Ordering of an Exponentiated Multimode Quadratic Operator
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 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 .
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References and Footnotes
- 1.W. H. Louisell, Quantum Statistical Properties of Radiation (John Wiley f, Sons, New York, 1973 ).Google Scholar
- 3.We put a circumflex over all quantities which denote operators.Google Scholar
- 5.J. Schwinger, Quantum Theory of Angular Momentum, ed. by L. C. Biedenharn and H. Van Dam ( Adademic, New York, 1965 ).Google Scholar
- 6.S. Kumar and C. L. Mehta, presented at the International Con- ference on Multiphoton Processes, University of Rochester, Rochester, New York, June 6–9, 1977.Google Scholar
- 12.C.L. Mehta, J. Math. Phys. 18, 404 (1977)Google Scholar
- 14.F.A. Berezin, The Method of Second Quantization (Academic, New York, 1966) p. 143; see also R.M. Wilcox, J. Math. Phys. 8, 962 (1967); R. Balian and E. Brezin, Nuovo Cimento B64, 37, (1969).Google Scholar
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