Critical fluctuations in quantum parametric oscillation
Paul Kinsler, Peter D. Drummond
Department of Physics
University of Queensland
Queensland 4072
Australia
Phys. Rev. A 52, 783 (1995).
We calculate the scale of the critical fluctuations in the quantum
parametric oscillator at threshold. This allows us to
asymptotically calculate the size of both the depletion of the
pump mode and the amount of squeezing produced in the signal mode
for large system size. In this driven, open quantum system, there
is no known solution to the equilibrium density matrix. For this
reason these results cannot be obtained using standard canonical
ensemble methods. The calculations are compared to time dependent
quantum stochastic simulations of the fully nonlinear coupled mode
equations. We find that the critical squeezing variance in the
output spectrum will scale as $N^{-1/2}$, giving the novel feature
that these fluctuations are reduced rather than enhanced near the
critical point.
Email: Dr.Paul.Kinsler@physics.org