# Controlling the Floquet state population and observing micromotion in a periodically driven two-body quantum system

## TL;DR

This paper demonstrates control over Floquet states and observes micromotion in a driven two-body quantum system, advancing quantum state engineering in periodically driven fermionic systems.

## Contribution

It introduces protocols for adiabatically preparing specific Floquet states and provides a detailed analysis of micromotion in a driven interacting fermionic system.

## Key findings

- Full control of Floquet state populations achieved.
- Ramping protocols successfully connect initial and target states.
- Micromotion observed and analytically described.

## Abstract

Near-resonant periodic driving of quantum systems promises the implementation of a large variety of novel effective Hamiltonians. The challenge of Floquet engineering lies in the preparation and measurement of the desired quantum state. We address these aspects in a model system consisting of interacting fermions in a periodically driven array of double wells created by an optical lattice. The singlet and triplet fractions and the double occupancy of the Floquet states are measured, and their behavior as a function of the interaction strength is analyzed in the high- and low-frequency regimes. We demonstrate full control of the Floquet state population and find suitable ramping protocols and time-scales which adiabatically connect the initial ground state to different targeted Floquet states. The micromotion which exactly describes the time evolution of the system within one driving cycle is observed. Additionally, we provide an analytic description of the model and compare it to numerical simulations.