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Off-diagonal geometric phases.

N Manini1, F Pistolesi

  • 1European Synchrotron Radiation Facility, B.P. 220, F-38043 Grenoble Cedex, France. manini@sissa.it

Physical Review Letters
|October 6, 2000
PubMed
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We explore geometric phases for multiple quantum states evolving together. This extends the Berry phase concept, revealing measurable geometric quantities for complex systems.

Area of Science:

  • Quantum mechanics
  • Geometric phase theory

Background:

  • The Berry phase describes the geometric phase acquired by a quantum state undergoing adiabatic evolution.
  • Extending this concept to multiple states is crucial for understanding complex quantum systems.

Purpose of the Study:

  • To investigate the adiabatic evolution of nondegenerate eigenstates of a parametrized Hamiltonian.
  • To relate relative phase changes to measurable geometric quantities.

Main Methods:

  • Theoretical analysis of adiabatic evolution for multiple eigenstates.
  • Application to physical systems, including microwave cavities.

Main Results:

  • Developed a framework to generalize the Berry phase to multiple quantum states.

Related Experiment Videos

  • Identified relative phase changes linked to geometric measurable quantities.
  • Demonstrated applicability to microwave cavity experiments using published data.

    • Conclusions:

    • The study provides a generalized geometric phase applicable to the evolution of multiple quantum states.
    • This framework offers new insights into quantum phase phenomena and their measurement.