Overview of Floquet engineering of quantum gases

13 August 2021

Illustration of the modification of the properties of a lattice via periodic shaking as example for Floquet engineering.

Photo: UHH/Weitenberg, Simonet

Modification of the properties of a lattice via periodic shaking as example for Floquet engineering. The energies E of the Bloch eigenfunctions with quasimomentum k form a band of width 4J with tunnel coupling J and the minimum at k=0. Due to the lattice shaking, the quasimomentum oscillates and in an effective static description as Floquet system, one obtains an effective band width 4J_eff as well as minima of the band structure at finite quasimomenta.

How can we control a system and induce new properties at will? One important technique is periodic driving of the system, also known as Floquet engineering. For ultracold atoms in optical lattices used as an experimental platform for quantum simulation, this technique has proven very fruitful in realizing fascinating new phenomena such as artificial gauge fields. Dr. Christof Weitenberg and Dr. Juliette Simonet of the Institute of Laser Physics at Universität Hamburg, where significant contributions to these developments were made, have now presented an overview article in the journal Nature Physics.

Periodic driving is a way to change the properties of systems - often with astonishing effects: if you drive the suspension point of a pendulum very fast, the pendulum can oscillate around the upright position. Similarly, in quantum systems, one can induce new properties by periodically modulating various parameters. For ultracold atoms in optical lattices this can be done, for example, by periodic lattice shaking or by periodically modulating the interaction strength.

Since ultracold atoms allow for excellent dynamic control, Floquet engineering is used to realize a wide variety of effects. Here artificial gauge fields are of particular interest, which are also a research focus in Hamburg. They can be used to study the effects of magnetic fields on solids, such as the quantum Hall effect, even with neutral atoms. In the future, it will be important to suppress heating in the Floquet systems to study strongly correlated systems such as fractional quantum Hall states or even dynamical gauge fields. Another actively pursued direction is the study of phenomena that exist genuinely in Floquet systems, such as anomalous Floquet phases or discrete time crystals.

In the Cluster of Excellence "CUI: Advanced Imaging of Matter", in which Weitenberg and Simonet are conducting research, such Floquet techniques play an important role in the experiments with ultracold atoms, but also in solid-state systems, in which, for example, intensive Terahertz radiation can induce superconductivity or topological phases.

The new overview article of the cluster researchers explains the most important concepts and gives a snapshot of this exciting research field.