gauge theories with fermionic Ytterbium atoms Project Objectives
The goal of this ambitious research project is to develop a new experimental platform based on ultracold atoms in optical lattices, that will allow for local controllability of tunnel events and thereby pave the way towards quantum simulation of lattice gauge theories with fermionic Yb atoms to study phenomena related to condensed matter and highenergy physics.
Project Funding
This project receives funding from the Cluster of Excellence (MCQST), and also the Deutsche Forschungsgemeinschaft (DFG).
Contact Details
Project Coordinator, Professor Monika Aidelsburger Ludwig-Maximilians-Universität München Fakultät für Physik Schellingstr. 4 80799 München T: +49 89 2180 6143 E: monika.aidelsburger@physik.uni-muenchen.de W: https://www.physik.uni-muenchen.de/ personen/professoren/aidelsburger/index.html
Professor Monika Aidelsburger
Monika Aidelsburger received her PhD at LMU Munich in 2015. After a PostDoc period at Collège de France in Paris, she returned to LMU as a group leader, where she is a professor since 2019. Her group is working on quantum simulations of topological models and out-of-equilibrium phenomena using ultracold atoms. In 2018 she received an ERC Starting Grant for studying gauge theories.
37