Floquet approach to $\mathbb{Z}_{2}$ lattice gauge theories with ultracold atoms in optical lattices

Abstract: Quantum simulation has the potential to investigate gauge theories in strongly-interacting regimes, which are up to now inaccessible through conventional numerical techniques. Here, we take a first step in this direction by implementing a Floquet-based method for studying $\mathbb{Z}_2$ lattice gauge theories using two-component ultracold atoms in a double-well potential. For resonant periodic driving at the on-site interaction strength and an appropriate choice of the modulation parameters, the effective Floquet Hamiltonian exhibits $\mathbb{Z}_2$ symmetry. We study the dynamics of the system for different initial states and critically contrast the observed evolution with a theoretical analysis of the full time-dependent Hamiltonian of the periodically-driven lattice model. We reveal challenges that arise due to symmetry-breaking terms and outline potential pathways to overcome these limitations. Our results provide important insights for future studies of lattice gauge theories based on Floquet techniques.

• The paper introduces a Floquet-based scheme that uses periodic modulation in double-well potentials to emulate Z₂ lattice gauge theories.
• It demonstrates control over gauge-invariant interactions by resonantly tuning on-site interactions with the driving frequency.
• Numerical simulations validate the method and propose strategies to mitigate symmetry-breaking effects in quantum simulations.

Floquet Approach to $\mathbb{Z}_{2}$ Lattice Gauge Theories with Ultracold Atoms

The paper presents an exploration of $\mathbb{Z}_2$ lattice gauge theories (LGTs) using a Floquet-based approach in ultracold atomic systems arranged in optical lattices. The authors propose a method to simulate complex quantum systems by periodically driving two-component ultracold atoms in a double-well potential to emulate gauge theories, a fundamental framework for understanding quantum many-body systems.

Key Contributions

The researchers have developed a Floquet-based experimental scheme to address the challenge of implementing $\mathbb{Z}_2$ LGTs. The focus is on achieving a realistic model that captures the core properties of gauge-theory dynamics using cold atoms in optical lattice setups. This is a pioneering application that leverages the latest advancements in quantum simulations to overcome analytical limitations in standard numerical techniques that break down in strongly interacting regimes.

Theoretical and Experimental Approach

1. Floquet Engineering: The paper introduces a resonant periodic modulation of on-site interactions to engineer the desired $\mathbb{Z}_2$ symmetry in a double-well lattice. The resonant condition matches the driving frequency with the interaction energy, effectively generating Hamiltonians that emulate gauge-like symmetry.
2. Experimental Setup: Two distinct atomic states are used to represent matter and gauge fields. They implement interactions using density-dependent laser-assisted tunneling. The modulation-based scheme allows for the manipulation of tunneling parameters and helps in observing the dynamics that highlight gauge-invariant properties.
3. Dynamics and Floquet Hamiltonian: The paper provides a detailed theoretical framework for deriving the effective Floquet Hamiltonian and conducting an experimental investigation of the system's dynamics, validating its predictions with empirical data.
4. Numerical Simulations: The paper complements its experiments with numerical simulations to predict the role of symmetry-breaking terms and proposes strategies to mitigate these effects, enhancing the fidelity of quantum simulations.

Results and Implications

The authors successfully demonstrated the capability to control lattice gauge simulations with finely tuned parameters. Their specific results align with theoretical predictions, showcasing effective symmetries in simulated environments analogous to electric fields in $\mathbb{Z}_2$ gauge theories. Moreover, certain configurations presented challenge points, such as symmetry-breaking terms, that call for improvements in experimental setups.

Broader Implications

This research not only expands the toolkit for simulating gauge theories within controllable experimental environments but also pushes the boundaries of simulating high-energy physics phenomena in condensed matter systems. The work paves the way for future studies that can leverage these techniques to explore extended lattice gauge theories and their implications in higher-dimensional systems.

Future Directions

The authors suggest future efforts should focus on scaling the system to larger arrays and exploring other forms of LGTs. The effective control over tunneling and interactions can further empower the study of exotic phases of matter, and possibly contribute to advancements in the still nascent field of quantum computing.

This paper represents a significant stride in cold atom quantum simulations and sets a groundwork for continuing to bridge high-energy physics representations with tangible quantum systems, thereby refining our understanding of quantum materials and gaining insights into undiscovered quantum phenomena.