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Density matrix negativity for two oscillators in an Agarwal bath.

Y Zhao1, G H Chen

  • 1Department of Chemistry, University of Hong Kong, Hong Kong, People's Republic of China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2002
PubMed
Summary

Quantum master equations reveal density matrix negativity in two harmonic oscillators within an Agarwal bath. This occurs at low temperatures for specific squeezed states, impacting quantum dissipation theory.

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Area of Science:

  • Quantum mechanics
  • Quantum optics
  • Statistical mechanics

Background:

  • The study of quantum systems interacting with their environment is crucial for understanding quantum dissipation.
  • Maintaining positivity of the density matrix is a key challenge in developing accurate quantum dissipation theories.

Purpose of the Study:

  • To investigate quantum master equations for two harmonic oscillators in an Agarwal bath.
  • To analyze density matrix positivity and negativity.
  • To derive criteria for quantum separability.

Main Methods:

  • Utilizing quantum characteristic functions to study quantum master equations.
  • Deriving an analytical criterion for density matrix negativity in uncoupled oscillators.
  • Analyzing the influence of temperature and squeezing parameters.

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Main Results:

  • An analytical criterion for density matrix negativity was derived for two uncoupled oscillators.
  • Density matrix negativity was found for specific squeezed states at temperatures below a derived threshold.
  • An analytical expression for quantum separability was obtained.

Conclusions:

  • The findings provide insights into quantum dissipation theory and density matrix behavior.
  • Temperature and initial state (squeezing) significantly influence quantum properties.
  • Interoscillator coupling effects on negativity warrant further investigation.