Quantum dynamics of the parametric oscillator.
P. Kinsler, P.D. Drummond.
Department of Physics
University of Queensland
Queensland 4072
Australia
Phys. Rev. A 43, 6194 (1991).
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.
Email: Dr.Paul.Kinsler@physics.org