Floquet group theory and its application to selection rules in harmonic generation

Area of Science:

• Physics
• Quantum Mechanics
• Group Theory

Background:

• Symmetry is a fundamental concept in science, often associated with conservation laws and selection rules.
• Dynamical symmetries (DSs) in time-periodic Floquet systems are crucial for understanding their behavior.
• Existing theories may not fully explain all observed selection rules in these systems.

Purpose of the Study:

• To formulate a general group theory for dynamical symmetries (DSs) in time-periodic Floquet systems.
• To establish the correspondence between these DSs and observable selection rules.
• To apply the theory to harmonic generation and identify novel selection rules.

Main Methods:

• Development of a general group theory for dynamical symmetries in Floquet systems.
• Application of the theory to harmonic generation in (2+1)D and (3+1)D geometries.
• Derivation of closed-form tables linking DSs to harmonic orders and polarizations.

Main Results:

• A general group theory for dynamical symmetries in Floquet systems is established.
• The theory successfully links DSs to observable selection rules in harmonic generation.
• New selection rules, including time-reversal, reflection, and elliptical symmetries, are identified, some unexplained by current laws.

Conclusions:

• The developed theory provides a powerful framework for understanding dynamical symmetries in Floquet systems.
• It offers new insights into harmonic generation and predicts novel selection rules.
• The theory is expected to advance ultrafast high harmonic symmetry-breaking spectroscopy and applications in Floquet topological insulators.