Quantummechanical parametric amplification. L. S. Brown and L. J. Carson
Abstract
Parametric amplification may be obtained in a harmonic oscillator if its spring constant is replaced by a timedependent function. It is shown that the quantum transition probabilities may be expressed in a simple closed analytic form which involves only the classical amplification factor of the oscillator. The authors also compute the time evolution of the density matrix which initially describes a thermodynamic ensemble at temperature T and show that this matrix can similarly be expressed in such a closed form.
 Publication:

Physical Review A
 Pub Date:
 December 1979
 DOI:
 10.1103/PhysRevA.20.2486
 Bibcode:
 1979PhRvA..20.2486.
 Keywords:

 Harmonic Oscillators;
 Parametric Amplifiers;
 Quantum Mechanics;
 Transition Probabilities;
 Electron Transitions;
 S Matrix Theory;
 Thermodynamics;
 Lasers and Masers