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Geometric phase distributions for open quantum systems.

K-P Marzlin1, S Ghose, B C Sanders

  • 1Institute for Quantum Information Science, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada.

Physical Review Letters
|February 9, 2005
PubMed
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Geometric phase in open quantum systems is usually ambiguous. However, applying physical constraints to the environment and system coupling provides a unique geometric phase distribution for mixed states and noncyclic evolutions.

Area of Science:

  • Quantum mechanics
  • Quantum information theory
  • Statistical physics

Background:

  • Geometric phase is a fundamental concept in quantum mechanics, crucial for understanding quantum phenomena.
  • Describing geometric phase in open quantum systems, which interact with their environment, presents unique challenges.
  • Existing methods often struggle with ambiguity, especially for mixed states and non-ideal evolutions.

Purpose of the Study:

  • To resolve the ambiguity in defining geometric phase distributions for open quantum systems.
  • To establish a unique and universally applicable geometric phase distribution.
  • To extend the concept of geometric phase to mixed states, non-unitary dynamics, and noncyclic evolutions.

Main Methods:

  • Theoretical analysis of geometric phase in open quantum systems.

Related Experiment Videos

  • Imposition of physically motivated constraints on environmental coupling.
  • Development of a framework applicable to mixed quantum states and general evolutions.

    • Main Results:

    • Demonstrated that geometric phase distributions in open systems are generally ambiguous.
    • Showcased how specific physical constraints lead to a unique geometric phase distribution.
    • Validated the framework for mixed states, non-unitary dynamics, and noncyclic evolutions.

    Conclusions:

    • A unique geometric phase distribution for open quantum systems can be rigorously defined.
    • The derived distribution provides a robust tool for analyzing quantum dynamics beyond idealized scenarios.
    • This work offers a more complete understanding of geometric phase in realistic quantum systems.