Entangling Different Degrees of Freedom by Quadrature Squeezing Cylindrically Polarized Modes

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.

Figure 1

Three types of entanglement are contained in a squeezed azimuthally polarized mode which can be observed by utilizing a mode splitter: (a) polarization entanglement, (b) spatial entanglement, and (c) hybrid entanglement.

Figure 2

(a) The specially designed photonic crystal fiber which supports the azimuthally polarized mode. (b) Normalized mode intensity profile of the azimuthally polarized mode at $\lambda =810\mathrm{nm}$, measured after the fiber.

Figure 3

(a) The experimental setup of the Sagnac loop to generate amplitude squeezing in the azimuthally polarized mode [beam splitter (BS)]. (b) Direct detection is used to measure the amplitude squeezing. (c) The detection system to measure amplitude correlations between the horizontally polarized ${\mathrm{TEM}}_{01}$ mode and the vertically polarized ${\mathrm{TEM}}_{10}$ mode [polarizing beam splitter (PBS)].

Figure 4

(a) A quantum noise reduction of 0.6 dB is observed in the azimuthally polarized mode. (b) Anticorrelations of 0.5 dB below the QNL of the horizontally polarized ${\mathrm{TEM}}_{01}$ and vertically polarized ${\mathrm{TEM}}_{10}$ have been measured. The insets illustrate the measured spatial modes and the arrows indicate the polarization of the state.