Conservation of Quantum Correlations in Multimode Systems with U(1) Symmetry

Area of Science:

• Quantum optics
• Theoretical physics
• Quantum information science

Background:

• Quantum correlation functions are crucial for understanding the behavior of quantum systems.
• Multimode systems present complex dynamics that are challenging to analyze.
• Symmetries and dissipation significantly influence quantum properties.

Purpose of the Study:

• To theoretically investigate the conservation properties of quantum correlation functions in multimode systems.
• To define and analyze a total mth order equal-time correlation function.
• To explore the conditions under which this correlation function is conserved.

Main Methods:

• Theoretical derivation of the conservation law for the mth order equal-time correlation function.
• Analysis of conservation under U(1) symmetry.
• Investigation of conservation in the presence of uniform dissipation across all modes.
• Numerical simulations of specific models (coupled cavity system, Jaynes-Cummings model).

Main Results:

• A total mth order equal-time correlation function is defined and shown to be conserved.
• Conservation is demonstrated when the system's Hamiltonian possesses U(1) symmetry.
• The correlation function remains conserved even with dissipation, provided the loss rate is identical for all modes.
• Numerical simulations confirm the theoretical predictions for coupled cavities and the Jaynes-Cummings model.

Conclusions:

• The defined quantum correlation function exhibits robust conservation properties under specific conditions.
• This finding simplifies the study of quantum correlations in complex, open multimode systems.
• The results have implications for quantum information processing and understanding quantum dynamics.