Limits to squeezing in the degenerate optical parametric.pdfVIP

PHYSICAL REVIEW A, VOLUME 65, 033805 Limits to squeezing in the degenerate optical parametric oscillator S. Chaturvedi,1 K. Dechoum,2 and P. D. Drummond2 1School of Physics, University of Hyderabad, Hyderabad 500046, India 2Department of Physics, University of Queensland, St. Lucia 4067, Queensland, Australia Received 12 January 2001; published 6 February 2002 We develop a systematic theory of quantum fluctuations in the driven optical parametric oscillator, including the region near threshold. This allows us to treat the limits imposed by nonlinearities to quantum squeezing and noise reduction in this nonequilibrium quantum phase transition. In particular, we compute the squeezing spectrum near threshold and calculate the optimum value. We find that the optimal noise reduction occurs at different driving fields, depending on the ratio of damping rates. The largest spectral noise reductions are predicted to occur with a very high-Q second-harmonic cavity. Our analytic results agree well with stochastic numerical simulations. We also 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 the semiclas- sical theory. DOI: 10.1103/PhysRevA.65.033805 PACS numbers: 42.65.Yj, 42.50.Dv I. INTRODUCTION theory 13–15 using a many-body-theory analog of Feyn-