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arXiv:1302.2438 · Optics Communications

Improved quantum correlations in second harmonic generation with a squeezed pump

Elizabeth Marcellina, Joel Frederick Corney, M. K. Olsen

Published Jul 12, 2013• 6 citations
arXivHTMLPDF
DOI
10.1016/j.optcom.2013.06.063

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Second-harmonic generation, in a cavity resonant only at the fundamental, produces amplitude squeezing in both the fundamental and the second harmonic, with optimal squeezing of -1/3 and -8/9, respectively, at low frequency. It also produces nonclassical correlations between the two output beams. We show that these correlations can be used to enhance the squeezing in either beam by constructing a feedback loop. By using the second-harmonic photocurrent to control the amplitude of the pump, the optimal fundamental squeezing is enhanced by 50% to -1/2. The limit of -8/9 for the seocnd harmonic (for infinite nonlinearity strength) cannot be improved by feeding back the fundamental. However, for any fixed finite nonlinearity, such feedback can produce significant enhancement, with a maximum of 50%. Even with the losses characteristic of a practical experiment included, the enchancement offered by the feedback is still significant, being greater than 20% in either mode.
The classical behavior and the quantum fluctuations are analyzed for the system of nondegenerate second-harmonic generation inside a cavity, where two frequency degenerate but orthogonally polarized harmonic modes are coupled to a second-harmonic mode via a ${\mathrm{\ensuremath{\chi}}}^{(2)}$ medium. We consider the consequences of asymmetrically pumping the two harmonic modes. Asymmetric pumping causes large changes in the classical dynamical behavior of the system; the pitchfork bifurcation, predicted by Ou [Phys. Rev. A 49, 4902 (1994)] and Eschmann and Reid [Phys. Rev. A 49, 2881 (1994)] for symmetric pumping, is transformed into a saddle node for any antisymmetric pumping. This new dynamics brings about the possibility of the system reaching a Hopf and a saddle-node--Hopf bifurcation point. Squeezed-state production is investigated at the critical points of the system. Large squeezing is predicted at the saddle-node and Hopf bifurcation points. The wealth of squeezing predicted by this model at the pitchfork bifurcation point is interpreted in terms of the dynamics of the system. For symmetric pumping, this system is shown to be able to produce two coherent amplitude and phase correlated beams both above and below the pitchfork bifurcation point and so is a candidate for an Einstein-Podolsky-Rosen experiment. \textcopyright{} 1996 The American Physical Society.