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The Physical Spectrum of a Driven Jaynes-Cummings Model.

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Approximate Evolution for A Hybrid System-An Optomechanical Jaynes-Cummings Model.

Luis Medina-Dozal1, Irán Ramos-Prieto1, José Récamier1

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Entropy (Basel, Switzerland)
|December 6, 2020
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Summary

This study develops an approximate method for analyzing forced optomechanical systems by combining elements of optomechanics and quantum optics. The new technique provides accurate results comparable to numerical simulations.

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Area of Science:

  • Quantum Optics
  • Optomechanics
  • Quantum Information

Background:

  • Optomechanical systems couple optical and mechanical degrees of freedom.
  • Jaynes-Cummings (JC) Hamiltonian describes light-matter interaction in quantum optics.
  • Analyzing forced quantum systems often requires complex numerical methods.

Purpose of the Study:

  • To develop an approximate analytical method for a forced optomechanical system.
  • To combine phenomenological Hamiltonians from optomechanics and quantum optics.
  • To linearize and simplify the system's Hamiltonian for easier analysis.

Main Methods:

  • Constructed a phenomenological Hamiltonian from pumped optomechanical and JC Hamiltonians.
  • Employed algebraic techniques to derive an approximate time evolution operator.
  • Transformed the JC Hamiltonian into a generalized interaction picture Hamiltonian.

Main Results:

  • Derived a linearized Hamiltonian with a time evolution operator in product form.
  • Achieved remarkable agreement between analytical results and full numerical calculations.
  • Demonstrated the validity and accuracy of the approximate analytical approach.

Conclusions:

  • The developed analytical technique offers an efficient alternative to numerical simulations.
  • This method provides valuable insights into the dynamics of forced optomechanical systems.
  • The approach is extendable to other complex quantum optical and optomechanical models.