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Interferometers and decoherence matrices

Han1, Kim, Noz

  • 1National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, Maryland 20771, USA. han@trmm.gsfc.nasa.gov

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 14, 2000
PubMed
Summary
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The Lorentz group naturally describes two-beam interferometers without decoherence. This framework, using Wigner

Area of Science:

  • Quantum optics and interferometer physics.

Background:

  • Two-beam interferometers exhibit symmetries related to the Lorentz group in the absence of decoherence.
  • Polarization optics provides an analogy, utilizing six-parameter representations of the Lorentz group.

Purpose of the Study:

  • To establish the Lorentz group as the fundamental mathematical framework for describing two-beam interferometers.
  • To explore symmetry properties and their connection to Wigner's little groups.
  • To develop a method for transitioning from pure to impure states using decoherence matrices.

Main Methods:

  • Formulating interferometer behavior using representations of the Lorentz group.
  • Applying concepts of Wigner's little groups to identify invariant transformations.
  • Constructing and analyzing decoherence matrices for state transitions.

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Main Results:

  • The Lorentz group is identified as the natural language for ideal two-beam interferometers.
  • Symmetry properties related to coherency and density matrices are linked to Wigner's little groups.
  • Decoherence matrices are developed to model the transition from pure to impure states.

Conclusions:

  • The Lorentz group provides a powerful framework for understanding two-beam interferometer physics.
  • Symmetry principles are crucial for characterizing state transitions in quantum systems.
  • The developed decoherence matrices offer a tool for experimental investigation.