Dynamical Symmetries and Symmetry-Protected Selection Rules in Periodically Driven Quantum Systems

Area of Science:

• Quantum Optics
• Condensed Matter Physics
• Theoretical Physics

Background:

• Ultrastrong light-matter coupling enables novel quantum phenomena.
• Periodically driven systems exhibit dynamical generalizations of spatial symmetries.

Purpose of the Study:

• To establish a unified framework for dynamical-symmetry-protected selection rules.
• To explore these rules in various symmetries and their spectroscopic consequences.

Main Methods:

• Floquet response theory provides the theoretical foundation.
• Analysis of rotational, parity, particle-hole, chiral, and time-reversal symmetries.

Main Results:

• Dynamical rotational and parity symmetries lead to symmetry-protected dark states (spDS) and dark bands.
• Particle-hole symmetry induces spDSs and symmetry-induced transparency.
• Chiral and time-reversal symmetries can combine to define particle-hole symmetry.

Conclusions:

• Symmetry conditions arise from destructive interference in synchronized quantum systems.
• Predictions reveal new phenomena in the ultrastrong coupling regime.
• Findings are relevant for superconducting qubits, cavity-coupled systems, and optomechanics.