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arXiv:quant-ph/0702113 · Physical Review A

Quadrature and polarization squeezing in a dispersive optical bistability model

Ferran V. García-Ferrer, Isabel Pérez–Arjona, Germán J. de Valcárcel, Eugenio Roldán

Published Jun 26, 2007• 5 citations
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Abstract

We theoretically study quadrature and polarization squeezing in dispersive optical bistability through a vectorial Kerr cavity model describing a nonlinear cavity filled with an isotropic ${\ensuremath{\chi}}^{(3)}$ medium in which self-phase- and cross-phase-modulation, as well as four-wave mixing, occur. We derive expressions for the quantum fluctuations of the output field quadratures as a function of which we express the spectrum of fluctuations of the output-field Stokes parameters. We pay particular attention to study how the bifurcations affecting the non-null linearly polarized output mode squeezes the orthogonally polarized vacuum mode, and show how this produces polarization squeezing.

DOI
10.1103/physreva.75.063823

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We analyze the classical behavior and the quantum fluctuations for the system of degenerate four-wave mixing inside a doubly resonant optical cavity. Two frequency-degenerate but orthogonally polarized modes are coupled together in a ${\mathrm{\ensuremath{\chi}}}^{(3)}$ medium. We include all significant phase-matched interactions that occur in a third-order polarization (self-phase modulation, cross-phase modulation, and four-wave mixing). Two critical points are predicted to occur in the system. The first occurs for low pumping, associated with the excitation of the single mode. The second critical point occurs for higher pumping, associated with the onset of self-pulsing. Quantum fluctuations are analyzed for the various regions of pumping. At the first critical point, perfect squeezing is possible in both the pump and the signal modes when the damping of the signal mode is greater than the damping of the pump (${\ensuremath{\gamma}}_{\mathit{a}}$>${\ensuremath{\gamma}}_{\mathit{b}}$). In the case where the damping of the signal mode is much greater than that of the pump (${\ensuremath{\gamma}}_{\mathit{a}}$\ensuremath{\gg}${\ensuremath{\gamma}}_{\mathit{b}}$), nearly perfectly squeezed states of the signal mode are possible in the entire region between the two critical points.
We study the interaction of a nearly resonant linearly polarized laser beam with a cloud of cold cesium atoms in a high finesse optical cavity. We show theoretically and experimentally that the cross-Kerr effect due to the saturation of the optical transition produces quadrature squeezing on both the mean field and the orthogonally polarized vacuum mode. An interpretation of this vacuum squeezing as polarization squeezing is given and a method for measuring quantum Stokes parameters for weak beams via a local oscillator is developed.
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