Ordering of an Exponentiated Multimode Quadratic Operator

  • G. P. Agrawal
  • C. L. Mehta
Conference paper


In quantum optics one often encounters a hamiltonian which is quadratic in boson annihilation and creation operators. One of the specific examples is a harmonic oscillator interacting with a reservoir. [1,2] The mutual exchange between the quanta of the harmonic oscillator and the reservoir leads to the quadratic coupling. The system hamiltonian can be written as [3]
where the symbols have their usual meaning. The coupling between the oscillator and N-mode reservoir leads to the well-known Lamb shift in the frequency and the exponential decay of the oscillator excitation energy [2].


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Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • G. P. Agrawal
    • 1
  • C. L. Mehta
    • 2
  1. 1.The City College of CUNYNew YorkUSA
  2. 2.Indian Institute of TechnologyNew DelhiIndia

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