Abstract

We investigate the theory of quantum fluctuations in non-equilibrium systems having large crit ical fluctuations. This allows us to treat the limits imposed by nonlinearities to quantum squeezing and noise reduction, and also to envisage future tests o f quantum theory in regions of macroscopic quantum fluctuations. A long-term objective of this research is to identify suitable physical sys tems in which macroscopic 'Schrödinger cat'-like behaviour may be observed. We investigate two systems in particular o f much current experimental interest, namely the degenerate parametric oscillator near threshold, and the evaporatively cooled (BEC). We compare the results obtained in the positive-P representation, as a fully quantum mechanical calculation, with the truncated Wigner phase space equation, also known as semi-classical theory. We show when these results agree and differ in calculations taken beyond the linearized approximation. In the region where the largest quantum fluctuations and Schrödinger cat-like behaviour might be expected, we find that the quantum predictions correspond very closely to the semi-classical theory. Nature abhors observing a Schrödinger cat. -Pacs: 03.65.Bz