Quantum dynamics of the parametric oscillator

Kinsler P. and Drummond P.D. (1991) Quantum dynamics of the parametric oscillator. Physical Review A, 43 11: 6194-6208. doi:10.1103/PhysRevA.43.6194

Author Kinsler P.
Drummond P.D.
Title Quantum dynamics of the parametric oscillator
Journal name Physical Review A   Check publisher's open access policy
ISSN 1050-2947
Publication date 1991-01-01
Sub-type Article (original research)
DOI 10.1103/PhysRevA.43.6194
Volume 43
Issue 11
Start page 6194
End page 6208
Total pages 15
Language eng
Subject 3100 Physics and Astronomy
3107 Atomic and Molecular Physics, and Optics
Abstract We present dynamical calculations for the quantum parametric oscillator using both number-state and coherent-state bases. The coherent-state methods use the positive-P representation, which has a nonclassical phase space an essential requirement in obtaining an exact stochastic representation of this nonlinear problem. This also provides a way to directly simulate quantum tunneling between the two above-threshold stable states of the oscillator. The coherent-state methods provide both analytic results at large photon numbers, and numerical results for any photon number, while our number-state calculations are restricted to numerical results in the low-photon-number regime. The number-state and coherent-state methods give precise agreement within the accuracy of the numerical calculations. We also compare our results with methods based on a truncated Wigner representation equivalent to stochastic electrodynamics, and find that these are unable to correctly predict the tunneling rate given by the other methods. An interesting feature of the results is the much faster tunneling predicted by the exact quantum-theory methods compared with earlier semiclassical calculations using an approximate potential barrier. This is similar to the faster tunneling found when comparing quantum penetration of a barrier to classical thermal activation. The quantum parametric oscillator, which has an exact steady-state solution, therefore provides a useful and accessible system in which nonlinear quantum effects can be studied far from thermal equilibrium.
Q-Index Code C1
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
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