Geometric phase of arbitrary Mueller evolutions and its two-level quantum analog

Area of Science:

• Optics and Photonics
• Quantum Information Science
• Geometric Phase Theory

Background:

• Mueller matrices describe the polarization properties of optical systems.
• Geometric phase (Pancharatnam phase) is a fundamental concept in interferometry and quantum mechanics.
• The relationship between Mueller transformations and intrinsic geometric phase is not fully understood.

Purpose of the Study:

• To identify the unique, invariant geometric-phase structure within general physically realizable Mueller transformations.
• To establish a canonical holonomic content for Mueller transformations.
• To explore the quantum analog for open two-level dynamics.

Main Methods:

• Characteristic decomposition of Mueller transformations.
• Identification of the retarding part of the characteristic pure component.
• Analysis within the Choi representation for quantum systems.

Main Results:

• The retarding part of the characteristic pure component uniquely defines the intrinsic geometric phase structure.
• Mueller matrices do not generally determine a unique observed geometric phase due to physical realization dependencies.
• Remaining characteristic layers can alter complex visibility but lack unique geometric holonomy.

Conclusions:

• A canonical geometric phase structure is identified for Mueller transformations.
• The study clarifies the ambiguity in observed geometric phase for Mueller matrices.
• A quantum analog for open two-level dynamics is established using the Choi representation.