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arXiv:1112.3534 · The European Physical Journal D

Tools for detecting entanglement between different degrees of freedom in quadrature squeezed cylindrically polarized modes

C. Gabriel, A. Aiello, S. Berg-Johansen, Ch. Marquardt, Gerd Leuchs

Published Jul 1, 2012• 11 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2012-20735-y

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Quadrature squeezed cylindrically polarized modes contain entanglement not only in the polarization and spatial electric field variables but also between these two degrees of freedom [C. Gabriel et al., Phys. Rev. Lett. 106, 060502 (2011)]. In this paper we present tools to generate and detect this entanglement. Experimentally we demonstrate the generation of quadrature squeezing in cylindrically polarized modes by mode transforming a squeezed Gaussian mode. Specifically, -1.2dB +/- 0.1 dB of amplitude squeezing are achieved in the radially and azimuthally polarized mode. Furthermore, theoretically it is shown how the entanglement contained within these modes can be measured and how strong the quantum correlations are, depending on the measurement scheme.
Quantum systems such as, for example, photons, atoms, or Bose-Einstein condensates, prepared in complex states where entanglement between distinct degrees of freedom is present, may display several intriguing features. In this Letter we introduce the concept of such complex quantum states for intense beams of light by exploiting the properties of cylindrically polarized modes. We show that already in a classical picture the spatial and polarization field variables of these modes cannot be factorized. Theoretically it is proven that by quadrature squeezing cylindrically polarized modes one generates entanglement between these two different degrees of freedom. Experimentally we demonstrate amplitude squeezing of an azimuthally polarized mode by exploiting the nonlinear Kerr effect in a specially tailored photonic crystal fiber. These results display that such novel continuous-variable entangled systems can, in principle, be realized.
Cluster states are an essential component in one-way quantum computation protocols. We present two schemes to generate addressable continuous-variable cluster states from quadrature squeezed cylindrically polarized modes. By including polarization in addition to the transverse spatial degree of freedom, elementary cluster states can be created in which four cluster nodes co-propagate within one paraxial vector beam. This approach is fundamentally compatible with existing time-multiplexed schemes that have been used to create the largest cluster states to date. We implement a proof-of-principle experiment of one of the proposed schemes and verify its feasibility by measuring the quantum correlations between the different nodes of the cluster state.