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Quantum geometric phase between orthogonal states.

Hon Man Wong1, Kai Ming Cheng, M-C Chu

  • 1Department of Physics, The Chinese University of Hong Kong, Hong Kong SAR, China.

Physical Review Letters
|March 24, 2005
PubMed
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Researchers demonstrate a new method to measure geometric phase, even for orthogonal quantum states. This technique allows extraction of topological numbers and reveals phase changes of pi or zero (mod 2pi) near orthogonal states.

Area of Science:

  • Quantum mechanics
  • Quantum information theory
  • Geometric phase analysis

Background:

  • Geometric phase is a fundamental concept in quantum mechanics.
  • Measuring geometric phase, especially for orthogonal states, presents significant challenges.
  • Existing methods may not fully capture phase information for all state pairs.

Purpose of the Study:

  • To introduce a novel method for extracting and measuring geometric phase for any two quantum states.
  • To demonstrate the extraction of topological numbers from geometric phase changes.
  • To analyze the Pancharatnam phase behavior near orthogonal states.

Main Methods:

  • Utilizing the concept of projective measurement to extract geometric phase.
  • Analyzing geometric phase changes in infinitesimal loops near orthogonal states.

Related Experiment Videos

  • Employing a generalized connection to calculate off-diagonal geometric phases.

    • Main Results:

    • Successfully extracted and measured geometric phase for both non-orthogonal and orthogonal quantum states.
    • Identified a topological number within the geometric phase change near orthogonal states.
    • Determined that the Pancharatnam phase change through an orthogonal state is either pi or zero (mod 2pi).

    Conclusions:

    • Projective measurement provides a robust tool for geometric phase determination.
    • The study reveals new insights into the topological properties of geometric phase.
    • The generalized connection offers a comprehensive approach to calculating off-diagonal geometric phases.