Geometric phases and multiple degeneracies in harmonic resonators

Area of Science:

• Quantum mechanics
• Quantum optics
• Spectroscopy

Background:

• Cyclic deformation of microwave resonators yields adiabatic normal-mode wave functions.
• Previous approximate theories explained some observed cyclic phases around threefold degeneracy.
• Discrepancies existed between experimental geometrical phases and open-path theories.

Purpose of the Study:

• To resolve the disagreement between experimental geometrical phases and theoretical predictions.
• To investigate the underlying quantum mechanical principles governing phase changes in deformed systems.
• To provide an exact solution for the adiabatic normal-mode wave functions during cyclic deformation.

Main Methods:

• Exact numerical solution of the quantum mechanical problem.
• Analysis of adiabatic normal-mode wave functions during cyclic deformation.
• Identification and characterization of degeneracies in the system.

Main Results:

• Unsuspected additional degeneracies were discovered around the multiple degeneracy.
• These extra degeneracies precisely account for the measured phase changes observed in the experiment.
• The proliferation of degeneracies near multiple ones is a common quantum mechanical phenomenon.

Conclusions:

• The exact solution provides a comprehensive explanation for experimental observations.
• Approximate theories were insufficient to capture the full complexity of the geometrical phases.
• The findings highlight the importance of considering all degeneracies in quantum systems for accurate phase predictions.